From 0abbb26b17f7b2147ceb3b9f7ef2a5e78939afed Mon Sep 17 00:00:00 2001 From: Vinit Keshri Date: Thu, 6 Jun 2024 13:00:11 +0530 Subject: [PATCH] Added links in vitepress website --- docs/.vitepress/config.mjs | 18 +- docs/.vitepress/dist/404.html | 8 +- docs/.vitepress/dist/MIPS/index.html | 18 +- docs/.vitepress/dist/MIPS/mips.html | 949 +++++++ docs/.vitepress/dist/NITC_Logo.png | Bin 0 -> 105936 bytes .../.vitepress/dist/Verilog/Intro/README.html | 18 +- docs/.vitepress/dist/Verilog/SingleCycle.html | 36 +- docs/.vitepress/dist/Verilog/index.html | 16 +- docs/.vitepress/dist/about.html | 16 +- .../dist/assets/MIPS_index.md.BShnq2Ay.js | 1 + .../assets/MIPS_index.md.BShnq2Ay.lean.js | 1 + .../dist/assets/MIPS_index.md.CY43yMpU.js | 1 - .../assets/MIPS_index.md.CY43yMpU.lean.js | 1 - .../dist/assets/MIPS_mips.md.C9wrwHux.js | 924 +++++++ .../dist/assets/MIPS_mips.md.C9wrwHux.lean.js | 1 + ...js => Verilog_Intro_README.md.B7knES9C.js} | 4 +- .../Verilog_Intro_README.md.B7knES9C.lean.js 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create mode 100644 docs/img/registers-image-0032.png create mode 100644 docs/img/registers-image-0041.png create mode 100644 docs/img/registers-image-0053.png create mode 100644 docs/img/registers-image-0057.png create mode 100644 docs/img/registers-image-0058.jpg create mode 100644 docs/img/registers-image-0061.png create mode 100644 docs/mips.md create mode 100644 docs/public/NITC_Logo.png create mode 100644 docs/registers.md diff --git a/docs/.vitepress/config.mjs b/docs/.vitepress/config.mjs index 2e73cfe..2633c3c 100644 --- a/docs/.vitepress/config.mjs +++ b/docs/.vitepress/config.mjs @@ -19,7 +19,22 @@ export default defineConfig({ provider: 'local', }, - sidebar: [ + sidebar: { + + '/MIPS/':[ + { + text: 'MIPS', + collapsed: false, + items: [ + { text: 'Introduction', link: '/MIPS/' }, + { text: 'Registers', link: '/MIPS/Registers' }, + { text: 'Instructions', link: '/MIPS/Instructions' }, + { text: 'Examples', link: '/MIPS/Examples' }, + ] + + }], + + '/':[ { text: 'Examples', items: [ @@ -28,6 +43,7 @@ export default defineConfig({ ] } ], + }, socialLinks: [ { icon: 'github', link: 'https://github.com/vuejs/vitepress' } diff --git a/docs/.vitepress/dist/404.html b/docs/.vitepress/dist/404.html index f4de818..69c2ae8 100644 --- a/docs/.vitepress/dist/404.html +++ b/docs/.vitepress/dist/404.html @@ -6,17 +6,17 @@ 404 | Hardware Lab NITC - + - - + +
- + \ No newline at end of file diff --git a/docs/.vitepress/dist/MIPS/index.html b/docs/.vitepress/dist/MIPS/index.html index 5bac6de..58676b9 100644 --- a/docs/.vitepress/dist/MIPS/index.html +++ b/docs/.vitepress/dist/MIPS/index.html @@ -3,23 +3,23 @@ - Welcome to the MIPS Guide | Hardware Lab NITC + Hardware Lab NITC - + - - - - - + + + + + -
Hardware Lab NITC

Appearance

Welcome to the MIPS Guide ​

This course covers the following topics-

​

  • Introduction to MIPS - Setting up and understanding MIPS ISA.
  • Basic Integer and String Handling - Learn the Basics of MIPS integers.
  • Integer Array Handling - Learn how to make integer arrays and operate them.
  • 2-D Array Handling - Extend your array knowledge with 2-D arrays.
  • Strings (Advanced) - String Handling explained in detail.
  • Floating Points - Learn how to handle floating point numbers.

Introduction to MIPS ​

Main Documentation :material-google-drive: : Click Here
Theory explanation: Video Link
Setting up MARS:

  1. Video Link

  2. Sample Code

Basic Integer and String Handling ​

Main Documentation :material-google-drive: : Click Here
Theory Explanation: Video Link
Sample Code Bank:

  1. Reversing 2 digit number

  2. Calculating Average Marks

  3. Finding Spy Number

Floating Point Handling ​

Main Documentation :material-google-drive: : Click Here

Farenheit to Celcius:
Sample Code

Maximum and Minimum in Float Array:
Sample Code

Round off to n digits:
Sample Code

Integer Array Handling ​

Main Documentation (Also contains String advanced):material-google-drive: : Click Here

Introduction to Integer Arrays:

  1. Video

  2. Sample Code

Sum of Elements of an Array:

  1. Video

  2. Sample Code

Greatest Element in Array:

  1. Video▶️
  2. Sample Code

Merge 2 Sorted Arrays:

  1. Video▶️
  2. Sample Code

Highest and Lowest occurrence of an element in an array:

  1. Video ▶️
  2. Sample Code

Binary Search:

  1. Video ▶️
  2. Sample Code

Quicksort:

  1. Video ▶️
  2. Sample Code

2-D Integer Array Handling ​

Main Documentation :material-google-drive: : Click Here

Theory Explanation: Video Link
Sample Code Bank:

  1. Taking Input
  2. Printing a Matrix
  3. Sum of Two Matrices

String Handling (advanced) ​

Input/Output of Strings:

  1. Video ▶️
  2. Sample Code

Traversal of Strings (Advanced string operations):

  1. Video ▶️
  2. Sample Code

Length of String:

  1. Video ▶️
  2. Sample Code

Palindrome Check:

  1. Video ▶️
  2. Sample Code

Concatenation of strings:

  1. Video ▶️
  2. Sample Code

Copyright © 2024 National Institute of Technology Calicut

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Hardware Lab NITC

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Welcome to the MIPS Guide

This part covers the following topics

Introduction to MIPS

Setting up and understanding MIPS ISA.

Basic Integer and String Handling

Learn the Basics of MIPS integers.

Integer Array Handling

Learn how to make integer arrays and operate them.

2-D Array Handling

Extend your array knowledge with 2-D arrays.

Strings (Advanced)

String Handling explained in detail.

Floating Points

Learn how to handle floating point numbers.

Introduction to MIPS ​

Main Documentation : Click Here
Theory explanation: Video Link

Setting up MARS: ​

Basic Integer and String Handling ​

Main Documentation : Click Here
Theory Explanation: Video Link

Sample Code Bank: ​

  1. Reversing 2 digit number
  2. Calculating Average Marks
  3. Finding Spy Number

Floating Point Handling ​

Main Documentation : Click Here

Farenheit to Celcius:
Sample Code

Maximum and Minimum in Float Array:
Sample Code

Round off to n digits:
Sample Code

Integer Array Handling ​

Main Documentation (Also contains String advanced : Click Here

Introduction to Integer Arrays:

  1. Video

  2. Sample Code

Sum of Elements of an Array:

  1. Video

  2. Sample Code

Greatest Element in Array:

  1. Video▶️
  2. Sample Code

Merge 2 Sorted Arrays:

  1. Video▶️
  2. Sample Code

Highest and Lowest occurrence of an element in an array:

  1. Video ▶️
  2. Sample Code

Binary Search:

  1. Video ▶️
  2. Sample Code

Quicksort:

  1. Video ▶️
  2. Sample Code

2-D Integer Array Handling ​

Main Documentation : Click Here

Theory Explanation: Video Link
Sample Code Bank:

  1. Taking Input
  2. Printing a Matrix
  3. Sum of Two Matrices

String Handling (advanced) ​

Input/Output of Strings:

  1. Video ▶️
  2. Sample Code

Traversal of Strings (Advanced string operations):

Length of String:

Palindrome Check:

Concatenation of strings:

Copyright © 2024 National Institute of Technology Calicut

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Hardware Lab NITC

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MIPS ​

Setting up the MARS Code Editor ​

Introduction to MARS Simulator ​

MARS simulator will be the software on which we will be running our MIPS code.

Setting up JAVA SDK ​

(Please note this tutorial is to download SDK Ver 11)

Downloading Java SDK on MacOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your macOS version (e.g., macOS x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the macOS version and click on the provided download link.
  8. The JDK installer package will be downloaded to your computer.
  9. Locate the downloaded package in your Downloads folder or the folder you specified for downloads.
  10. Double-click on the JDK installer package to launch the installation wizard.
  11. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your macOS computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Windows version (e.g., Windows x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Windows version and click on the provided download link.
  8. The JDK installer executable file (e.g., jdk-11.0.x_windows-x64_bin.exe) will be downloaded to your computer.
  9. Locate the downloaded executable file, and double-click on it to launch the installation wizard.
  10. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your Windows computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Linux computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Linux distribution.
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Linux version and click on the provided download link.
  8. The JDK archive file (e.g., jdk-11.0.x_linux-x64_bin.tar.gz) will be downloaded to your computer.
  9. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  10. Navigate to the directory where you downloaded the JDK archive file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads
  11. Extract the contents of the JDK archive using the following command: tar -xvzf jdk-11.0.x_linux-x64_bin

Setting Up MARS Simulator ​

Note: Is your MARS text unreadably small? Download and use a new release Java 9 or above which contains a fix to automatically scale and size AWT and Swing components for High Dots Per Inch (HiDPI) displays on Windows and Linux.

Downloading MIPS MARS Simulator on macOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the official website of MIPS MARS at [ http:// courses.missouristate.edu/kenvollmar/mars/]( http:// courses.missouristate.edu/kenvollmar/mars/).
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Double-click on the ZIP file to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Applications folder.
  8. Open Terminal on your macOS by going to Applications > Utilities > Terminal.
  9. In the Terminal window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Applications folder, you can use the following command: cd/Applications
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your macOS computer.
Downloading MIPS MARS Simulator on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/]([http://courses.missouristate.edu/ kenvollmar/mars/])
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Right-click on the ZIP file and select "Extract All" to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Program Files folder.
  8. Open the Command Prompt on your Windows computer by pressing the Windows key + R, typing "cmd," and hitting Enter.
  9. In the Command Prompt window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Program Files folder, you can use the following command: cd "C:\Program Files"
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your Windows computer.
Downloading MIPS MARS Simulator on Linux: ​
  1. Open a web browser on your Linux computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/](http://courses.missouristate.edu/ kenvollmar/mars/)
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "Mars4_5.jar.zip" will be downloaded to your computer.
  5. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  6. Navigate to the directory where you downloaded the ZIP file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads
  7. Unzip the ZIP file using the following command: unzip Mars4_5.jar.zip
  8. This will extract the "Mars4_5.jar" file from the ZIP archive.
  9. Move the "Mars4_5.jar" file to a suitable location on your computer. For instance, you can move it to the /opt directory using the following command: sudo mv Mars4_5.jar /opt
  10. To run the MIPS MARS simulator, open the terminal and navigate to the directory where you placed the JAR file. For example, if you moved it to the / opt directory, use the following command: cd /opt
  11. Execute the following command to launch the MIPS MARS simulator java -jar Mars4_5.jar
  12. The MIPS MARS simulator should now launch on your Linux computer.

MARS ASSEMBLY AND SYSTEM CALLS ​

Before assembling, the environment of this simulator can be simplisticly split to three segments: the editor at the upper left where all of the code is being written, the compiler/output right beneath the editor and the list of registers that represent the "CPU" for our program.

After assembling (by simply pressing F3) the environment changes, with two new segments getting the position of the editor: the text segment where

i) each line of assembly code gets cleared of "pseudoinstructions" (we'll talk about those in a sec) at the "basic" column and

ii) the machine code for each instruction at the "code" column, and the data segment where we can have a look at a representation of the memory of a processor with little-endian order.

After assembling, we can execute our code either all at once (F5) or step by step (F7), as well as rewinding the execution several steps backwards to the back (F8).

MARS accepts and exports files with the .asm filetype

Pseudo instructions ​

Before looking at the instruction set , let us look at a few pseudo instructions that’ll help you understand the IS better.

Here's a list of useful pseudo-instructions.

mov $t0, $t1: Copy contents of register t1 to register t0.

li $s0, immed: Load immediate into to register s0. The way this is translated depends on whether immed is 16 bits or 32 bits.

la $s0, addr: Load address into to register s0.

lw $t0, address: Load a word at address into register t0

Given below are some standard arithmetic and logical instructions standard to the MIPS Instruction Set Architecture.

**MARS provides a small set of operating system-like services through the system call (syscall) instruction **

**To request a service, a program loads the system call code into register $v0 and arguments into registers $a0~$a3 **

System calls that return values put their results in register $v0

Arithmetic Instructions ​
InstructionExampleMeaningComments
addadd $1,$2,$3$1=$2+$3
subtractsub $1,$2,$3$1=$2-$3
add immediateaddi $1,$2,100$1=$2+100"Immediate" means a constant number
add unsignedaddu $1,$2,$3$1=$2+$3Values are treated as unsigned integers,not two's complement integer
subtract unsignedsubu $1,$2,$3$1=$2-$3Values are treated as unsigned integers,not two's complement integers
add immediate unsignedaddiu $1,$2,100$1=$2+100Values are treated as unsigned integers,not two's complement integers
multiply (without overflow)mul $1,$2,$3$1=$2*$3Result is only 32 bits!
multiplymult $1,$2,$3$hi, $low=$2*$3Upper 32 bits stored in special register hi. Lower 32 bits stored in special register lo
dividediv $1,$2,$3$hi,$low=$2/$3Remainder stored in special register hi. Quotient stored in special register lo

Logical ​

InstructionExampleMeaningComments
andand $1,$2,$3$1=$2&$3Bitwise AND
oror $1,$2,$3$1=$2$3
and immediateandi $1,$2,100$1=$2&100Bitwise AND with immediate value
or immediateori $1,$2,100$1=$2100
shift left logicalsll $1,$2,10$1=$2<<10Shift left by constant number of bits
shift right logicalsrl $1,$2,10$1=$2>>10Shift right by constant number of bits

Data Transfer ​

InstructionExampleMeaningComments
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
store wordsw $1,100($2)Memory[$2+100]=$1Copy from register to memory
load upper immediatelui $1,100$1=100x2^16Load constant into upper 16 bits. Lower 16 bits are set to zero
load addressla $1,label$1=Address of the labelPseudo-instruction (provided by assembler). Loads computed address of label (not it's contents) into register
load immediateli $1,100$1=100Pseudo instruction (provided by assembler). Loads immediate value into the register.
move from himfhi $2$2=hiCopy from special register hi to general register
move from lomflo $2$2=loCopy from special register lo to general register
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
movemove $1,$2$1=$2Pseudo instruction (provided by assembler). Copy from register to register

Conditional Branch ​

InstructionExampleMeaningComments
branch on equalbeq $1,$2,100if($1==$2) go to PC+4+100Test if registers are equal
branch on not equalbne $1,$2,100if($1!=$2) go to PC+4+100Test if registers are not equal
branch on greater thanbgt $1,$2,100if($1>$2) go to PC+4+100Pseudo-instruction
branch on greater than or equalbge $1,$2,100if($1>=$2) go to PC+4+100Pseudo-instruction
branch on less thanblt $1,$2,100if($1<$2) go to PC+4+100Pseudo-instruction
branch on less than or equalble $1,$2,100if($1<=$2) go to PC+4+100Pseudo-instruction

Comparison ​

InstructionExampleMeaningComments
set on less thanslt $s1,$s2,$s3if($2<$3) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.
set on less than immediateslti $s1,$s2,100if($2<100) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.

Unconditional Jump ​

InstructionExampleMeaningComments
jumpj 1000go to address 1000Jump to target address
jump registerjr $1go to address stored in $1For switch procedure return
jump and linkjal 1000$ra=PC+4 go to address 1000Use when making procedure call. This saves the return address in $ra

System Calls ​

ServiceOperationCode(in $v0)ArgumentsResults
print_intPrint integer number (32 bit)1$a0 = integer to be printedNone
print_floatPrint floating-point number (32 bit)2$f12 = float to be printedNone
print_doublePrint floating-point number (64 bit)3$f12 = integer to be printedNone
print_stringPrint null-terminated character string4$a0 = address of string in memoryNone
read_intRead integer number from user5NoneInteger returned in $v0
read_floatRead floating-point number from user6 NoneFloat returned in $f0
read_doubleRead double floating-point number from user7NoneDouble returned in $f0
read_stringWorks the same as Standard Clibrary fgets()8$a0 = memory address of string input buffer $a1 = length of string buffer (n)None
sbrkReturns the address to a block of memory containing n additional bytes (Useful for dynamic memory allocation)9$a0=amountaddress in $v0
exitStop program from running10NoneNone
print_charPrint character11$a0 = character to be printedNone
read_charRead character from user12NoneChar returned in $v0
exit2Stops program from running and returns an integer17$a0 = result(integer number)None

The complete list of syscalls can be accessed at
https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html

Assembler Directives ​

DirectiveResult
.word w1, ..., wnStore n 32-bit values in successive memory words
.half h1, ..., hnStore n 16-bit values in successive memory words
.byte b1, ..., bnStore n 8-bit values in successive memory words
.ascii strStore the ASCII string str in memory. Strings are in double-quotes, i.e. "Computer Science"
.asciiz strStore the ASCII string str in memory and null terminate it. Strings are in double-quotes, i.e. "Computer Science"
.space nLeave an empty n-byte region of memory for later use
.align nAlign the next datum on a 2^n byte boundary. For example, .align 2 aligns the next value ona word boundary

Registers ​

Register NumberRegister NameDescription
0$zeroThe value 0
2-3$v0-$v1Values from expression evaluation and function results
4-7$a0-$a3(arguments) First four parameters for subroutine
8-15, 24-25$t0-$t9Temporary variables
16-23$s0-$s7Saved values representing final computed results
31$raReturn address

MARS(MIPS Assembler/Simulator) Tutorial ​

1. Input the Tutorial program

1.1) Open the MARS program and click from the file menu choose “File...New”. A black document will open which you can enter your assembly code into. Click “File...Save As” and save the file as “Tutorial1.asm ”.

1.2) Enter the code as shown below into the editor and save the file.

v
# Program File: Tutorial1.asm 
+# Written by:   MoSaad 
+# Date Created: 10/05/2023 
+# Description:  Tutorial program to introduce MARS simulator  including: breakpoints, single-
+stepping, and register and memory windows. 
+#----------------------------------------------------------- 
+#----------------------- 
+# Declare some constants 
+#----------------------- 
+.data 
+string1: .asciiz "Welcome to Hardware Lab at NIT Calicut\n" 
+string2: .asciiz "Hello World \n" 
+string3: .asciiz "\nLoop #" 
+#------------------ 
+# Main program body 
+#------------------ 
+.text 
+main: 
+li $v0,4 
+la $a0,string1 
+syscall 
+la $a0,string2 
+syscall 
+li $t0, 1 
+loop: 
+li $v0, 4 
+la $a0,string3 
+syscall 
+li $v0,1 
+move $a0,$t0 
+syscall 
+addi $t0,$t0,1 
+bne  $t0,4,loop 
+#----- 
+# Halt  
+#----- 
+li $v0, 10 
+syscall

1.4) From the menu, choose “Run...Assemble”. The “Mars Messages” window at the bottom of the screen will indicate if any errors occurred. No errors should occur.

2. Simulate the tutorial program

2.1) From the menu, choose “Run...Go” to execute the program. The program will execute displaying two lines of text and three iterations of a loop to the Run /IO window.

2.2) The buttons at the top of the window can be used as shortcuts for the run menu. Use the “Reset” button to reset the program, and then try tracing through the program by clicking the step button.

2.3) You can adjust the speed the program runs by moving the slider to the right of the buttons. If you have an infinite loop in your program, it may be necessary to adjust (slow down) the speed of the simulator to prevent the MARS program from crashing.

Run the program. If a breakpoint has been set the program will stop at the next breakpoint. Trace (Step) Into. Executes a single instruction. If the instruction is a procedure call (jal) the simulator will stop at the first instruction of the procedure. Backstep. Undo the last step taken in the code. Pause the currently running program. Press the run button to continue execution. Stop the currently running program. You will need to reset the simulator to execute the program again after stopping it. Reset. Resets the simulator, reinitializing the registers, program counter, and memory. Adjusts the speed that the simulator runs at.

3. Using the Debugging Tools

3.1) When a program does not work as expected you will need to use the debugging tools provided with the simulator.

3.2) One of the primary tools used to debug a program is setting a breakpoint. You can break before execution of an instruction by clicking on the checkbox associated with each instruction on the far left of the execute window. Set a breakpoint at the instruction: addi $t0,$t0,1

3.3) Run the program until the breakpoint by clicking “Run”. At this point in the program only the first loop iteration has been printed. (You will need to click back to the Run/IO window to see the output.)

3.4) Now use the “Trace Into” button to step through the loop that prints out the next line of text one character at a time. Step through the instructions until “Loop #2” is printed to the output window. Stop and find the value of the registers “t0” and “pc” at that point? Has the line of code that the program counter points to executed yet?

3.5) The simulator also allows you to view the memory contents. The memory window appears in the middle of the screen and is titled “Data Segment”. Remove the earlier breakpoint and add a breakpoint to line 33, “syscall”. Click the run button so that the program executes up until the new breakpoint. We are now in the code right before “Loop #” is about to be printed for the third iteration. Notice that the $a0 register is now a pointer to the address where the “Loop #” text is stored. What is the memory location the register is pointing to?

3.6) Now look in the data segment area, and find the address $a0 points to. This is the memory section where the characters of the text “Loop #” is stored. Using an ASCII table find the address where the ‘p’ in “Loop” is located?

3.7) Exercise: Can you find where the word “Welcome” is stored in the memory?

Integer Handling ​

Unlike NASM where numbers are stored as characters, MIPS can store single or multiple digit integers directly. This chapter describes how to read and print integers. Basic operations in integer handling (add, sub, mul, div) will also be covered.

1. Declaring an integer

Integers can be declared as constants in the ‘.data’ section as shown below:

Code to declare constants ‘x’ and ‘y’ with values 30 and 40 respectively:

v
.data 
+x: .word 30 
+y: .word 40

2. Loading an integer value into a register

Another way of using integers in MIPS is to read their values into temporary registers using ‘I’ type instructions. The two commonly used methods of reading integer values are:

  1. Loading a value into a temporary register.
  2. Adding the value of the zero register and any value into a temporary register.

Code to enter integer values 5 and 10 using add and load instructions respectively into temporary registers:

v
.text 
+addi  $t0, $0, 5 
+li $t1, 10

3. Reading integers as input from the user

Integers can be read from the user using syscall (system call) instructions. The system call code for reading an integer is ‘5’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The input is then stored in $v0.

Code to read an integer input from the user:

v
.text 
+li $v0, 5 
+syscall

4. Printing integers

Integers stored in registers can also be printed using syscall instructions. The system call code for printing an integer is ‘1’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The integer to be printed must be stored in the $a0 register.

Code to print the integer ‘5’ after storing it in a register:

v
.text 
+li $a0, 5 
+li $v0, 1 
+syscall

We have now learnt how to store single and multi digit integers and how to print their values. We shall now combine all of these into a single program for a more robust understanding of the covered concepts.

Code to declare a constant x with value 10, load values 20 and 30 into two registers and read an integer value from the user and print all these values:

v
.data 
+x: .word 10 
+.text 
+addi $t0, $0, 20   #load value 20 
+li $t1, 30    #load value 30 
+li $v0, 5     #read integer input
+syscall 
+move  $t2, $v0   #move integer input 
+lw $a0, x     #print x 
+li $v0, 1 
+syscall 
+move $a0, $t0    
+li $v0, 1     #print value of $t0  
+syscall    
+move $a0, $t1   #print value of $t1 
+li $v0, 1 
+syscall 
+move $a0, $t2   #print integer input 
+li $v0, 1 
+syscall 
+li $v0, 10    #exit program 
+syscall

Output:Assume the value ‘5’ is entered by the user as input.

v
5
+1020305
+-- program is finished running --

5. Adding integers

Integers can be added in two ways, either by adding fixed or immediate values to an integer value stored in a register, or by adding two integers that are both stored in registers. Both methods to add integers are demonstrated below:

Code to add integer values stored in registers:

v
.text 
+addi  $t0, $t1, 5   #t0=t1+5  
+add $t2, $t2, $t1   #t2=t2+t1 
+addi  $t1, $zero, 5   #t1=0+5 
+add   $t2, $zero, $t1    #t2=0+t1

6. Subtracting integers

Unlike addition, values can only be subtracted if they are stored in a register.

Code to subtract integer values stored in registers:

.text 
+sub $t2, $t2, $t1   #t2=t2-t1    
+sub   $t2, $zero, $t1    #t2=0-t1

7. Multiplying integers

MIPS allows you to multiply the values present in two registers and stores the 32 most significant bits in the HI special register and the 32 least significant bits in the LO special register.

The value obtained in the HI and LO registers can be accessed using the mfhi and mflo instructions respectively.

Code to multiply two integers values and access the result after multiplication:

.text 
+mult  $t0, $t1     #signed mult 
+mflo  $s0     #s0=t0*t1 
+multu $t2, $t3    #unsigned mult  
+mflo  $s1     #s1=t2*t3

8. Dividing integers

Division in MIPS is similar to multiplication except for a key difference, the HI special register stores the remainder while the LO special register will hold the quotient of the division.

Code to divide to integers and access the remainder and quotient after division:

.text 
+div $t1, $t2    #signed div 
+mfhi  $s0     #s0=t1%t2 
+mflo  $s1     #s1=t1/t2 
+divu  $t3, $t4    #unsigned div 
+mfhi  $s2     #s2=t3%t4 
+mflo  $s3      #s3=t3/t4

Points To Note ​

1. Entering number of size larger than 32 bits The largest integer that can be entered in 32 bit space is 2,147,483,647. Entering a number larger than that results in the following error:

``` Runtime exception at 0x0040002c: invalid integer input (syscall 5)```
+

2. Changing the value of $zero register It is not possible to change the value of the $zero register, any instructions that attempt to alter the value have no effect.

3. Multiplying numbers of size 32 bits In MIPS, all integer values must be 32 bits. So if there is a valid answer, it must be contained in the lower 32 bits of the answer. Thus to implement multiplication in MIPS, the two numbers must be multiplied using the mult operator, and the valid result moved from the lo register.

4. Division by zero If the divisor is zero, then the MIPS divide instructions do not compute any result in the HI and LO registers. Division by zero is ignored and no exception is produced.

5. Meaning of the .word directive The .word directive allocates 4 bytes of space in the data region. The .word directive can then be given an integer value, and it will initialize the allocated space to that integer value. Be careful as it is incorrect to think of a the .word directive as a declaration for an integer, as this directive simply allocates and initializes 4 bytes of memory, it is not a data type. What is stored in this memory can be any type of data.

String Operations ​

Strings in MIPS can be declared as constant in the .data part of the program. They are often stored this way so that they can be used as user prompts or to format output of a program. Strings can also be entered by the user during the runtime of the program. Both methods of using strings in MIPS will be demonstrated below.

1. Entering string constants

Pre-determined strings enclosed by double quotes can be declared in the .data section.

Code to store the string “enter an element:” in memory under the name “message”:

.data 
+message: .asciiz “enter an element:”

2. Enter strings as input from the user

To enter strings as input, the syscall code to be used is 8. Apart from that, the address of the memory space into which the string must be entered, is loaded into the $a0 register. The maximum size of the string must also be loaded into the $a1 register before performing the syscall.

Code to read a string as input from the user:

.data 
+input: .space 100 
+inputsize: .word 100 
+.text 
+li $v0, 8 
+la $a0, input 
+lw $a1, inputsize 
+syscall

3. Printing strings stored in memory

To print the required string, the syscall to be used is 4. The address of the string has to be loaded into the $a0 register.

Code to print a string named ‘message’ stored in memory:

.text 
+li $v0, 4 
+la $a0, output 
+syscall

We have now learnt how to declare strings constants as well as how to store strings entered by the user. We shall now write a program combining both the concepts for a more robust understanding of basic string operations.

Code to read a string, with prompts instructing the user:

.text 
+main: 
+    # Prompt for the string to enter 
+    li $v0, 4 
+    la $a0, prompt 
+    syscall 
+ 
+    # Read the string.  
+    li $v0, 8 
+    la $a0, input 
+    lw $a1, inputSize  
+    syscall 
+     
+    # Output the text 
+    li $v0, 4 
+    la $a0, output 
+    syscall
+
+    # Output the number 
+    li $v0, 4 
+    la $a0, input 
+    syscall 
+ 
+    # Exit the program 
+    li $v0, 10 
+    syscall 
+ 
+.data 
+input:        .space 81 
+inputSize:    .word 80 
+prompt:       .asciiz "Please enter a string: " 
+output:       .asciiz "\nYou typed the string: "

Points To Note ​

  • The .space directive allocates n bytes of memory in the data region of the program, where n=81 in this program. Since the size of a character is 1 byte, this is equivalent to saving 80 characters for data. 81 was used here because in MIPS a sequence of ASCII characters is terminated by a null value (byte containing 0). This is known as a null terminator.

  • If the string the user enters is larger than the maximum size of the string, it is truncated to the maximum size. This is to prevent the program from accessing memory not allocated to the string.

Floating Point Numbers ​

Floating point numbers are stored according to the IEEE 754 Standard. There are 2 types of floating point numbers, single precision and double precision.

Floating point number representation ​

According to IEE 754 Standard, floating point numbers follow the given representation.

Sign Exponent Fraction

  • The sign bit is 0 or 1, for positive or negative respectively.

  • The exponent stores the exponent of the number in scientific notation of its binary representation, plus a bias.

  • The fraction stores the fractional part of the binary representation of the number.

DataSingle PrecisionDouble Precision
Size32 bits64 bits
Exponent size8 bits11 bits
Fraction size23 bits52 bits
Bias1271023

Note

  • Since there are some numbers with non-ending decimal part in there binary representation ( For Example- ( 1 /3) 10 = (0.01 0011 0011 0011 ....) 2 ) and we have only limited bits to store the fraction part, there will be some slight inaccuracy while storing certain floating point numbers. Therefore, it is recommended to always use double, as it has a higher precision due to its increased no. of bits.

MIPS floating point architecture ​

In MIPS, all floating point calculations are computed in a separate processor, called co- processor 1.

The coprocessor contains 32 floating point registers, each of width 32 bits. The registers are numbered from $f 0 to $f3 1.

Each register is can store a single precision floating point number, while double precision is stored in 2 registers in an even-odd pair. For instructions concerning double precision numbers, the even numbered register is used in the instruction. Using an odd numbered register will throw an error.

In addition to the registers, there are 8 condition flags, which are used in floating point compare and branch instructions.

Floating point registers in MIPS ​

RegistersUsage
$f0 - $f3Used for results of floating point procedures
$f4 - $f11Temporary floating point registers, whose values are NOT preserved across procedure calls
$f12 - $f15Floating point parameters, whose values are NOT preserved across procedure calls
$f16 - $f19More temporary floating point registers, whose values are NOT preserved across procedure calls
$f20 - $f31Saved floating point registers, whose values are preserved across procedure calls

Among the 32 registers, only $f 4 - $f 11 , $f 16 - $f 19 and $f 20 - $f 31 can be used by the programmer for storing values, as the others are reserved for special purposes.

Note

  • Unlike the general purpose register $ 0 , $f 0 is not hardwired to be zero, and is used for storing results of procedures.

Declaring a Floating point number ​

.data
+  num1: .float 3.
+  num2: .double 4.5 3
+
+  .align 2 # Since float has 2^2 bytes
+  float_arr: .space 100 it has to be aligned to 2
+
+  .align 3 # Since double has 2^3 bytes it has to be aligned to 3
+  double_arr: .space 100

Reading and Printing Floating point numbers ​

Reading and printing a floating point number is similar to that of an integer, using syscall, only difference being in the $v0 value and parameter registers.

Single precision ​

The $v0 value for reading a single precision floating point number is 6 while that of printing is 2.

main: 
+  li $v0, 6 
+  syscall    # The number is stored in $f0 
+        
+  li $v0, 2 
+  mov.s $f12, $f0   # The number to be printed is moved to $f12 
+  syscall

Double precision ​

The $v0 value for reading a double precision floating point number is 7 while that of printing is 3.

main: 
+  li $v0, 7 
+  syscall    # The number is stored in $f0/$f1 
+        
+  li $v0, 3 
+  mov.d $f12, $f0   # The number to be printed is 
+  syscall     moved to $f12/$f13

Data Movement Instructions ​

InstructionSyntaxRemarks
Load single/doublel.s fdest, address l.d fdest, addressThe single/double floating-point stored in address is loaded onto register fdest
Store single/doubles.s fsrc, address s.d fsrc, addressThe single/double floating-point stored in register fsrc is stored to address
Move single/doublemov.s fdest, fsrc mov.d fdest, fsrcThe single/double floating-point stored in register fsrc is moved to register fdest
Move from coprocessor 1mfc1 dest, fsrcThe 32 - bit data from floating register fsrc is copied to general purpose register dest
Move to coprocessor 1mtc1 src, fdestThe 32 - bit data from general purpose register src is copied to floating point register fdest

Note

  • There is no load immediate for floating point. So if a constant is needed, it has to be stored in the data segment and loaded to the required register.
  • For the move to/from coprocessor 1 instructions, the first operand is a general purpose register and the second one is the floating point register.

Arithmetic Instructions ​

InstructionSyntaxRemarks
Additionadd.s fdest, fsrc1, fsrc2
add.d fdest, fsrc1, fsrc		The single/double floating-point numbers stored in fsrc1 and fsrc2
are added and stored in register fdest
Subtractionsub.s fdest, fsrc1, fsrc2
sub.d fdest, fsrc1, fsrc2		The single/double floating-point number stored in fsrc
subtracted from fsrc1 and stored in register fdest
Multiplicationmul.s fdest, fsrc1, fsrc2
mul.d fdest, fsrc1, fsrc2		The single/double floating-point numbers stored in fsrc1 and fsrc2
are multiplied and stored in register fdest
Divisiondiv.s fdest, fsrc1, fsrc2
div.d fdest, fsrc1, fsrc		The single/double floating-point number stored in fsrc1 is divided by fsrc2
and the quotient is stored in register fdest
Negationneg.s fdest, fsrc
neg.d fdest, fsrc		The single/double floating-point number stored in fsrc
is negated (Sign changed) and stored in register fdest
Absolute valueabs.s fdest, fsrc
abs.d fdest, fsrc		Absolute value (Magnitude) of the single/double floating-point number stored in fsrc
is stored in register fdest
Square rootsqrt.s fdest, fsrc
sqrt.d fdest, fsrc		Square root of the single/double floating-point number stored in fsrc
is stored in register fdest

Sample Question 1 ​

Given a temperature in Fahrenheit, convert it into Celsius (Input and output has to be floating point values).

Temperature in degrees Celsius = (Temperature in degrees Fahrenheit - 32 ) * 5 / 9.

data 
+  # Constants used for calculation 
+  const1: .double 32.0 
+  const2: .double 5.0 
+  const3: .double 9.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the temperature in Fahrenheit: " 
+  msg2: .asciiz "The temperature in Celsius is: " 
+ 
+
+.text 
+.globl main 
+main: 
+ 
+  li $v0, 4                    # Printing msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7                    # Reading user input 
+  syscall 
+  
+  mov.d $f12, $f0              # $f12 = User Input 
+  l.d $f14, const1             # $f12 = $f12 - 32 
+  sub.d $f12, $f12, $f14 
+  
+  l.d $f14, const2             # $f12 = $f12 * 5 
+  mul.d $f12, $f12, $f14 
+  
+  l.d $f14, const3             # $f12 = $f12 / 9 
+  div.d $f12, $f12, $f14 
+  
+  li $v0, 4                    # Printing msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 3                    # Printing final answer 
+  syscall 
+  
+  li $v0, 10                   # Exit 
+  syscall

Comparison/Branch Instructions ​

InstructionSyntaxRemarks
Compare equalc.eq.s cc, fsrc1, fsrc2
c.eq.s fsrc1, fsrc2
c.eq.d cc, fsrc1, fsrc2
c.eq.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the numbers in fsrc1
and fsrc2 are equal, 0 otherwise.
Compare less thanc.lt.s cc, fsrc1, fsrc2
c.lt.s fsrc1, fsrc2
c.lt.d cc, fsrc1, fsrc2
c.lt.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the number in fsrc1
is less than that in fsrc2, 0 otherwise.
Compare less than or equal toc.le.s cc, fsrc1, fsrc2
c.le.s fsrc1, fsrc2
c.le.d cc, fsrc1, fsrc2
c.le.d fsrc1, fsrc		Sets the condition flag cc as 1 if the number in fsrc1
is less thanor equal to that in fsrc2, 0 otherwise.
Branch if truebc1t cc, label
bc1t label		Jumps to label if the condition flag cc is set as 1
Branch if falsebc1f cc, label
bc1f label		Jumps to label if the condition flag cc is set as 0

Note

  • The condition flag can be omitted in the above instructions, in which case condition flag 0 is taken as default.
  • As there is no comparison instruction for “Not equal to”, it has to be implemented by reversing the required branch condition Ex. We need to branch to label if $f4 and $f6 are not equal. This can be written as
      c.eq.d $f4, $f6
+  bc1.f label
  • For greater than and greater than and equal to, it is simpler to reverse the input registers. Ex. We need to branch to label if $f4 if greater than $f6. This can be written as
      c.le.d $f6 , $f4
+  bc1.t label

Sample Question 2 ​

Given an array of floating numbers of size n, print the maximum and minimum element

data 
+  # Array 
+  .align 3 
+  arr: .space 1000 
+  
+  # Characters 
+  newline: .asciiz "\n" 
+ 
+  # User Prompts 
+  msg1: .asciiz "Enter n: " 
+  msg2: .asciiz "Enter no. " 
+  msg3: .asciiz ": " 
+  msg4: .asciiz "The maximum no. is: " 
+  msg5: .asciiz "The minimum no. is: " 
+ 
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4    # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 5    # Read n 
+  syscall 
+  move $t0, $v0 
+  
+  li $t1, 0    # $t1 will be the loop variable  
+               # going from 0,1,2.. 
+  li $t2, 0    # $t2 will be the element indices 
+               # going from 0,8,16.. 
+  loop1:                      # Loop to read n elements 
+    beq $t0, $t1, end_loop1   # Termination condition 
+   
+    li $v0, 4                 # Print msg2 
+    la $a0, msg2 
+    syscall 
+   
+    li $v0, 1                 # Print position of                    
+    move $a0, $t1             # number to be inputted 
+    addi $a0, $a0, 1 
+    syscall 
+   
+    li $v0, 4                 # Print msg3 
+    la $a0, msg3 
+    syscall 
+   
+    li $v0, 7                 # Read input and  
+    syscall                   # store in arr 
+    s.d $f0, arr($t2) 
+   
+    addi $t1, $t1, 1   # Increamenting #t1  
+    addi $t2, $t2, 8   # and $t2 
+    j loop1 
+  
+  end_loop1: 
+  
+  li $t1, 0    # Resetting $t1 and $t2 
+  li $t2, 0 
+  l.d $f4, arr($zero)  # $f4 stores the max value 
+  l.d $f6, arr($zero)  # $f6 stores the min value
+
+  loop2:                        # Loop to compute max and min 
+    beq $t0, $t1, end_loop2     # Termination Condition 
+   
+    l.d $f8, arr($t2)           # Load a number from arr 
+   
+    c.lt.d $f4, $f8             # Compare if the number is  
+                                # greater than current max 
+    bc1f not_max  
+      mov.d $f4, $f8            # If yes then update new max 
+    not_max: 
+   
+    c.lt.d $f8, $f6             # Compare if the number is  
+                                # less than current min 
+    bc1f not_min 
+      mov.d $f6, $f8            # If yes then update new min 
+    not_min: 
+   
+    addi $t1, $t1, 1            # Incrementing $t1 and $t2 
+    addi $t2, $t2, 8 
+    j loop2 
+  
+  end_loop2: 
+  
+  li $v0, 4                      # Print msg4 
+  la $a0, msg4 
+  syscall 
+  
+  li $v0, 3                      # Print max number 
+  mov.d $f12, $f4 
+  syscall 
+
+  i $v0, 4    # Print newline 
+  la $a0, newline 
+  syscall 
+  
+  li $v0, 4    # Print msg5 
+  la $a0, msg5 
+  syscall 
+  
+  li $v0, 3    # Print min number 
+  mov.d $f12, $f6 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall

Data Conversion Instructions ​

Conversion within floating point ​

InstructionSyntaxRemarks
Convert single to doublecvt.d.s fdest, fsrcThe single floating-point stored in fsrc is converted to double and stored in fdest
Convert double to singlecvt.s.d fdest, fsrcThe double floating-point stored in fsrc is converted to single and stored in fdest

Conversion to integers ​

InstructionSyntaxRemarks
Convert single to integercvt.w.s fdest, fsrcThe single floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point)
and stored in 2 ’s compliment form in fdest
Convert double to integercvt.w.d fdest, fsrcThe double floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) and
stored in 2 ’s compliment form in fdest

Note

  • The output of the above two instructions is in 2 ’s compliment form, which should not be used with any other instructions other than mfc1. Other instructions always assume the data in registers are according to IEEE standards, which can cause errors.

Conversion from integers ​

InstructionSyntaxRemarks
Convert integer to singlecvt.s.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to single precision floating point and is stored in fdest
Convert integer to doublecvt.d.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to double precision floating point and is stored in fdest

Special Instructions ​

InstructionSyntaxRemarks
Ceilingceil.w.s fdest, fsrc
ceil.w.d fdest, fsrc		The smallest integer not greater than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form
Floorfloor.w.s fdest, fsrc
floor.w.d fdest, fsrc		The greatest integer not smaller than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form
Round to nearest integerround.w.s fdest, fsrc
round.w.d fdest, fsrc		The floating-point stored in fsrc is rounded off to
nearest integer and stored in fdest in 2 ’s compliment form

Sample Question 3 ​

Given a floating point number and an integer n, round off the floating point number to n digits.

Hint-

Multiplty then given number with 10^n, and round off using round.w.d instruction. Divide the result by 10^n to obtain the final result.

data 
+  # Constants used for calculation 
+  const1: .double 0.0 
+  const2: .double 1.0 
+  const3: .double 10.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the number : " 
+  msg2: .asciiz "Enter number of digits to round off to: " 
+  msg3: .asciiz "The rounded off number is: " 
+  
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4     # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7     # Read number to round off 
+  syscall 
+  
+  mov.d $f12, $f0    # $f12 = user input 
+  
+  li $v0, 4     # Print msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 7     # Read n 
+  syscall 
+
+  mov.d $f16, $f0    # $f16 = n 
+  l.d $f4, const1    # $f4 used as a loop varibale 
+                     # initialised to 0 
+  l.d $f6, const2    # $f6 used to store 10^n 
+  l.d $f8, const3    # $f8 used to store 10 for  
+                     # calculating power 
+  l.d $f10, const2   # $f10 used to store 1 for  
+                     # incrementing loop variable 
+  loop1:    # Loop to compute 10^n 
+    c.eq.d $f4, $f16  # Ternminaltion Condition 
+    bc1t end_loop1 
+  
+    mul.d $f6, $f6, $f8 # $f6 = $f6 * 10 
+    add.d $f4, $f4, $f10  # $f4 = $f4 + 1 
+  
+    j loop1 
+  end_loop1: 
+  
+  mul.d $f12, $f12, $f6  # $f12 = $f12 * (10^n) 
+  round.w.d $f12, $f12   # $f12 is rounded to nearest 
+                         # integer 
+  cvt.d.w $f12, $f12     # Output after rounding,  
+                         # which is a word, is  
+                         # converted back to double 
+  div.d $f12, $f12, $f6  # $f12 = $f12 / (10^n) 
+  
+  li $v0, 4    # Print msg3 
+  la $a0, msg3 
+  syscall  
+ 
+  li $v0, 3    # Print final answer 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall

Integer Arrays ​

An Integer Array is continuous storage block in memory in which each element is an integer. Each element of an array is accessed using the base address of the array and the index of the element we must access.

Declaration and Initialization ​

Integer arrays can be initialized using .word or an empty array can be declared using the .space keyword inside the .data section of the program

data: 
+arr: .word 3,4,-5,6    #initialized an array arr=[3,4,-5,6] 
+arr2: .space 40  # empty array with 40 bytes reserved for arr2

Array Traversal ​

Array traversal refers to accessing each element of the array using its index.

Each integer element of an array occupies a word (4 bytes). Therefore,4 bytes needed to be added to the current address to obtain the address of the following element.

Address of arr [k] = base address of arr + 4 * k

Eg: To access arr[3] and store it to $t

a $s0,arr   # base add address of array is stored in $s0 
+addi $s0,$s0,12    #  $s0 = address of arr[3] = arr + 4 * 3 
+lw $t2,0($s0)    # $t2=arr[3]

or

a $s0,arr   # base add address of array is stored in $s0 
+lw $t2,12($s0)  # $t2=value of (arr + 12)

Array Input ​

The elements of an integer array can be received from the user using the syscall for integer input and a for loop.

An empty array must be declared in the .data by allocating the necessary space as shown before.

Each integer element of an array occupies 4 bytes. Therefore, 4 bytes needed to be added to the current address after each insertion.

The following code segment can be used to create an array of size n by receiving inputs from the user:

Assume $s1 contains n, $s0 contains base address of an empty array and $t0 is the loop counter

for: 
+  beq $t0,$s1,exit      # loop termination condition 
+  sll $t1,$t0,2         # $t1=i*4 
+  add $t1,$t1,$s0   # $t1 = arr + i * 4         
+       
+  li $v0,5           # input integer and store in $t2 
+  syscall 
+  move $t2,$v0 
+  sw $t2,0($t1)      # $t2 = arr[i] 
+  addi $t0,$t0,1     # increment loop counter i 
+  j for

Printing an Integer Array ​

Integer Array can be printed by traversing each element by using array traversal rules (as discussed above) and integer printing (code 1 is loaded to $v0).

Consider the following code snippet to print the array created in the previous example in which every element is provided by the user:

la $s0,arr             # store base address of array in $s0 
+li $t0,0 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       # array traversal to access arr[i] 
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)       # $t2=arr[i] 
+  li $v0,1            # 1 is the syscall number to print integers 
+  move $a0,$t2         # print $t2   
+  syscall 
+    
+  li $a0, 32     # 32 is the ASCII code for space  
+  li $v0, 11          # syscall number for printing character 
+  syscall 
+  addi $t0,$t0,1 # increment loop counter 
+  j print 
+end:                         
+li $v0,10   #end program        
+syscall

Negative Numbers as Elements ​

All integer operations in MIPS support both positive and negative numbers. No changes are required to the program for the input and output of positive integers.

enter array element: -5 
+enter array element: -6 
+enter array element: 8 
+enter array element: -2 
+The elements of the array are: -5.0 -6.0 8.0 -2.0  
+-- program is finished running --

Floating Point Numbers as Elements ​

An array of floating-point numbers can be created by replacing all the integer operations with floating-point operations. The following changes need to be made to convert an integer array into an array of floating-point numbers:

  1. Replace the integer code loaded to $v0 by floating-point code
  2. Replace the load, store and move operation by l.s , s.s and mov.s where floating point data type is used
# program to input array 
+for: 
+  beq $t0,$s1,exit
+  sll $t1,$t0,2
+  add $t1,$t1,$s0  
+  li $v0,6          # code for floating point input 
+  syscall
+  s.s $f0,0($t1)    # arr[i]=$f0 
+  addi $t0,$t0,1 
+  j for  
+exit: 
+
+# print array 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       
+  add $t1,$t1,$s0 
+  l.s $f0,0($t1)       # $f0=arr[i] 
+  li $v0,2           # code for printing floating point 
+  mov.s $f12,$f0   
+  syscall 
+  li $a0, 32           
+  li $v0, 11           
+  syscall 
+  addi $t0,$t0,1  
+  j print 
+end

One Dimensional Arrays ​

To calculate the sum of n numbers in an n sized array ​

li $t0,0 
+la $s0,arr 
+li $t3,0        #t3 stores the sum 
+sum:          #for loop 
+  beq $t0,$s1,end     # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)      # $t2=arr[i] 
+  add $t3,$t3,$t2    # $t3=$t3+$t2 
+  addi $t0,$t0,1     # increment loop counter 
+  j sum 
+end:                 
+li $v0,1              # print sum 
+move $a0,$t3                 
+syscall

To find the largest element in an n sized array ​

la $s0,arr 
+li $t0,0 
+li $t3,-1000 # $t3=max 
+  # initialized to -1000   
+max: 
+  beq $t0,$s1,end # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)  # $t2=arr[i] 
+  ble $t2,$t3,inc_i  # if arr[i]<=max, jump to inc_count 
+  move $t3,$t2   # if arr[i]>max, max=arr[i] 
+  inc_count: 
+    addi $t0,$t0,1  # increment loop counter 
+    j max 
+end:  
+li $v0,1                  # print max 
+move $a0,$t3                 
+syscall

String Operations (Advanced) ​

Null Character and Newline ​

When strings are created by using user input (code 8 passed to $vo), it forms a sequence of ASCII characters that are terminated by a newline character, followed by a NULL character. The newline character is triggered by the pressing of enter key during user input.

The ASCII code for newline is 10. Hence beq, $t1,10,label can be used as a comparing instruction

MIPS treats NULL character as a zero. Hence beqz, $t1, label can be used as a comparing instruction

String Traversal ​

Strings are made up of characters, in which each character occupies a byte. Hence, unlike an Integer Array, each character must be traversed byte by byte.

Eg:

To find the length of a string (newline character need not be included)

# assume string is input to str1 
+li $s1,0 #loop counter (i) 
+  
+len: 
+  lb $t1,str1($s1)  # $t1=str[i] 
+  beq $t1,10,start  # termination condition 
+  addi $s1,$s1,1    # i=i+1 
+  j len 
+start: 
+  li $v0,1          # print len=i  
+  move $a0,$s1 
+  syscall

If the newline character needs to be included in the length, beq should be replaced with beqz

String Concatenation ​

Concatenation of two strings can be done using 2 loops. The presence of newline and null character at the end of each string should be considered.

Consider two strings, str1 and str2. The following is the pseudocode and the code snippet for concatenating str2 to str1:
Pseudo Code:

c
i=0
+
+j=0
+
+while str1[i]!='\n'
+
+i++
+
+while str2[j]!='\0'
+
+str1[i]=str2[j]
+
+i++
+
+j++

MIPS:

mips
i $s1,0           # i=0 
+li $s2,0           # j=0 
+loop1: 
+   lb $t1,str1($s1)  
+  beq $t1,10,loop2 
+  addi $s1,$s1,1           # i++ 
+  j loop1 
+loop2: 
+  lb $t1,str2($s2) 
+  beqz $t1,end 
+  sb $t1,str1($s1)    # str1[i]=str[j] 
+  addi $s1,$s1,1      # i++ 
+  addi $s2,$s2,1      # j++ 
+  j loop2 
+end:

Palindrome Checking ​

A palindrome sequence that reads the same backwards as forwards. Palindrome checking uses two pointer method.

Assume a string str, whole length is n. Length of the string is calculated by previous method and stored in $s1. The following code snippet shows the while loop necessary for checking whether the string is palindrome

addi $s1,$s1,-1 # j=n-1  
+li $s0,0        # i=0 
+for: 
+  lb $t1,str($s0)   
+  lb $t2,str($s1)   
+  bge $s0,$s1,true    # if i>=j,exit loop. return True 
+  bne $t1,$t2,false   # if str[i]!=str[j], return False 
+  addi $s0,$s0,1      #  i++ 
+  addi $s1,$s1,-1     #  j-- 
+  j for

Two Dimensional Arrays ​

2-DArrays/Matrices/Tables aren’t stored in memory the way it is normally visualized; rather it is stored as a single array in either row major form or column major form. Let’s see how a matrix is represented in memory in both the forms with a starting address of 1230. (Remember:In an array each element is 4 bytes long).

a) Row Major form : Here elements are stored row wise. First we store the first row, then the second and soon.

b) Column Major form: Here elements are stored column wise. First we store the first column, then the second and soon.

Row Major form ( starting address 1000 )

Column Major form ( starting address 1000 )

Sample code ​

->Insertion of elements and printing the 2D-array

**We are using row major form to input the elements as a string

**NOTE: all characters need to be space separated, the end of the sequence also need to have a space

Pseudo code-> ​

Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D array
+Print the matrix:
+- Loop through rows:
+- Loop through columns:
+- Print each element of the matrix
+- Print a space between elements
+- Print a newline after each row
+Exit the program

MIPS Code-> ​

.data
+newline: .asciiz "\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+mat1: .space 100
+input: .space 100
+
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0         # $t0 = number of rows
+
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+
+  li $v0, 5
+  syscall
+  move $t1, $v0         # $t1 = number of columns
+
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+
+  li $t5, 0
+
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+# when a space is detected add the number calculated to the array and continue
+
+  beq $t4, $zero , end_input
+
+#In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+
+#This loop exist to calculate numbers that have more than one digit , since our input is a string.
+
+# We need to iterate and add the characters until we detect a space
+
+  sub $t6 , $t4, 48 # converts character to integer
+
+# for calculating the number
+  
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  
+  j input_loop
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+print_loop:
+  beq $t6 , $t0 , end_programme
+  li $t7 , 0 # Initialize column index
+
+print_column_loop:
+  lw $t9 , 0($t8) # Load number from array
+  li $v0, 1 # syscall for print_int
+  move $a0, $t9 # Load number to print
+  syscall
+
+  li $v0, 4 # syscall for print_str 
+  la $a0, space # Load address of space
+  syscall
+
+  addi $t7, $t7, 1 # Increment column index
+  addi $t8 , $t8 , 4 # Increment base address
+  blt $t7, $t1 , print_column_loop # Print all elements in the row
+
+# Print newline after each row
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+
+# Reset column index for next row
+  li $t7 , 0
+
+# Increment row index
+  addi $t6 , $t6 , 1
+
+  j print_loop
+  
+end_programme :
+  li $v0, 10 # syscall for exit
+  syscall

Output ​

  Enter number of rows:3
+  Enter number of columns:3
+  Enter matrix(row major form) : 1 2 3 4 5 6 7 8 9
+
+  1 2 3 
+  4 5 6 
+  7 8 9

->To find maximum and minimum element in a 2-D array ​

**We are using row major form to input the elements as a string

**same process of taking the input as the above

**NOTE: all characters need to be space separated, the end of the sequence also need to have a space

Pseudo code-> ​

Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D
+array
+Find minimum and maximum elements in the matrix:
+- Initialize minimum element to maximum possible value
+and maximum element to 0
+- Loop through each element of the matrix:
+- Update minimum and maximum elements if necessary
+Print the maximum element message:
+- Print "The maximum element is: "
+- Print the maximum element
+Print the minimum element message:
+- Print "The minimum element is: "
+- Print the minimum element
+Exit the program

MIPS Code-> ​

.data
+newline: .asciiz "\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+maximum : .asciiz"The maximum element is : "
+minimum : .asciiz"The minimum element is :
+mat1: .space 100
+input: .space 100
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0 # $t0 = number of rows
+  
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+  
+  li $v0, 5
+  syscall 
+  move $t1, $v0 # $t1 = number of columns
+  
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+  
+  li $t5, 0
+  
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+  # when a space is detected add the number calculated to the array and continue
+  
+  beq $t4, $zero , end_input
+  
+  #In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+  
+  #This loop exist to calculate numbers that have more than one digit , since our input is a string
+  # we need to iterate and add the characters until we detect a space
+  
+  sub $t6 , $t4, 48 # converts character to integer
+
+  # for calculating the number
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  j input_loop
+
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+find_min_max:
+  li $t3 , 0 # Initialize max element to 0
+  li $t2 , 0xffffffff
+  li $t6 , 0 # Initialize row index to 0
+  la $a0 , mat1
+
+row_loop:
+  beq $t6, $t0 , end # If all rows have been checked, exit
+  
+  li $t7, 0 # Initialize column index to 0 
+
+column_loop:
+  beq $t7, $t1 , end_column_loop # If all columns have been checked, move to next row
+  
+  lw $t8, 0($a0) # Load current element from array
+
+# Compare current element with max element and the min element
+  bgt $t8, $t3, update_max # if element greater than max element , update max
+  
+  min :
+  blt $t8 , $t2 , update_min # if element smaller than min element, update min
+  
+  increment :
+  addi $a0, $a0, 4 # Move to next column
+  addi $t7, $t7, 1 # Increment column index
+  j column_loop
+
+update_max:
+  move $t3 , $t8 # Update max element
+  j min # control goes back to checking for the conditional statement of min element
+
+update_min:
+  move $t2 , $t8 # Update min element
+  j increment # control goes back to incrementing the looping values
+
+End_column_loop:
+  addi $t6, $t6, 1 # Increment row index
+  j row_loop
+
+end :
+  li $v0 , 4
+  la $a0 , maximum  
+  syscall
+  
+  li $v0 , 1
+  move $a0 , $t3 # printing the maximum element
+  syscall
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+  
+  li $v0 , 4
+  la $a0 , minimum # printing the minimum element
+  syscall
+
+  li $v0 , 1
+  move $a0 , $t2
+  syscall
+  
+  li $v0 , 10
+  syscall

Output ​

  Enter number of rows :3
+  Enter number of columns :3
+  Enter matrix ( row major form ) : 1 2 34 5 6 7 300 9 22
+
+  The maximum element is : 300
+  The minimum element is : 1

More Questions ​

->Searching in Matrix: Write a MIPS assembly program to search for a given element in a matrix and return its position if found.

->Matrix Addition: Write a MIPS program to add two matrices of the same size

->Transpose of a Matrix: Write a MIPS assembly program to find the transpose of a given matrix.

★ MIPS code for if statements ● Iftheconditionisanequalityusebeq,bne ● Iftheconditionisacomparisoncombinebeq/bnewithset-on-less-than

Why not blt or bge? While blt and bge (pseudo-instructions) are available in MIPS, beq and bne are favoured inconditional statements for their efficiency making them the common choice.

Example 1) Given,f:$s0, g:$s1, h:$s2, i:$s3, j:$s4

  if(i==j)
+    f = g + h;
+  else
+    f = g - h;

Solution 1 :- Corresponding MIPS code

  bne $s3, $s4, else
+  add $s0, $s1, $s2
+  j endif
+else: sub $s0, $s1, $s2
+endif: ...........

Example 2) Given,f:$s0 ,g:$s1 ,h:$s2 ,i:$s3 ,j:$s4

  if(i<j)
+    f=g+h;
+  else
+    f=g-h;

Solution 2 :- Corresponding MIPS code

  slt $to, $s3, $s4
+  beq $to, $zero, else
+  add $s0, $s1, $s2
+  j endif
+else:
+  sub $s0, $s1, $s2
+endif: .......

★ MIPS code for Loop statements

Although there are said to be 3 different types of loops in C namely, do/while, while and for loop, they are all functionally identical. In other words, you can take any for-loop and easily turn it into a while-loop.

asm
  int i;
+  for(i= 0 ;i< 10 ;i++){
+    loopbody;
+  }

or

asm
  inti=0;
+  while(i< 10 ){
+    loopbody;
+    i++;
+  }

Example 1) Given, i:$s3, k:$s

asm
  while(i < j)
+    i+=1;

Solution 1 :- Corresponding MIPS code

asm
loop:
+  slt $t0, $s3, $s4
+  beq $t0, $zero, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit: ...

Example 2) Given i:$t0, k is some integer

asm
  int i;
+  for(i = 0; i < k; i++){
+    // loop body
+  }

Solution 2 :- Corresponding MIPS code

asm
  add $t0, $zero, $zero # i is initialized to 0, $t0 = 0
+Loop: // loop body
+  addi $t0, $t0, 1 # i ++
+  slti $t1, $t0, 4 # $t1 = 1 if i < 4
+  bne $t1, $zero, Loop # go to Loop if i < 4

Example 3) Given, i:$s3, base address of arr:$s6, k:$s

asm
  while(arr[i] == k)
+    i+=3;

Solution 3 :- Corresponding MIPS code

asm
loop:
+  sll $t0, $s3, 3
+  add $t1, $t0, $s6
+  lw $t2, 0($t1)
+  bne $t2, $s5, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit:...

★ Procedures in MIPS

Understanding the memory layout and the way procedures are called is crucial for writing efficient and correct MIPS assembly code.

➢ Memory Layout

➢ Stack allocation (refer Recursion in MIPS(non-leaf procedure) for detailed explanation)

(a) before, (b) during, and (c) after a procedure call.

There are two types of procedure calling-

1) Leaf Procedures: These procedures do not call other procedures.

When a leaf procedure is called:

● There turn address is saved on the stack. ● A stack frame/procedure frame/activation record is setup to store local variables. ● Arguments may be passed in registers or on the stack. ● The procedure executes its code.

Upon completion,it restores the stack pointer and returns to the saved return address.

2) Non-leaf Procedures(NestedProcedures): These procedures call other procedures, eg.- Recursive Functions/Procedures.

In addition to the steps for leaf procedures, non-leaf procedures must manage:

● Saving and restoring additional registers beyond there turn address. ● Managing multiple levels of procedure calls and returns. ● Ensuring that data in registers is preserved a cross nested calls. ● Properly handling there turn value from called procedures.

★ Function (Procedure) calling in MIPS

In MIPS assembly language, passing parameters to functions involves using registers. Unlike high-level languages where parameters are often passed on the stack,MIPS typically uses specific registers for passing arguments.

● $a0 to $a3 :These are argument registers and are used to pass the first four arguments to a function. If a function has more than four parameters,additional parameters are typically passed on the stack.

● $v0 and $v1: These are value registers and are used to return values from functions. Functions can return up to two values using these registers.

(Note:-i) Register 1, called $at, is reserved for the assembler.
ii) Registers 26–27, called $k0–$k1 are reserved for the operating system.)

➢ Steps in calling a procedure (function)

In MIPS assembly language, procedure calling follows a similar structure to function calls in high-level languages like C.

The following steps typically occur in both leaf and non-leaf functions but there are some nuances in how they're implemented, especially regarding the handling of the stack:

● Arguments Passing :.Arguments to the function can be passed via registers or the stack, depending on the calling convention. In register-based passing, arguments are loaded in to designated argument registers like $a0-$a3. If there are more arguments than available registers, excess arguments are typically passed on the stack.

● Jump and Link (jal) :jal makes the control jump to the given address while storing there turn address at PC+4 in the $ra register This effectively sets up the return mechanism for the function call.

● Function Prologue (Non-leaf functions): Non-leaf functions need to setup a stack frame. This involves: Saving the return address($ra) on to the stack, saving any callee- saved registers on to the stack(these are typically $s0-$s7),setting up the frame pointer($fp) to establish a reference point for accessing local variables and saved registers.

● Function Execution :The function performs its task, accessing arguments, local variables, and performing computations.

● Function Epilogue (Non-leaf functions): Before returning, non-leaf functions need to cleanup the stack frame and restore the state of callee-saved registers.This involves restoring callee-saved registers from the stack, restoring the return address($ra) from the stack resetting the stack pointer($sp) to deallocate the stack frame, jumping back to the return address using the jr $ra instruction.

● Return: Upon completing its task, the function returns control to the caller. If it's a leaf function, it typically involves jumping back to the return address stored in $ra using the jr $ra instruction. For non-leaf functions, the return sequence includes restoring the stack frame and registers before jumping back to the caller.

(Note:-For simplicity we will only use $sp and extend the stack at procedure entry/exit)

Example 1) Calling a procedure which prints a string

asm
//code
+printFunction();
+a=a+2;
+//code

Solution 1 :- Corresponding MIPS code

asm
data
+hello_string: .asciiz "Hello, world!\n" # String definition
+
+.text
+main:
+....previous code
+jal printFunction #jump to printFunction
+addi $s2, 2
+....further code
+li $v0, 10 # Set syscall code 10 for exit
+syscall # Perform syscall to exit the program
+
+printFunction:
+li $v0, 4 # Set syscall code 4 to print a string
+la $a0, hello_string # Load the address of the string
+syscall # Perform syscall to print
+jr $ra # Return control to PC + 4

● When jal is used, the control moves to the address specified in the instruction and the address of the next instruction is stored in $ra.

● When the procedure ends jr $ra is used to return control back to the next address from where it jumped.

● These procedures are usually placed after the “main” procedure to avoid instruction overlap.

Example 1) Calling a function with parameters

asm
//code
+result=addNumbers(5,7);
+//code

Solution 1 :- Corresponding MIPS code

asm
text
+main:
+  li $a0, 5 # Load first parameter (5) into $a0
+  li $a1, 7 # Load second parameter (7) into $a1
+  jal addNumbers # Jump to addNumbers function
+  move $s0, $v0 # Store the result returned by addNumbers in $s0
+  # Further code
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+addNumbers:
+  add $v0, $a0, $a1 # Add the values of $a0 and $a1 and store the result in $v0
+  jr $ra # Return control to the next instruction after jal

● In the main function, parameters are passed to the addNumbers function by loading values into registers $a0 and $a1.

● The jal instruction is used to jump to the addNumbers function.

● Inside the addNumbers function, the parameters are accessed from the $a0 and $a1 registers.

● The result of the addition is stored in register $v0, which is commonly used to return function results in MIPS.

● Finally, jr $ra is used to return control back to the instruction after the jal in the main function.

★ Recursion in MIPS (non-leaf procedure)

In MIPS assembly language, implementing recursion involves understanding function calls and stack manipulation.

The Stack in MIPS Assembly

● The stack is a crucial data structure used in MIPS assembly language for managing function calls, local variables, and return addresses. ● It operates based on the Last-In-First-Out (LIFO) principle, meaning the last item pushed onto the stack is the first item to be popped off.

Stack Operations:

Stack Pointer ($sp): ● The stack pointer register, $sp, points to the top of the stack. It keeps track of the current position in memory where new items are pushed onto or popped off the stack.

Push Operation: ● To push data onto the stack, the stack pointer is decremented to reserve space for the new item, and then the data is stored at the memory location pointed to by the stack pointer.

Pop Operation: ● To pop data off the stack,the data is retrieved from the memory location pointed to by the stack pointer, and then the stack pointer is incremented to remove the item from the stack.

Stack Usage in Function Calls:Function Prologue: ● When a function is called, the current contents of relevant registers (such as there turn address and callee-saved registers) are typically saved on the stack to ensure they are preserved. ● This process is often referred to as the function prologue.

Function Epilogue: ● Upon completion of the function, the saved values on the stack are restored to their original registers. ● This process is known as the function epilogue.

Example) Function Call and Stack Usage

● When main calls my Function using jal, the return address (the address of the instruction following the function call) is automatically saved in register $ra. ● Inside my Function, the function prologue allocates space on the stack to save the return address. ● The function body executes the desired operations. ● Finally, in the function epilogue, the return address is restored, and the stack space allocated in the prologue is deallocated before returning control to the caller.

To understand recursion in MIPS, a good understanding of the stack pointer and how it operates on memory is imperative. Recursion involves careful management of the function call stack, ensuring that return addresses and local variables are properly saved and restored. This example illustrates the process of calculating the factorial of a number using recursion in MIPS assembly language.

Example) Calculating the factorial of a number using recursion

asm
//code
+result = factorial(5);
+//code

Solution 1 :- Corresponding MIPS code

asm
text
+main:
+  li $a0, 5 # Load the value 5 (number whose factorial is to be calculated) into $a0
+  jal factorial # Jump to the factorial function
+  move $s0, $v0 # Store the result returned by factorial in $s0
+  
+  # Further code using the result stored in $s0
+  # ...
+
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+factorial:
+  # Function prologue
+  addi $sp, $sp, -4 # Allocate space on the stack for local variables
+  sw $ra, 0($sp) # Save the return address on the stack
+  
+  # Check for base case: if n <= 1, return 1
+  li $t0, 1 # Load the value 1 into $t0
+  ble $a0, $t0, base_case # Branch to base_case if $a0 (n) <= $t0 (1)
+
+  # Recursive case: n * factorial(n - 1)
+  addi $a0, $a0, -1 # Decrement $a0 (n) by 1
+  jal factorial # Recursive call to factorial function
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  mul $v0, $a0, $v0 # Multiply n by the result of factorial(n - 1)
+  jr $ra # Return control to the caller
+
+base_case:
+  # Base case: n <= 1, return 1
+  li $v0, 1 # Load the value 1 into $v0
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  jr $ra # Return control to the caller

● In the main function, the value 5 is loaded into register $a0 to calculate its factorial.
● The factorial function is then called using the jal instruction.
● Inside the factorial function, the base case checks if the input value n is less than or equal to 1.If so,it returns 1.
● Otherwise,the function decrements n by 1 and recursively calls itself with the decremented value.
● The result of the recursive call is then multiplied by n to compute the factorial. ● Finally,the result is returned to the caller using register $v0.

References ​

J.L.Hennessy and D.A.Patterson Computer Organization and Design:The Hardware/Software Interface, Fifth Edition
“Digital Logic and Computer Design” by M.Morris Mano “Digital Fundamentals” by Thomas L.Flyod http://www.cs.missouristate.edu/MARS/https://www.d.umn.edu/~gshute/mips/directives-registers.pdfhttps://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.htmlhttps://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.htmlhttps://riptutorial.com/mips/example/29993/mars-mips-simulatorhttps://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf

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zAxxb4uS8zo71Kuh8hPkqUtYlbZxq$(6|??X_y)s@4>%H$S*~_a{3#I_ zMjgNpwJwnIPnXJ}{(5Cvtl`IJ>f&9qQT=^^!Xz5-Aq=oy4CME=J>PTVjx3crXV=DA~%bs}?gX`$aLX+OKK%cs0-NQ!#sHy5#a}Va{uF zI=a{r4@8vA^p~z!u=;~a@?h{6K90}EbokB1R!~(>Cyc_}whOfy{SzXNR>m(c0GD7} zZOg*#G=(d0qDaWVnoa4g5XsO=eUXAHbSL->jcQS`OoOI;E=Xi(fLhKKCzTo{yssM!RvUx zKC_uO$-Qf*_hP&K7(fg95&YOBLvu2kM^-?Nu8=_wv-~WwQ3k`Mj(AB>I)rA9{Fx7| znA7sXlh!iQtvGZO9_NYux9phRTIWw;Q7hyA;ZOf1vHJhG@mwAgPp|SHmTv`ce77~!vDP4zfn;Aw|9l$tJ6e0`cLWGMY@+INTRODUCTION | Hardware Lab NITC - + - - - - - + + + + + - + \ No newline at end of file diff --git a/docs/.vitepress/dist/Verilog/SingleCycle.html b/docs/.vitepress/dist/Verilog/SingleCycle.html index e93e69f..9b5a809 100644 --- a/docs/.vitepress/dist/Verilog/SingleCycle.html +++ b/docs/.vitepress/dist/Verilog/SingleCycle.html @@ -6,19 +6,19 @@ Single Cycle Processor | Hardware Lab NITC - + - - - - - + + + + + -
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Single Cycle Processor ​

Table of Contents ​

Sl No.TopicPage No.
1Overview1
2Prerequisites2
3Theory- Control Unit3
4Theory- Datapath8
5Implementation22
1Top Level Module22
2Data Memory24
3Instruction Memory25
4Microprocessor Top Level (MIPS)27
5Controller29
6Main Decoder31
7ALU Decoder33
8Datapath35
9Register File38
10Other Functional Units41
6How to Run Instructions?44
7Test Cases for Various Instructions46
8References53

1. Overview ​

Till now you have learned to design sequential and combinational logic, in this section you will learn how to create a single cycle processor, specifically the MIPS microprocessor.

This section combines almost every concept covered so far. Abstraction of block diagrams and Verilog HDLis used to describe the arrangement of each component. We exploit regularity and modularity by reusing already created blocks such as ALUs, multiplexers and register files. The microarchitecture is partitioned into datapath and control units. The MIPS microprocessor datapath uses the register file, ALU, memory unit, and instruction decoder to execute instructions. The register file stores data and instructions, the ALU performs operations, the memory unit accesses and stores data, and the instruction decoder controls data flow. The control unit of a MIPS microprocessor generates control signals that direct the flow of data between components in the datapath, ensuring that instructions are executed correctly. It receives instructions from the decoder, directs data flow to the correct components, and controls instruction timing.
Together, the datapath and control units work to execute instructions in the MIPS microprocessor.
We will focus on the single-cycle implementation of a subset of MIPS instructions. Additionally, we will compare single-cycle, multicycle, and pipelined microarchitectures for the MIPS processor.

2. Prerequisites ​

To create a Verilog MIPS single cycle processor, you should have a strong understanding of digital logic design, computer architecture, and Verilog programming.

Some of the specific prerequisites include-

  • Knowledge of digital logic design concepts, such as combinational and sequential circuits, logic gates, flip-flops, and registers and implementing these in Verilog HDL.

  • Understanding of computer architecture principles, including datapath and control unit design, memory organisation, instruction decoding, and input/output interfaces. These are also covered once more in the “Theory” section of our module.

  • Experience with Verilog programming, including the ability to write and understand Verilog code, testbenches, and simulation results.

  • Ability to use simulation and synthesis tools, such as ModelSim, Quartus, to simulate and synthesise Verilog code.

  • Knowledge of computer organisation and assembly language programming is also beneficial, as it provides context for understanding the MIPS single cycle processor and its operation.

Additionally, it would be helpful if you were familiar with the MIPS instruction set architecture, including its various instruction formats, opcode values, and functionality.

3. Control Unit ​

This section covers an implementation of our MIPS subset, which is created by adding a basic control function to the datapath discussed in the previous section. Support for load word (lw), store word (sw), branch equal (beq), and arithmetic-logical instructions like add, sub, AND, OR, and set on less than are all included in this version. It is implemented in 2 parts: the main control Unit and ALU Control Unit. Firstly we look at the instruction format.

CU

Instruction Format ​

The 32 bit MIPS instruction can be broken down into the following parts

fig 2

The op field, called the opcode, is always contained in bits 31:26. We will refer to this field as Op[5:0] by standard notation.

  • The two registers to be read are always specified by the rs and rt fields, at positions 25:21 and 20:16. This is true for the R-type instructions, branch equal, and store.

  • The base register for load and store instructions is always in bit positions 25:21 (rs).

  • The 16-bit offset for branch equal, load, and store is always in positions 15:0.

  • The destination register is in one of two places. For a load, it is in bit positions 20:16 (rt), while for an R-type instruction it is in bit positions 15:11 (rd). Thus, we will need to add a multiplexor to select which field of the instruction is used to indicate the register number to be written.

Main Control Unit (Main Decoder) ​

The control unit computes the control ignals based on the opcode and funct fields of the instruction, [31:26] and [5:0].

Most of the control information comes from the opcode, but R-type instructions also use the funct field to determine the ALU operation. The majority of the outputs from the opcode are computed by the main decoder. The 6 bits of the opcode are decoded into various control signals of the Main Decoder as shown in Fig. 3.

Simple PLA Implementation

Fig 3. Simple PLA Implementation

Table 1 explains each of the control signals in detail with all the important information. These nine control (two from ALUOp which are explained later) signals are set on the basis of six input signals to the control unit, which are the opcode bits 31 to 26.

Control SignalsDeassertedAsserted
RegDstThe write register number comes from the rt field (20:16)The write register number comes from the rd field (15:11)
RegWrite-The register on the write register input is written with the value of the Write data input.
ALUSrcSecond ALU Operand is the second register file output.Second ALU Operand is the sign extended offset (16 bit to 32 bits)
PCSrcPC = PC + 4 (For sequential exec.)PC is replaced by branch target.
MemRead-Data memory contents designated by address input are put in Read Data Output.
MemWrite-Data memory contents designated by address input are put in Write Data Output.
MemtoRegWrite Data is fed input from ALU.Write Data is fed input from Data Memory.

Table 1. Different Control Signals for the different MUXs

With the exception of the PCSrc control line, the control unit can set all of the control signals based only on the opcode field of the instruction. If the instruction is branch on equal and the ALU's Zero output is asserted, then the PCSrc control line should also be asserted. We must AND the Zero signal from the ALU with the Branch signal from the control unit in order to produce the PCSrc signal.

ALU Control Unit (ALU Decoder) ​

Depending on the instruction class, the ALU will need to perform one of these functions.

Table 2. ALU Control Lines

The main decoder determines a 2-bit ALUOp signal which is used as input for ALU Decoder along with the 6-bit funct (or function) field in the low-order bits of the instruction. The 4 bit output signal of the ALU Control Unit represents the operation to be carried out by the ALU. Fig 4. ALU Hardware Implementation

The 2 bit ALUOp sent by the Control Unit indicates whether the operation to be performed should be add (00) for loads and stores, subtract (01) for beq, or determined by the operation encoded in the funct field (10).

Understanding the optimal implementation: ​

Using multiple levels of control can reduce the size of the main control unit. Using several smaller control units may also potentially increase the speed of the control unit. Such optimizations are important, since the speed of the control unit is often critical to clock cycle time

ALU Control Truth Table ​

Input-Output Truth Table ​

4. Datapath ​

A datapath is the part of a computer processor that performs arithmetic and logic operations on data. It is a digital circuit that consists of registers, an arithmetic logic unit (ALU), and multiplexers.

The datapath receives instructions and data from the processor's memory and performs the necessary operations specified by the instructions. The ALU performs arithmetic and logical operations on the data, and the registers store intermediate and final results.

The datapath also includes multiplexers that allow the selection of different input values based on control signals. The control signals are generated by the control unit, which coordinates the operations of the datapath to execute instructions.

The datapath operates on words of data. MIPS is a 32-bit architecture, so we will use a 32-bit datapath. The datapath first decodes the instruction for the control unit which then sets the different multiplexers thereby fixing the datapath. We will split the datapath into different state elements and try to learn them one by one and finally piece them together to create a complete datapath.

State elements ​

There are 5 main state elements required for building the datapath.

a Instruction Memory ​

The program counter contains the address of the instruction to be executed. The first step is to read this instruction from the element called instruction memory. The instruction memory takes the address in PC as the input and fetches the 32 bit instruction, labelled instr.

The processor’s actions depend on the specific instruction that was fetched.

b Register File ​

The register file contains all the available registers. It has two read ports and one write port. Since MIPS architecture contains 32 registers, each register is identified by a unique 5 bit number (log2 32). This unique 5 bit number is given as the input in both read and write ports. The contents of the registers specified via the read ports are given as the output. If the control signal RegWrite is set, the data given in the data port is written into the register given in the write port.

c) ALU ​

ALU performs different arithmetic operations on the data depending on the signal received from the control unit. It has two data input ports and an input from the control unit which specifies the operation to be performed. The final result is output through ALU result and zero port is set to 1 if the result is zero.

d Data Memory ​

The memory unit is a state element with inputs for the address and the write data, and a single output for the read result.There are separate read and write controls, called MemRead and MemWrite. Only one of these may be asserted at a time.

  • If MemRead is set then value at the address given is fetched and outputted through the read data port.
  • If MemWrite is set then the value at the address is changed to write data.

e) Sign extension ​

To understand what sign extension is, let’s take an example. Consider the 4 bit number 1100. If we were to sign extend it to an 8 bit number, we take the MSB which in this case is 1 and extend it to make the upper half of the 8 bit number keeping the lower same as the initial 4 bits which gives us 1111 1100. Similarly, this element sign extends a 16 bit number into a 32 bit number.

Now that we have seen the different state elements involved in a datapath, let's see the datapath followed by different MIPS instructions. Since we are considering MIPS microprocessor, each instruction is 32 bits long.

  • add It is an R-type instruction of the form add $rd,$rs,$rt The R-type instruction format is

The datapath for add instruction is as follows :

  1. Grab the instruction address from the PC.

PC

  1. Decode instruction.

Decoder

  1. Pass rs,rt and rd into read register and write register ports.

Register

  1. Retrieve data from read register 1 and register 2 (rs and rt).

  1. Pass contents of rs and rt into the ALU as operands for the addition operation. The only difference between different arithmetic operations is in the ALU operation performed.

  1. Return back the ALU result to the register file as the Write data argument. The data will be written into the Write register specified by the rd field.

  1. Increment the value of PC to PC+4 to move on to the next instruction.

  • lw(load word)
    The lw instruction is of the form lw $rt immediate($rs). It has an I-type instruction format.

lw

The load word instruction copies the data stored at the address ‘immediate+value(rs)’ and stores it into the register rt.
The datapath for lw instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. The control unit examines the most significant five bits of the instruction to determine the necessary datapath configuration.

  3. The register file receives the two register numbers rs and rt, with rs connected to the read port and rt to the write port. Read data 1 port outputs the data stored in rs.

  4. This output is then added to the sign-extended immediate using ALU.

  5. The ALU result is sent to the data memory unit, which reads the data stored at the address specified by the ALU result.

  6. Finally, the data read from the memory is returned to the register file, which writes it into register rt.

  7. PC is incremented to PC+4.

lw

  • sw(store word) sw instruction is of the form

    v
    sw $rt immediate($rs)

    The instruction format is again of the form I-type with an opcode 43.

The store word instruction writes the data stored in the register rt into the memory address ‘value(rs)+immediate ’.

The datapath for sw instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five bits and determines the necessary datapath configuration by setting the multiplexers.

  3. The register file receives two register numbers rs and rt, with rs connected to read port1 and rt connected to read port2. The data stored in registers rs and rt is output through the read data port1 and read data port2 respectively.

  4. The read data1 is then added to the sign-extended immediate using ALU.

  5. The ALU result along with read data2 (which contains the value stored in register rt) is sent to the data memory unit, which writes the read data2 into the address specified by the ALU result.

  6. PC is incremented to PC+4.

sw

  • beq(branch if equal)

The beq instruction is of the form

mips
    beq $rs ,$rt ,immediate

It has an I-type instruction format.

I-type

It compares the contents of rs and rt to check if they are equal and uses the 16-bit immediate field to compute the target address of the branch relative to the current address.

The datapath for beq instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five its and determines the necessary datapath configuration.

  3. The register file receives two register numbers rs and rt in the read register port and outputs the contents in rs and rt.

  4. ALU subtracts the value of rs from rt and sets the zero port to 1 if the result is 0.

  5. The immediate value is sign extended and then shifted left by 2 bits.

  6. PC is incremented to PC+4 and is added with the immediate value to give the branch target.

  7. PC is changed to the branch target if zero port was set to 1.

beq

  • j (jump)

The jump instruction is of the form j targaddr. It has a J-type instruction format with opcode 2.

This instruction uses the 26 bit targaddr to compute jump address and updates the value of PC to jump address.

J-type

The datapath for j instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five bits and determines the necessary datapath configuration.

  3. The 26 bit targaddr is shifted left by 2 bits to create a 28 bit result

  4. Concatenate the result with the upper 4 bits of PC+4 to get the jump address.

  5. Finally, the PC gets updated to the jump address.

j

The Final Datapath ​

Final

Fig 4. Simple datapath with control unit (for R-type and I-type)

Here, the input to the control unit is the 6-bit opcode field from the instruction. The outputs are the control signals which serve various purposes :-

  • RegDst, ALUSrc, MemtoReg - 1-bit signals that control the multiplexors.

  • RegWrite, MemRead, MemWrite - Signals that control reads and writes in the data memory and register file.

  • Branch - Signal used in checking if a branch is required.

  • ALUOp - 2-bit control signal for the ALU.

Note that here, the AND gate is used to combine the Branch control signal with the Zero output from the ALU. This is responsible for the selection of the next PC.

Role of Multiplexors ​

As seen above, there are 4 multiplexors required at various stages of the datapath. They are needed in order to implement both R-type and I-type instructions using the same datapath. Their roles are explained below :-

  1. MUX 1 - This MUX determines which register needs to be written into using the RegDst control signal. If it’s 0, the write register number comes from the rt field (in the case of I-type), whereas if it’s 1, the write register number comes from the rd field (for R-type instructions)

  2. MUX 2 - This MUX is placed at the ALU input with ALUSrc as the select line. When it’s 0, an arithmetic-logical instruction is taking place, and the second ALU operand is the data read from the second register. When it’s 1, a memory instruction is taking place, with the second ALU operand being the sign-extended 16-bit immediate field from instruction.

  3. MUX 3 - It chooses which value is stored in the destination register using the MemtoReg control signal. This value comes from the ALU (for an R-type instruction) or the memory (for a load).

  4. MUX 4 - The final MUX is used to select if the PC moves onto the sequentially following instruction address (PC + 4) or branches to a target address. The control signal that achieves this is the output of the AND gate which is 1 in case of a branch instruction and 0 otherwise.

Final

Fig 4. Datapath with Jump implementation

Additionally to implement the Jump instruction in the same datapath, an additional MUX, controlled by the jump control signal, is used to determine whether to move to the jump target address or the next consequent instruction. This jump target is obtained by shifting the lower 26 bits of the jump instruction left 2 bits (ie. multiplying by 4) and then concatenating the upper 4 bits of PC + 4 as the high-order bits, thus yielding a 32-bit address.

5. Implementation ​

1. Top level module ​

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module top (input clk, reset, 
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Single Cycle Processor ​
Table of Contents ​
Sl No.TopicPage No.
1Overview1
2Prerequisites2
3Theory- Control Unit3
4Theory- Datapath8
5Implementation22
1Top Level Module22
2Data Memory24
3Instruction Memory25
4Microprocessor Top Level (MIPS)27
5Controller29
6Main Decoder31
7ALU Decoder33
8Datapath35
9Register File38
10Other Functional Units41
6How to Run Instructions?44
7Test Cases for Various Instructions46
8References53
1. Overview ​
Till now you have learned to design sequential and combinational logic, in this section you will learn how to create a single cycle processor, specifically the MIPS microprocessor.
This section combines almost every concept covered so far. Abstraction of block diagrams and Verilog HDLis used to describe the arrangement of each component. We exploit regularity and modularity by reusing already created blocks such as ALUs, multiplexers and register files. The microarchitecture is partitioned into datapath and control units. The MIPS microprocessor datapath uses the register file, ALU, memory unit, and instruction decoder to execute instructions. The register file stores data and instructions, the ALU performs operations, the memory unit accesses and stores data, and the instruction decoder controls data flow. The control unit of a MIPS microprocessor generates control signals that direct the flow of data between components in the datapath, ensuring that instructions are executed correctly. It receives instructions from the decoder, directs data flow to the correct components, and controls instruction timing.
 Together, the datapath and control units work to execute instructions in the MIPS microprocessor.
 We will focus on the single-cycle implementation of a subset of MIPS instructions. Additionally, we will compare single-cycle, multicycle, and pipelined microarchitectures for the MIPS processor.
2. Prerequisites ​
To create a Verilog MIPS single cycle processor, you should have a strong understanding of digital logic design, computer architecture, and Verilog programming.
Some of the specific prerequisites include-
  • Knowledge of digital logic design concepts, such as combinational and sequential circuits, logic gates, flip-flops, and registers and implementing these in Verilog HDL.
  • Understanding of computer architecture principles, including datapath and control unit design, memory organisation, instruction decoding, and input/output interfaces. These are also covered once more in the “Theory” section of our module.
  • Experience with Verilog programming, including the ability to write and understand Verilog code, testbenches, and simulation results.
  • Ability to use simulation and synthesis tools, such as ModelSim, Quartus, to simulate and synthesise Verilog code.
  • Knowledge of computer organisation and assembly language programming is also beneficial, as it provides context for understanding the MIPS single cycle processor and its operation.
Additionally, it would be helpful if you were familiar with the MIPS instruction set architecture, including its various instruction formats, opcode values, and functionality.
3. Control Unit ​
This section covers an implementation of our MIPS subset, which is created by adding a basic control function to the datapath discussed in the previous section. Support for load word (lw), store word (sw), branch equal (beq), and arithmetic-logical instructions like add, sub, AND, OR, and set on less than are all included in this version. It is implemented in 2 parts: the main control Unit and ALU Control Unit. Firstly we look at the instruction format.
CU
Instruction Format ​
The 32 bit MIPS instruction can be broken down into the following parts
fig 2
The op field, called the opcode, is always contained in bits 31:26. We will refer to this field as Op[5:0] by standard notation.
  • The two registers to be read are always specified by the rs and rt fields, at positions 25:21 and 20:16. This is true for the R-type instructions, branch equal, and store.
  • The base register for load and store instructions is always in bit positions 25:21 (rs).
  • The 16-bit offset for branch equal, load, and store is always in positions 15:0.
  • The destination register is in one of two places. For a load, it is in bit positions 20:16 (rt), while for an R-type instruction it is in bit positions 15:11 (rd). Thus, we will need to add a multiplexor to select which field of the instruction is used to indicate the register number to be written.
Main Control Unit (Main Decoder) ​
The control unit computes the control ignals based on the opcode and funct fields of the instruction, [31:26] and [5:0].
Most of the control information comes from the opcode, but R-type instructions also use the funct field to determine the ALU operation. The majority of the outputs from the opcode are computed by the main decoder. The 6 bits of the opcode are decoded into various control signals of the Main Decoder as shown in Fig. 3.
Simple PLA Implementation 
Fig 3. Simple PLA Implementation
Table 1 explains each of the control signals in detail with all the important information. These nine control (two from ALUOp which are explained later) signals are set on the basis of six input signals to the control unit, which are the opcode bits 31 to 26.
Control SignalsDeassertedAsserted
RegDstThe write register number comes from the rt field (20:16)The write register number comes from the rd field (15:11)
RegWrite-The register on the write register input is written with the value of the Write data input.
ALUSrcSecond ALU Operand is the second register file output.Second ALU Operand is the sign extended offset (16 bit to 32 bits)
PCSrcPC = PC + 4 (For sequential exec.)PC is replaced by branch target.
MemRead-Data memory contents designated by address input are put in Read Data Output.
MemWrite-Data memory contents designated by address input are put in Write Data Output.
MemtoRegWrite Data is fed input from ALU.Write Data is fed input from Data Memory.
Table 1. Different Control Signals for the different MUXs
With the exception of the PCSrc control line, the control unit can set all of the control signals based only on the opcode field of the instruction. If the instruction is branch on equal and the ALU's Zero output is asserted, then the PCSrc control line should also be asserted. We must AND the Zero signal from the ALU with the Branch signal from the control unit in order to produce the PCSrc signal.
ALU Control Unit (ALU Decoder) ​
Depending on the instruction class, the ALU will need to perform one of these functions.
 Table 2. ALU Control Lines
The main decoder determines a 2-bit ALUOp signal which is used as input for ALU Decoder along with the 6-bit funct (or function) field in the low-order bits of the instruction. The 4 bit output signal of the ALU Control Unit represents the operation to be carried out by the ALU.  Fig 4. ALU Hardware Implementation
The 2 bit ALUOp sent by the Control Unit indicates whether the operation to be performed should be add (00) for loads and stores, subtract (01) for beq, or determined by the operation encoded in the funct field (10).
Understanding the optimal implementation: ​
Using multiple levels of control can reduce the size of the main control unit. Using several smaller control units may also potentially increase the speed of the control unit. Such optimizations are important, since the speed of the control unit is often critical to clock cycle time
ALU Control Truth Table ​
Input-Output Truth Table ​
4. Datapath ​
A datapath is the part of a computer processor that performs arithmetic and logic operations on data. It is a digital circuit that consists of registers, an arithmetic logic unit (ALU), and multiplexers.
The datapath receives instructions and data from the processor's memory and performs the necessary operations specified by the instructions. The ALU performs arithmetic and logical operations on the data, and the registers store intermediate and final results.
The datapath also includes multiplexers that allow the selection of different input values based on control signals. The control signals are generated by the control unit, which coordinates the operations of the datapath to execute instructions.
The datapath operates on words of data. MIPS  is a 32-bit architecture, so we will use a 32-bit datapath. The datapath first decodes the instruction for the control unit which then sets the different multiplexers thereby fixing the datapath. We will split the datapath into different state elements and try to learn them one by one and finally piece them together to create a complete datapath.
State elements ​
There are 5 main state elements required for building the datapath.
a Instruction Memory ​
The program counter contains the address of the instruction to be executed. The first step is to read this instruction from the element called instruction memory. The instruction memory takes the address in PC as the input and fetches the 32 bit instruction, labelled instr.
The processor’s actions depend on the specific instruction that was fetched.
b Register File ​
The register file contains all the available registers. It has two read ports and one write port. Since MIPS architecture contains 32 registers, each register is identified by a unique 5 bit number (log2 32). This unique 5 bit number is given as the input in both read and write ports. The contents of the registers specified via the read ports are given as the output. If the control signal RegWrite is set, the data given in the data port is written into the register given in the write port.
c) ALU ​
ALU performs different arithmetic operations on the data depending on the signal received from the control unit. It has two data input ports and an input from the control unit which specifies the operation to be performed. The final result is output through ALU result and zero port is set to 1 if the result is zero.
d Data Memory ​
The memory unit is a state element with inputs for the address and the write data, and a single output for the read result.There are separate read and write controls, called MemRead and MemWrite. Only one of these may be asserted at a time.
  • If MemRead is set then value at the address given is fetched and outputted through the read data port.
  • If MemWrite is set then the value at the address is changed to write data.
e) Sign extension ​
To understand what sign extension is, let’s take an example. Consider the 4 bit number 1100. If we were to sign extend it to an 8 bit number, we take the MSB which in this case is 1 and extend it to make the upper half of the 8 bit number keeping the lower same as the initial 4 bits which gives us 1111 1100. Similarly, this element sign extends a 16 bit number into a 32 bit number.
Now that we have seen the different state elements involved in a datapath, let's see the datapath followed by different MIPS instructions. Since we are considering MIPS microprocessor, each instruction is 32 bits long.
  • add It is an R-type instruction of the form add $rd,$rs,$rt The R-type instruction format is
The datapath for add instruction is as follows :
  1. Grab the instruction address from the PC.
PC
  1. Decode instruction.
Decoder
  1. Pass rs,rt and rd into read register and write register ports.
Register
  1. Retrieve data from read register 1 and register 2 (rs and rt).
  1. Pass contents of rs and rt into the ALU as operands for the addition operation. The only difference between different arithmetic operations is in the ALU operation performed.
  1. Return back the ALU result to the register file as the Write data argument. The data will be written into the Write register specified by the rd field.
  1. Increment the value of PC to PC+4 to move on to the next instruction.
  • lw(load word)
     The lw instruction is of the form lw $rt immediate($rs). It has an I-type instruction format.
lw
The load word instruction copies the data stored at the address ‘immediate+value(rs)’ and stores it into the register rt.
 The datapath for lw instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. The control unit examines the most significant five bits of the instruction to determine the necessary datapath configuration.
  3. The register file receives the two register numbers rs and rt, with rs connected to the read port and rt to the write port. Read data 1 port outputs the data stored in rs.
  4. This output is then added to the sign-extended immediate using ALU.
  5. The ALU result is sent to the data memory unit, which reads the data stored at the address specified by the ALU result.
  6. Finally, the data read from the memory is returned to the register file, which writes it into register rt.
  7. PC is incremented to PC+4.
lw
  •  sw(store word) sw instruction is of the form
    v
    sw $rt immediate($rs)
    The instruction format is again of the form I-type with an opcode 43.
The store word instruction writes the data stored in the register rt into the memory address ‘value(rs)+immediate ’.
The datapath for sw instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five bits and determines the necessary datapath configuration by setting the multiplexers.
  3. The register file receives two register numbers rs and rt, with rs connected to read port1 and rt connected to read port2. The data stored in registers rs and rt is output through the read data port1 and read data port2 respectively.
  4. The read data1 is then added to the sign-extended immediate using ALU.
  5. The ALU result along with read data2 (which contains the value stored in register rt) is sent to the data memory unit, which writes the read data2 into the address specified by the ALU result.
  6. PC is incremented to PC+4.
sw
  • beq(branch if equal)
The beq instruction is of the form
mips
    beq $rs ,$rt ,immediate
It has an I-type instruction format.
I-type
It compares the contents of rs and rt to check if they are equal and uses the 16-bit immediate field to compute the target address of the branch relative to the current address.
The datapath for beq instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five its and determines the necessary datapath configuration.
  3. The register file receives two register numbers rs and rt in the read register port and outputs the contents in rs and rt.
  4. ALU subtracts the value of rs from rt and sets the zero port to 1 if the result is 0.
  5. The immediate value is sign extended and then shifted left by 2 bits.
  6. PC is incremented to PC+4 and is added with the immediate value to give the branch target.
  7. PC is changed to the branch target if zero port was set to 1.
beq
  • j (jump)
The jump instruction is of the form j targaddr. It has a J-type instruction format with opcode 2.
This instruction uses the 26 bit targaddr to compute jump address and updates the value of PC to jump address.
J-type
The datapath for j instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five bits and determines the necessary datapath configuration.
  3. The 26 bit targaddr is shifted left by 2 bits to create a 28 bit result
  4. Concatenate the result with the upper 4 bits of PC+4 to get the jump address.
  5. Finally, the PC gets updated to the jump address.
j
The Final Datapath ​
Final
Fig 4. Simple datapath with control unit (for R-type and I-type)
Here, the input to the control unit is the 6-bit opcode field from the instruction. The outputs are the control signals which serve various purposes :-
  • RegDst, ALUSrc, MemtoReg - 1-bit signals that control the multiplexors.
  • RegWrite, MemRead, MemWrite - Signals that control reads and writes in the data memory and register file.
  • Branch - Signal used in checking if a branch is required.
  • ALUOp - 2-bit control signal for the ALU.
Note that here, the AND gate is used to combine the Branch control signal with the Zero output from the ALU. This is responsible for the selection of the next PC.
Role of Multiplexors ​
As seen above, there are 4 multiplexors required at various stages of the datapath. They are needed in order to implement both R-type and I-type instructions using the same datapath. Their roles are explained below :-
  1. MUX 1 - This MUX determines which register needs to be written into using the RegDst control signal. If it’s 0, the write register number comes from the rt field (in the case of I-type), whereas if it’s 1, the write register number comes from the rd field (for R-type instructions)
  2. MUX 2 - This MUX is placed at the ALU input with ALUSrc as the select line. When it’s 0, an arithmetic-logical instruction is taking place, and the second ALU operand is the data read from the second register. When it’s 1, a memory instruction is taking place, with the second ALU operand being the sign-extended 16-bit immediate field from instruction.
  3. MUX 3 - It chooses which value is stored in the destination register using the MemtoReg control signal. This value comes from the ALU (for an R-type instruction) or the memory (for a load).
  4. MUX 4 - The final MUX is used to select if the PC moves onto the sequentially following instruction address (PC + 4) or branches to a target address. The control signal that achieves this is the output of the AND gate which is 1 in case of a branch instruction and 0 otherwise.
Final
Fig 4. Datapath with Jump implementation
Additionally to implement the Jump instruction in the same datapath, an additional MUX, controlled by the jump control signal, is used to determine whether to move to the jump target address or the next consequent instruction. This jump target is obtained by shifting the lower 26 bits of the jump instruction left 2 bits (ie. multiplying by 4) and then concatenating the upper 4 bits of PC + 4 as the high-order bits, thus yielding a 32-bit address.
5. Implementation ​
1. Top level module ​
Top
v
module top (input clk, reset, 
     output [31:0] writedata, dataadr, 
     output memwrite); 
     wire [31:0] pc, instr, readdata; 
@@ -27,7 +27,7 @@
     mips mips (clk, reset, pc, instr, memwrite, dataadr, writedata, readdata); 
     imem imem (pc[7:2], instr); 
     dmem dmem (clk, memwrite, dataadr, writedata,readdata); 
-endmodule
The top level module instantiates 3 sub modules mips , imem and dmem The mips module is the main processor that is responsible for executing instructions. The imem module is the instruction memory, which contains the program instructions. The dmem module is the data memory, which is used for load/store instructions. Here is a brief description of the input and output ports of the top module:
Inputs ​
  1. clk - the clock signal used to synchronise the processor.
  2. reset - the reset signal used to initialise the processor.
Outputs ​
  1. writedata - the data to be written to memory.
  2. dataadr - the memory address to access.
  3. memwrite - the control signal for writing to memory.
  4. pc - the program counter, which contains the memory address of the current instruction.
  5. instr - the current instruction being executed.
  6. readdata - the data read from memory.
Overall, the top module provides the infrastructure to execute programs on the MIPS processor. It loads the program instructions from memory, executes them, and stores the results back into memory if necessary.
Top
RTL view of top level module
2. Data Memory ​
v
module dmem (input clk, we, 
+endmodule
The top level module instantiates 3 sub modules mips , imem and dmem The mips module is the main processor that is responsible for executing instructions. The imem module is the instruction memory, which contains the program instructions. The dmem module is the data memory, which is used for load/store instructions. Here is a brief description of the input and output ports of the top module:
Inputs ​
  1. clk - the clock signal used to synchronise the processor.
  2. reset - the reset signal used to initialise the processor.
Outputs ​
  1. writedata - the data to be written to memory.
  2. dataadr - the memory address to access.
  3. memwrite - the control signal for writing to memory.
  4. pc - the program counter, which contains the memory address of the current instruction.
  5. instr - the current instruction being executed.
  6. readdata - the data read from memory.
Overall, the top module provides the infrastructure to execute programs on the MIPS processor. It loads the program instructions from memory, executes them, and stores the results back into memory if necessary.
Top
RTL view of top level module
2. Data Memory ​
v
module dmem (input clk, we, 
             input [31:0] a, wd, 
             output [31:0] rd); 
 
@@ -36,7 +36,7 @@
     always @ (posedge clk) 
         if (we) 
             RAM[a[31:2]] wd; 
-endmodule
dmem represents a random access memory (RAM) block that can store and retrieve 32-bit data values.
Inputs- ​
  1. clk
  2. MemWrite we - control signal that determines whether to write data to memory.
  3. 32 bit memory address a
  4. 32 bit WriteData ‘wd’- data to be written to the location specified by a.
Output- ​
  1. 32 bit ReadData rd - data read from memory location a. The dmem module contains a RAM that stores 64 words each of size 32 bits. When the we input is set to 1, the 32 bit data wd gets written into the memory location a at the positive edge of clk .
dmem
3. Instruction Memory ​
v
module imem (input [5:0] a,output [31:0] rd); 
+endmodule
dmem represents a random access memory (RAM) block that can store and retrieve 32-bit data values.
Inputs- ​
  1. clk
  2. MemWrite we - control signal that determines whether to write data to memory.
  3. 32 bit memory address a
  4. 32 bit WriteData ‘wd’- data to be written to the location specified by a.
Output- ​
  1. 32 bit ReadData rd - data read from memory location a. The dmem module contains a RAM that stores 64 words each of size 32 bits. When the we input is set to 1, the 32 bit data wd gets written into the memory location a at the positive edge of clk .
dmem
3. Instruction Memory ​
v
module imem (input [5:0] a,output [31:0] rd); 
     reg [31:0] RAM[63:0]; 
     integer i; 
     initial 
@@ -44,7 +44,7 @@
             $readmemh ("E:\memfile.dat",RAM); 
         end 
     assign rd = RAM[a]; // word aligned 
-endmodule
Input :
  1. 6 bit address a : This is generated by the mips module.
Output :
  1. 32 bit instruction rd :
     The instructions are stored initially in a file called memfile.dat. This file gets loaded into the RAM array using the $readmemh system task. The $readmemh system task reads a memory file in HEX format and initialises the memory array with these values.
The syntax is :
v
$readmemh("hex_memory_file.mem", memory_array,[start_address],[end_address]) (The start and end address arguments are optional)
The imem module is a combinational logic block which is driven by the RAM array.
The input address a is used to index into the RAM array to retrieve the instruction located at that address.
The instruction is then assigned to rd .
imem
RTL view of Instruction Memory
4.MIPS ​
v
module mips(input clk, reset, 
+endmodule
Input :
  1. 6 bit address a : This is generated by the mips module.
Output :
  1. 32 bit instruction rd :
     The instructions are stored initially in a file called memfile.dat. This file gets loaded into the RAM array using the $readmemh system task. The $readmemh system task reads a memory file in HEX format and initialises the memory array with these values.
The syntax is :
v
$readmemh("hex_memory_file.mem", memory_array,[start_address],[end_address]) (The start and end address arguments are optional)
The imem module is a combinational logic block which is driven by the RAM array.
The input address a is used to index into the RAM array to retrieve the instruction located at that address.
The instruction is then assigned to rd .
imem
RTL view of Instruction Memory
4.MIPS ​
v
module mips(input clk, reset, 
             output [31:0] pc, 
             input [31:0] instr, 
             output memwrite, 
@@ -60,7 +60,7 @@
 
    datapath dp(clk, reset, memtoreg, pcsrc,alusrc, regdst, regwrite, jump,alucontrol,zero, pc, instr,aluout, writedata, readdata); 
 
-endmodule
Inputs :
  1. clk
  2. reset
  3. instr - current instruction being executed.
  4. 32 bit readdata - data read from the memory.
Outputs :
  1. 32 bit pc - current program counter.
  2. 32 bit aluout - result of ALU operation(i applicable).
  3. 32 bit writedata
  4. memwrite - control signal (discussed earlier).
The mips module instantiates two other modules, controller and datapath , which work together to execute instructions. Both these modules are discussed in detail in the upcoming sections.
Overall the mips module acts like a traffic signal, directing the flow of data and control signals between the datapath and controller modules to execute instructions and maintain the processor’s state.
mips
RTL view of MIPS module
5. Controller ​
v
module controller (input [5:0] op, funct, 
+endmodule
Inputs :
  1. clk
  2. reset
  3. instr - current instruction being executed.
  4. 32 bit readdata - data read from the memory.
Outputs :
  1. 32 bit pc - current program counter.
  2. 32 bit aluout - result of ALU operation(i applicable).
  3. 32 bit writedata
  4. memwrite - control signal (discussed earlier).
The mips module instantiates two other modules, controller and datapath , which work together to execute instructions. Both these modules are discussed in detail in the upcoming sections.
Overall the mips module acts like a traffic signal, directing the flow of data and control signals between the datapath and controller modules to execute instructions and maintain the processor’s state.
mips
RTL view of MIPS module
5. Controller ​
v
module controller (input [5:0] op, funct, 
                 input zero, 
                    output memtoreg, memwrite, 
              output pcsrc, alusrc, 
@@ -75,7 +75,7 @@
      aludec ad (funct, aluop, alucontrol); 
      
      assign pcsrc = branch & zero; 
-     endmodule
Inputs-
  1. 6 bit Opcode
  2. 6 bit funct
  3. Zero bit (for PCSrc)
Outputs-
  1. 7 control signals
    1. memtoreg
    2. memwrite
    3. pcsrc
    4. alusrc
    5. regdst
    6. regwrite
    7. jump
  2. 3 bit alu control
Temporary Variables
  1. 2 bit AluOP
  2. Branch bit
Working ​
It acts as a top level module connecting the main decoder and alu decoder. It has some additional logic to make the PCSrc control signal by AND-ing the branch (intermediate) signal from the main decoder and the Zero from the ALU.
controller
RTL View of Main Controller
6. Main Decoder ​
v
module maindec(input [5:0] op, 
+     endmodule
Inputs-
  1. 6 bit Opcode
  2. 6 bit funct
  3. Zero bit (for PCSrc)
Outputs-
  1. 7 control signals
    1. memtoreg
    2. memwrite
    3. pcsrc
    4. alusrc
    5. regdst
    6. regwrite
    7. jump
  2. 3 bit alu control
Temporary Variables
  1. 2 bit AluOP
  2. Branch bit
Working ​
It acts as a top level module connecting the main decoder and alu decoder. It has some additional logic to make the PCSrc control signal by AND-ing the branch (intermediate) signal from the main decoder and the Zero from the ALU.
controller
RTL View of Main Controller
6. Main Decoder ​
v
module maindec(input [5:0] op, 
             output memtoreg, memwrite, 
             output branch, alusrc, 
             output regdst, regwrite, 
@@ -95,7 +95,7 @@
         6'b000010: controls <= 9'b000000100; //J 
         default: controls <= 9'bxxxxxxxxx; //??? 
     endcase 
-endmodule
Input :
6 Bit Opcode
Outputs :
  1. memtoreg
  2. memwrite
  3. branch
  4. alusrc
  5. regdst
  6. regwrite
  7. jump
(These 7 represent the 7 control signals which originate from the Control Unit and are explained in Theory section Table 1) 1. 2 Bit ALUOp
Temporary Variables ​
  1. 9 bit register control - It represents all the control signals together for easier assignment during the case statement.
Working ​
It is the main decoder which sets the control signals to 1s and 0s according to the opcode instruction. It uses a switch-case statement to decide what control to set inside a “always” procedural block.
Note:
always@(*) blocks are used to describe Combinational Logic, or Logic Gates. * sets the sensitivity list of the “always” to any values that can have an impact on a value(s) determined by the always@(*) block.
maindec RTL View of Main Decoder
7. ALU Decoder ​
v
module aludec (input [5:0] funct, 
+endmodule
Input :
6 Bit Opcode
Outputs :
  1. memtoreg
  2. memwrite
  3. branch
  4. alusrc
  5. regdst
  6. regwrite
  7. jump
(These 7 represent the 7 control signals which originate from the Control Unit and are explained in Theory section Table 1) 1. 2 Bit ALUOp
Temporary Variables ​
  1. 9 bit register control - It represents all the control signals together for easier assignment during the case statement.
Working ​
It is the main decoder which sets the control signals to 1s and 0s according to the opcode instruction. It uses a switch-case statement to decide what control to set inside a “always” procedural block.
Note:
always@(*) blocks are used to describe Combinational Logic, or Logic Gates. * sets the sensitivity list of the “always” to any values that can have an impact on a value(s) determined by the always@(*) block.
maindec RTL View of Main Decoder
7. ALU Decoder ​
v
module aludec (input [5:0] funct, 
                input [1:0] aluop, 
          output reg [2:0] alucontrol); 
 
@@ -112,7 +112,7 @@
                 default: alucontrol <= 3’bxxx; // ??? 
         endcase
 endcase
-endmodule
Inputs :
  1. 16 bit funct (from 32 bit MIPS Instruction)
  2. 2 bit ALUOp (coming from Main decoder)
Output :
  1. 3 bit ALU control
Working
It decides what function the ALU will carry out. It works with a nested switch-case statement. First it checks the ALUop
  1. If ALUOp = 1 -> ALU has to perform addition. (lw,sw)
  2. If ALUOp = 2 -> ALU has to perform subtraction. (beq)
  3. If ALUOp = 3 -> It depends on the 6 bit funct which will ADD, SUB, AND, OR, SLT (R-type)
aludec RTL View of ALU Decoder
8. Datapath ​
v
module datapath (input clk, reset, 
+endmodule
Inputs :
  1. 16 bit funct (from 32 bit MIPS Instruction)
  2. 2 bit ALUOp (coming from Main decoder)
Output :
  1. 3 bit ALU control
Working
It decides what function the ALU will carry out. It works with a nested switch-case statement. First it checks the ALUop
  1. If ALUOp = 1 -> ALU has to perform addition. (lw,sw)
  2. If ALUOp = 2 -> ALU has to perform subtraction. (beq)
  3. If ALUOp = 3 -> It depends on the 6 bit funct which will ADD, SUB, AND, OR, SLT (R-type)
aludec RTL View of ALU Decoder
8. Datapath ​
v
module datapath (input clk, reset, 
     input memtoreg, pcsrc, 
     input alusrc, regdst, 
     input regwrite, jump, 
@@ -189,7 +189,7 @@
     if (we3) rf[wa3] <= wd3;
         assign rd1 = (ra1 != 0) ? (rf[ra1]) : 0;
         assign rd2 = (ra2 != 0) ? (rf[ra2]): 0;
-endmodule
Inputs :
  1. Clk signal for third port
  2. Read register 1 ra1
  3. Read register 2 ra2
  4. Write register wa3
  5. Write data we3
Outputs :
  1. Read data 1 rd1
  2. Read data 2 rd2
Temporary Variables :
  1. 32 element Array of 32 bit registers
Working :
Two ports read combinationally. Third port written on the rising edge of the clock. If any of the registers are ‘0’ it is hardwired to be 0 value by default.
regfile RTL View of Register File
10. Some Other Functional Units ​
These units were explained in previous modules. As such explanation and theory is not repeated and can be referred to from those modules.
1. ADDER MODULE ​
v
module adder (input [31:0] a, b,output [31:0] y); assign y=a + b; 
+endmodule
Inputs :
  1. Clk signal for third port
  2. Read register 1 ra1
  3. Read register 2 ra2
  4. Write register wa3
  5. Write data we3
Outputs :
  1. Read data 1 rd1
  2. Read data 2 rd2
Temporary Variables :
  1. 32 element Array of 32 bit registers
Working :
Two ports read combinationally. Third port written on the rising edge of the clock. If any of the registers are ‘0’ it is hardwired to be 0 value by default.
regfile RTL View of Register File
10. Some Other Functional Units ​
These units were explained in previous modules. As such explanation and theory is not repeated and can be referred to from those modules.
1. ADDER MODULE ​
v
module adder (input [31:0] a, b,output [31:0] y); assign y=a + b; 
 endmodule
2. SHIFT LEFT BY 2 MODULE ​
v
module sl2 (input [31:0] a, 
 output [31:0] y); 
 assign y = {a[29:01], 2'b00}; 
@@ -240,7 +240,7 @@
             end 
         endcase 
     end 
-endmodule
6. How to Run Instructions ​
Great! Now we have our single cycle microprocessor ready but how do we run assembly code in it? The following steps explain that in detail. ( Since its a MIPS implementation of a 32 Bit Microprocessor we shall use MIPS code as the assembly code. )
Steps to run
  1. Write Down the MIPS code you want to execute. 
    1. Your code should have an instance of the instruction you want to test.
    2. Make sure the set of instructions ends with a store word (sw) instruction. The output of this “store word” should be dependent on the instruction to be tested. (This will be used for checking if the instruction is executed correctly or not.)
  2. Convert the MIPS Code into machine code with the help of an online convertor.
  3. Save the machine code as “memfile.dat” in your preferred directory.
  4. Update the path (line 6) of “memfile.dat” in the imem module (Instruction Memory) of your Verilog code to the absolute path of the memfile.dat
  5. Change the test bench to check the following 
    1. dataaddr- should contain the address of the last store word (X) in the last line of our machine code in memfile.dat
    2. writedata- should contain the data being written in memory (Y) in the last store word instruction.
    3. So, in the testbench make the change : (dataadr === X & writedata === Y )
  6. Save the module and compile your Verilog code.
  7. Run RTL Simulation.
  8. The transcript section should contain “Simulation succeeded” in the case of a correct implementation and matching dataaddr and writedata.
transcript
Fig. Sample transcript output
7. Test cases for Various Instructions ​
Now we will try to check if our microprocessor implements instructions properly.
1. add ​
mips
addi $2, $0, 450 //initialise $2 =450 
+endmodule
6. How to Run Instructions ​
Great! Now we have our single cycle microprocessor ready but how do we run assembly code in it? The following steps explain that in detail. ( Since its a MIPS implementation of a 32 Bit Microprocessor we shall use MIPS code as the assembly code. )
Steps to run
  1. Write Down the MIPS code you want to execute. 
    1. Your code should have an instance of the instruction you want to test.
    2. Make sure the set of instructions ends with a store word (sw) instruction. The output of this “store word” should be dependent on the instruction to be tested. (This will be used for checking if the instruction is executed correctly or not.)
  2. Convert the MIPS Code into machine code with the help of an online convertor.
  3. Save the machine code as “memfile.dat” in your preferred directory.
  4. Update the path (line 6) of “memfile.dat” in the imem module (Instruction Memory) of your Verilog code to the absolute path of the memfile.dat
  5. Change the test bench to check the following 
    1. dataaddr- should contain the address of the last store word (X) in the last line of our machine code in memfile.dat
    2. writedata- should contain the data being written in memory (Y) in the last store word instruction.
    3. So, in the testbench make the change : (dataadr === X & writedata === Y )
  6. Save the module and compile your Verilog code.
  7. Run RTL Simulation.
  8. The transcript section should contain “Simulation succeeded” in the case of a correct implementation and matching dataaddr and writedata.
transcript
Fig. Sample transcript output
7. Test cases for Various Instructions ​
Now we will try to check if our microprocessor implements instructions properly.
1. add ​
mips
addi $2, $0, 450 //initialise $2 =450 
 addi $3, $0, 550 //initialise $3 =550 
 add  $4, $2, $3  //$4=$2+$3 ,$4=450+550=1000 
 sw   $4, 20($0)  //write address 20 = 1000
Machine code
hex
200201c2 
@@ -437,8 +437,8 @@
             end 
         end 
     end 
-endmodule
8. References ​
  • "Computer Organization and Design: The Hardware/Software Interface" by David Patterson and John Hennessy
  • “Digital design and Computer architecture” by David Money Harris & Sarah L. Harris.
  • “Digital Logic and Computer Design ”by M. Morris Mano.
  • “Verilog HDL: A Guide to Digital Design and Synthesis ” by Samir Palnitkar.
Copyright © 2024 National Institute of Technology Calicut

-    
+endmodule

8. References ​

  • "Computer Organization and Design: The Hardware/Software Interface" by David Patterson and John Hennessy
  • “Digital design and Computer architecture” by David Money Harris & Sarah L. Harris.
  • “Digital Logic and Computer Design ”by M. Morris Mano.
  • “Verilog HDL: A Guide to Digital Design and Synthesis ” by Samir Palnitkar.

Copyright © 2024 National Institute of Technology Calicut

+ \ No newline at end of file diff --git a/docs/.vitepress/dist/Verilog/index.html b/docs/.vitepress/dist/Verilog/index.html index 0ad44e9..6a2715b 100644 --- a/docs/.vitepress/dist/Verilog/index.html +++ b/docs/.vitepress/dist/Verilog/index.html @@ -6,20 +6,20 @@ Hardware Lab NITC - + - - - - - + + + + + -
Hardware Lab NITC

Appearance

Welcome to the Verilog Guide

This course covers the following topics :

Introduction To Verilog

Learn the Basics of Verilog HDL and implement various circuits using Verilog.

Finite State Machines

Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.

MIPS Single Cycle Processor

Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.

​

Introduction to Verilog ​

Theory :

Documentation: Link to Main Documentation
Video Explanation of Theory:

  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS)
  2. Theory Vid Part 2 (PARITY-TILL END)

Implementation :
How to Run Verilog Files in Quartus: How to Run ?
Sample Codes: Link to Sample Codes
Video Explanation of Select Codes:

  1. Verilog Syntax
  2. Adder Subtractor
  3. DEMUX
  4. Counter
  5. Decoder
    Assignment 1: Download Here

Finite State Machines ​

Theory :
Documentation: Link to Main Documentation :simple-googledrive:
Video Explanation of Concept:

  1. Main Concept
  2. Syntax (Optional)

Implementation :

Video Explanation of Code (From Documentation):
Examples of FSM along with Code explanation

Code Bank: Link to Sample Codes

Assignment 2: Download Here

Single Cycle MIPS Processor ​

Theory :

Documentation: Link to Main Documentation Video Explanation of Concept:

  1. Control Unit Theory
  2. Datapath Theory

Implementation :
Video Explanation of Code (From Documentation) :

  1. Code Modules 1 to 5 explained
  2. Code Modules 6 to 10 explained
  3. All Testbenches explained
    Code Bank:
    Link to Sample Codes
    Assignment 3: Download Here

Copyright © 2024 National Institute of Technology Calicut

- +
Hardware Lab NITC

Appearance

Welcome to the Verilog Guide

This course covers the following topics :

Introduction To Verilog

Learn the Basics of Verilog HDL and implement various circuits using Verilog.

Finite State Machines

Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.

MIPS Single Cycle Processor

Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.

​

Introduction to Verilog ​

Theory :

Documentation: Link to Main Documentation
Video Explanation of Theory:

  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS)
  2. Theory Vid Part 2 (PARITY-TILL END)

Implementation :
How to Run Verilog Files in Quartus: How to Run ?
Sample Codes: Link to Sample Codes
Video Explanation of Select Codes:

  1. Verilog Syntax
  2. Adder Subtractor
  3. DEMUX
  4. Counter
  5. Decoder
    Assignment 1: Download Here

Finite State Machines ​

Theory :
Documentation: Link to Main Documentation :simple-googledrive:
Video Explanation of Concept:

  1. Main Concept
  2. Syntax (Optional)

Implementation :

Video Explanation of Code (From Documentation):
Examples of FSM along with Code explanation

Code Bank: Link to Sample Codes

Assignment 2: Download Here

Single Cycle MIPS Processor ​

Theory :

Documentation: Link to Main Documentation Video Explanation of Concept:

  1. Control Unit Theory
  2. Datapath Theory

Implementation :
Video Explanation of Code (From Documentation) :

  1. Code Modules 1 to 5 explained
  2. Code Modules 6 to 10 explained
  3. All Testbenches explained
    Code Bank:
    Link to Sample Codes
    Assignment 3: Download Here

Copyright © 2024 National Institute of Technology Calicut

+ \ No newline at end of file diff --git a/docs/.vitepress/dist/about.html b/docs/.vitepress/dist/about.html index 01cd534..1eec003 100644 --- a/docs/.vitepress/dist/about.html +++ b/docs/.vitepress/dist/about.html @@ -6,20 +6,20 @@ About Us | Hardware Lab NITC - + - - - - - + + + + + -
Hardware Lab NITC

Appearance

About Us ​

Welcome to the Hardware Lab at Computer Science and Engineering Department of National Institute of Technology, Calicut. We are a team of dedicated individuals who have come together to create a comprehensive resource for students studying computer hardware in the department.

Our Philosophy ​

Our mission is to provide students with a valuable tool that enhances their learning experience in the hardware lab course. We aim to simplify complex concepts, offer practical tips, and provide step-by-step guides to help students excel in their studies.

The Computer Science Department ​

The Computer Science Department of NITC is a leading academic department that fosters innovation, research, and excellence in the field of computer science. Our department offers a wide range of courses and programs designed to equip students with the knowledge and skills required to thrive in the ever-evolving world of technology.For more information visit https://minerva.nitc.ac.in/

The Hardware Lab Course Guide Team ​

Faculty :fontawesome-solid-computer: ​

The MIPS Team :simple-linkedin: ​

The Verilog Team :simple-linkedin: ​

Web and Repository Maintenance :simple-github: ​

Join Our Team ​

We are always looking to expand our team and welcome individuals who share our passion for computer hardware education. If you are interested in contributing to the Hardware Lab Course Guide or have any suggestions, we would love to hear from you. Please reach out to us at hwlab_csed@nitc.ac.in :octicons-mail-16:

Thank you for visiting the Computer Science Department's Hardware Lab Course Guide. We hope this resource serves as a valuable tool for your studies and contributes to your success in the fascinating world of computer hardware.

Copyright © 2024 National Institute of Technology Calicut

- +
Hardware Lab NITC

Appearance

About Us ​

Welcome to the Hardware Lab at Computer Science and Engineering Department of National Institute of Technology, Calicut. We are a team of dedicated individuals who have come together to create a comprehensive resource for students studying computer hardware in the department.

Our Philosophy ​

Our mission is to provide students with a valuable tool that enhances their learning experience in the hardware lab course. We aim to simplify complex concepts, offer practical tips, and provide step-by-step guides to help students excel in their studies.

The Computer Science Department ​

The Computer Science Department of NITC is a leading academic department that fosters innovation, research, and excellence in the field of computer science. Our department offers a wide range of courses and programs designed to equip students with the knowledge and skills required to thrive in the ever-evolving world of technology.For more information visit https://minerva.nitc.ac.in/

The Hardware Lab Course Guide Team ​

Faculty :fontawesome-solid-computer: ​

The MIPS Team :simple-linkedin: ​

The Verilog Team :simple-linkedin: ​

Web and Repository Maintenance :simple-github: ​

Join Our Team ​

We are always looking to expand our team and welcome individuals who share our passion for computer hardware education. If you are interested in contributing to the Hardware Lab Course Guide or have any suggestions, we would love to hear from you. Please reach out to us at hwlab_csed@nitc.ac.in :octicons-mail-16:

Thank you for visiting the Computer Science Department's Hardware Lab Course Guide. We hope this resource serves as a valuable tool for your studies and contributes to your success in the fascinating world of computer hardware.

Copyright © 2024 National Institute of Technology Calicut

+ \ No newline at end of file diff --git a/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.js b/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.js new file mode 100644 index 0000000..3bbd6a0 --- /dev/null +++ b/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.js @@ -0,0 +1 @@ +import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.DRnJpP2i.js";const m=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the MIPS Guide","text":"","tagline":"This part covers the following topics"},"features":[{"title":"Introduction to MIPS","details":"Setting up and understanding MIPS ISA.","link":"#introduction-to-mips"},{"title":"Basic Integer and String Handling","details":"Learn the Basics of MIPS integers.","link":"#introduction-to-mips"},{"title":"Integer Array Handling","details":"Learn how to make integer arrays and operate them.","link":"#introduction-to-mips"},{"title":"2-D Array Handling","details":"Extend your array knowledge with 2-D arrays.","link":"#introduction-to-mips"},{"title":"Strings (Advanced)","details":"String Handling explained in detail.","link":"#introduction-to-mips"},{"title":"Floating Points","details":"Learn how to handle floating point numbers.","link":"#introduction-to-mips"}]},"headers":[],"relativePath":"MIPS/index.md","filePath":"MIPS/index.md"}'),n={name:"MIPS/index.md"},i=t('

Introduction to MIPS ​

Main Documentation : Click Here
Theory explanation: Video Link

Setting up MARS: ​

Basic Integer and String Handling ​

Main Documentation : Click Here
Theory Explanation: Video Link

Sample Code Bank: ​

  1. Reversing 2 digit number
  2. Calculating Average Marks
  3. Finding Spy Number

Floating Point Handling ​

Main Documentation : Click Here

Farenheit to Celcius:
Sample Code

Maximum and Minimum in Float Array:
Sample Code

Round off to n digits:
Sample Code

Integer Array Handling ​

Main Documentation (Also contains String advanced : Click Here

Introduction to Integer Arrays:

  1. Video

  2. Sample Code

Sum of Elements of an Array:

  1. Video

  2. Sample Code

Greatest Element in Array:

  1. Video▶️
  2. Sample Code

Merge 2 Sorted Arrays:

  1. Video▶️
  2. Sample Code

Highest and Lowest occurrence of an element in an array:

  1. Video ▶️
  2. Sample Code

Binary Search:

  1. Video ▶️
  2. Sample Code

Quicksort:

  1. Video ▶️
  2. Sample Code

2-D Integer Array Handling ​

Main Documentation : Click Here

Theory Explanation: Video Link
Sample Code Bank:

  1. Taking Input
  2. Printing a Matrix
  3. Sum of Two Matrices

String Handling (advanced) ​

Input/Output of Strings:

  1. Video ▶️
  2. Sample Code

Traversal of Strings (Advanced string operations):

Length of String:

Palindrome Check:

Concatenation of strings:

',46),o=[i];function l(s,d,h,g,c,b){return a(),r("div",null,o)}const _=e(n,[["render",l]]);export{m as __pageData,_ as default}; diff --git a/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.lean.js b/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.lean.js new file mode 100644 index 0000000..0962f8e --- /dev/null +++ b/docs/.vitepress/dist/assets/MIPS_index.md.BShnq2Ay.lean.js @@ -0,0 +1 @@ +import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.DRnJpP2i.js";const m=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the MIPS Guide","text":"","tagline":"This part covers the following topics"},"features":[{"title":"Introduction to MIPS","details":"Setting up and understanding MIPS ISA.","link":"#introduction-to-mips"},{"title":"Basic Integer and String Handling","details":"Learn the Basics of MIPS integers.","link":"#introduction-to-mips"},{"title":"Integer Array Handling","details":"Learn how to make integer arrays and operate them.","link":"#introduction-to-mips"},{"title":"2-D Array Handling","details":"Extend your array knowledge with 2-D arrays.","link":"#introduction-to-mips"},{"title":"Strings (Advanced)","details":"String Handling explained in detail.","link":"#introduction-to-mips"},{"title":"Floating Points","details":"Learn how to handle floating point numbers.","link":"#introduction-to-mips"}]},"headers":[],"relativePath":"MIPS/index.md","filePath":"MIPS/index.md"}'),n={name:"MIPS/index.md"},i=t("",46),o=[i];function l(s,d,h,g,c,b){return a(),r("div",null,o)}const _=e(n,[["render",l]]);export{m as __pageData,_ as default}; diff --git a/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.js b/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.js deleted file mode 100644 index bd2c5c6..0000000 --- a/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.CgMb17D3.js";const m=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"MIPS/index.md","filePath":"MIPS/index.md"}'),n={name:"MIPS/index.md"},o=t('

Welcome to the MIPS Guide ​

This course covers the following topics-

​

  • Introduction to MIPS - Setting up and understanding MIPS ISA.
  • Basic Integer and String Handling - Learn the Basics of MIPS integers.
  • Integer Array Handling - Learn how to make integer arrays and operate them.
  • 2-D Array Handling - Extend your array knowledge with 2-D arrays.
  • Strings (Advanced) - String Handling explained in detail.
  • Floating Points - Learn how to handle floating point numbers.

Introduction to MIPS ​

Main Documentation :material-google-drive: : Click Here
Theory explanation: Video Link
Setting up MARS:

  1. Video Link

  2. Sample Code

Basic Integer and String Handling ​

Main Documentation :material-google-drive: : Click Here
Theory Explanation: Video Link
Sample Code Bank:

  1. Reversing 2 digit number

  2. Calculating Average Marks

  3. Finding Spy Number

Floating Point Handling ​

Main Documentation :material-google-drive: : Click Here

Farenheit to Celcius:
Sample Code

Maximum and Minimum in Float Array:
Sample Code

Round off to n digits:
Sample Code

Integer Array Handling ​

Main Documentation (Also contains String advanced):material-google-drive: : Click Here

Introduction to Integer Arrays:

  1. Video

  2. Sample Code

Sum of Elements of an Array:

  1. Video

  2. Sample Code

Greatest Element in Array:

  1. Video▶️
  2. Sample Code

Merge 2 Sorted Arrays:

  1. Video▶️
  2. Sample Code

Highest and Lowest occurrence of an element in an array:

  1. Video ▶️
  2. Sample Code

Binary Search:

  1. Video ▶️
  2. Sample Code

Quicksort:

  1. Video ▶️
  2. Sample Code

2-D Integer Array Handling ​

Main Documentation :material-google-drive: : Click Here

Theory Explanation: Video Link
Sample Code Bank:

  1. Taking Input
  2. Printing a Matrix
  3. Sum of Two Matrices

String Handling (advanced) ​

Input/Output of Strings:

  1. Video ▶️
  2. Sample Code

Traversal of Strings (Advanced string operations):

  1. Video ▶️
  2. Sample Code

Length of String:

  1. Video ▶️
  2. Sample Code

Palindrome Check:

  1. Video ▶️
  2. Sample Code

Concatenation of strings:

  1. Video ▶️
  2. Sample Code
',49),i=[o];function l(s,d,g,h,c,b){return a(),r("div",null,i)}const _=e(n,[["render",l]]);export{m as __pageData,_ as default}; diff --git a/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.lean.js b/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.lean.js deleted file mode 100644 index c7f43af..0000000 --- a/docs/.vitepress/dist/assets/MIPS_index.md.CY43yMpU.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.CgMb17D3.js";const m=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"MIPS/index.md","filePath":"MIPS/index.md"}'),n={name:"MIPS/index.md"},o=t("",49),i=[o];function l(s,d,g,h,c,b){return a(),r("div",null,i)}const _=e(n,[["render",l]]);export{m as __pageData,_ as default}; diff --git a/docs/.vitepress/dist/assets/MIPS_mips.md.C9wrwHux.js b/docs/.vitepress/dist/assets/MIPS_mips.md.C9wrwHux.js new file mode 100644 index 0000000..94c1485 --- /dev/null +++ b/docs/.vitepress/dist/assets/MIPS_mips.md.C9wrwHux.js @@ -0,0 +1,924 @@ +import{_ as e,a as t,b as i,c as p,d as l,e as r,f as o,g as d,h,i as c,j as g,k as u,l as k,m,n as b,o as f}from"./chunks/mips2-image-0009.DFxqnWYO.js";import{_ as y,c as E,a as s,a4 as n,j as a,o as $}from"./chunks/framework.DRnJpP2i.js";const L=JSON.parse('{"title":"MIPS","description":"","frontmatter":{},"headers":[],"relativePath":"MIPS/mips.md","filePath":"MIPS/mips.md"}'),v={name:"MIPS/mips.md"},w=n(`

MIPS ​

Setting up the MARS Code Editor ​

Introduction to MARS Simulator ​

MARS simulator will be the software on which we will be running our MIPS code.

Setting up JAVA SDK ​

(Please note this tutorial is to download SDK Ver 11)

Downloading Java SDK on MacOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your macOS version (e.g., macOS x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the macOS version and click on the provided download link.
  8. The JDK installer package will be downloaded to your computer.
  9. Locate the downloaded package in your Downloads folder or the folder you specified for downloads.
  10. Double-click on the JDK installer package to launch the installation wizard.
  11. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your macOS computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Windows version (e.g., Windows x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Windows version and click on the provided download link.
  8. The JDK installer executable file (e.g., jdk-11.0.x_windows-x64_bin.exe) will be downloaded to your computer.
  9. Locate the downloaded executable file, and double-click on it to launch the installation wizard.
  10. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your Windows computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Linux computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Linux distribution.
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Linux version and click on the provided download link.
  8. The JDK archive file (e.g., jdk-11.0.x_linux-x64_bin.tar.gz) will be downloaded to your computer.
  9. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  10. Navigate to the directory where you downloaded the JDK archive file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads
  11. Extract the contents of the JDK archive using the following command: tar -xvzf jdk-11.0.x_linux-x64_bin

Setting Up MARS Simulator ​

Note: Is your MARS text unreadably small? Download and use a new release Java 9 or above which contains a fix to automatically scale and size AWT and Swing components for High Dots Per Inch (HiDPI) displays on Windows and Linux.

Downloading MIPS MARS Simulator on macOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the official website of MIPS MARS at [ http:// courses.missouristate.edu/kenvollmar/mars/]( http:// courses.missouristate.edu/kenvollmar/mars/).
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Double-click on the ZIP file to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Applications folder.
  8. Open Terminal on your macOS by going to Applications > Utilities > Terminal.
  9. In the Terminal window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Applications folder, you can use the following command: cd/Applications
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your macOS computer.
Downloading MIPS MARS Simulator on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/]([http://courses.missouristate.edu/ kenvollmar/mars/])
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Right-click on the ZIP file and select "Extract All" to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Program Files folder.
  8. Open the Command Prompt on your Windows computer by pressing the Windows key + R, typing "cmd," and hitting Enter.
  9. In the Command Prompt window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Program Files folder, you can use the following command: cd "C:\\Program Files"
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your Windows computer.
Downloading MIPS MARS Simulator on Linux: ​
  1. Open a web browser on your Linux computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/](http://courses.missouristate.edu/ kenvollmar/mars/)
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "Mars4_5.jar.zip" will be downloaded to your computer.
  5. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  6. Navigate to the directory where you downloaded the ZIP file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads
  7. Unzip the ZIP file using the following command: unzip Mars4_5.jar.zip
  8. This will extract the "Mars4_5.jar" file from the ZIP archive.
  9. Move the "Mars4_5.jar" file to a suitable location on your computer. For instance, you can move it to the /opt directory using the following command: sudo mv Mars4_5.jar /opt
  10. To run the MIPS MARS simulator, open the terminal and navigate to the directory where you placed the JAR file. For example, if you moved it to the / opt directory, use the following command: cd /opt
  11. Execute the following command to launch the MIPS MARS simulator java -jar Mars4_5.jar
  12. The MIPS MARS simulator should now launch on your Linux computer.

MARS ASSEMBLY AND SYSTEM CALLS ​

Before assembling, the environment of this simulator can be simplisticly split to three segments: the editor at the upper left where all of the code is being written, the compiler/output right beneath the editor and the list of registers that represent the "CPU" for our program.

After assembling (by simply pressing F3) the environment changes, with two new segments getting the position of the editor: the text segment where

i) each line of assembly code gets cleared of "pseudoinstructions" (we'll talk about those in a sec) at the "basic" column and

ii) the machine code for each instruction at the "code" column, and the data segment where we can have a look at a representation of the memory of a processor with little-endian order.

After assembling, we can execute our code either all at once (F5) or step by step (F7), as well as rewinding the execution several steps backwards to the back (F8).

MARS accepts and exports files with the .asm filetype

Pseudo instructions ​

Before looking at the instruction set , let us look at a few pseudo instructions that’ll help you understand the IS better.

Here's a list of useful pseudo-instructions.

mov $t0, $t1: Copy contents of register t1 to register t0.

li $s0, immed: Load immediate into to register s0. The way this is translated depends on whether immed is 16 bits or 32 bits.

la $s0, addr: Load address into to register s0.

lw $t0, address: Load a word at address into register t0

Given below are some standard arithmetic and logical instructions standard to the MIPS Instruction Set Architecture.

**MARS provides a small set of operating system-like services through the system call (syscall) instruction **

**To request a service, a program loads the system call code into register $v0 and arguments into registers $a0~$a3 **

System calls that return values put their results in register $v0

Arithmetic Instructions ​
InstructionExampleMeaningComments
addadd $1,$2,$3$1=$2+$3
subtractsub $1,$2,$3$1=$2-$3
add immediateaddi $1,$2,100$1=$2+100"Immediate" means a constant number
add unsignedaddu $1,$2,$3$1=$2+$3Values are treated as unsigned integers,not two's complement integer
subtract unsignedsubu $1,$2,$3$1=$2-$3Values are treated as unsigned integers,not two's complement integers
add immediate unsignedaddiu $1,$2,100$1=$2+100Values are treated as unsigned integers,not two's complement integers
multiply (without overflow)mul $1,$2,$3$1=$2*$3Result is only 32 bits!
multiplymult $1,$2,$3$hi, $low=$2*$3Upper 32 bits stored in special register hi. Lower 32 bits stored in special register lo
dividediv $1,$2,$3$hi,$low=$2/$3Remainder stored in special register hi. Quotient stored in special register lo

Logical ​

InstructionExampleMeaningComments
andand $1,$2,$3$1=$2&$3Bitwise AND
oror $1,$2,$3$1=$2$3
and immediateandi $1,$2,100$1=$2&100Bitwise AND with immediate value
or immediateori $1,$2,100$1=$2100
shift left logicalsll $1,$2,10$1=$2<<10Shift left by constant number of bits
shift right logicalsrl $1,$2,10$1=$2>>10Shift right by constant number of bits

Data Transfer ​

InstructionExampleMeaningComments
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
store wordsw $1,100($2)Memory[$2+100]=$1Copy from register to memory
load upper immediatelui $1,100$1=100x2^16Load constant into upper 16 bits. Lower 16 bits are set to zero
load addressla $1,label$1=Address of the labelPseudo-instruction (provided by assembler). Loads computed address of label (not it's contents) into register
load immediateli $1,100$1=100Pseudo instruction (provided by assembler). Loads immediate value into the register.
move from himfhi $2$2=hiCopy from special register hi to general register
move from lomflo $2$2=loCopy from special register lo to general register
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
movemove $1,$2$1=$2Pseudo instruction (provided by assembler). Copy from register to register

Conditional Branch ​

InstructionExampleMeaningComments
branch on equalbeq $1,$2,100if($1==$2) go to PC+4+100Test if registers are equal
branch on not equalbne $1,$2,100if($1!=$2) go to PC+4+100Test if registers are not equal
branch on greater thanbgt $1,$2,100if($1>$2) go to PC+4+100Pseudo-instruction
branch on greater than or equalbge $1,$2,100if($1>=$2) go to PC+4+100Pseudo-instruction
branch on less thanblt $1,$2,100if($1<$2) go to PC+4+100Pseudo-instruction
branch on less than or equalble $1,$2,100if($1<=$2) go to PC+4+100Pseudo-instruction

Comparison ​

InstructionExampleMeaningComments
set on less thanslt $s1,$s2,$s3if($2<$3) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.
set on less than immediateslti $s1,$s2,100if($2<100) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.

Unconditional Jump ​

InstructionExampleMeaningComments
jumpj 1000go to address 1000Jump to target address
jump registerjr $1go to address stored in $1For switch procedure return
jump and linkjal 1000$ra=PC+4 go to address 1000Use when making procedure call. This saves the return address in $ra

System Calls ​

ServiceOperationCode(in $v0)ArgumentsResults
print_intPrint integer number (32 bit)1$a0 = integer to be printedNone
print_floatPrint floating-point number (32 bit)2$f12 = float to be printedNone
print_doublePrint floating-point number (64 bit)3$f12 = integer to be printedNone
print_stringPrint null-terminated character string4$a0 = address of string in memoryNone
read_intRead integer number from user5NoneInteger returned in $v0
read_floatRead floating-point number from user6 NoneFloat returned in $f0
read_doubleRead double floating-point number from user7NoneDouble returned in $f0
read_stringWorks the same as Standard Clibrary fgets()8$a0 = memory address of string input buffer $a1 = length of string buffer (n)None
sbrkReturns the address to a block of memory containing n additional bytes (Useful for dynamic memory allocation)9$a0=amountaddress in $v0
exitStop program from running10NoneNone
print_charPrint character11$a0 = character to be printedNone
read_charRead character from user12NoneChar returned in $v0
exit2Stops program from running and returns an integer17$a0 = result(integer number)None

The complete list of syscalls can be accessed at
https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html

Assembler Directives ​

DirectiveResult
.word w1, ..., wnStore n 32-bit values in successive memory words
.half h1, ..., hnStore n 16-bit values in successive memory words
.byte b1, ..., bnStore n 8-bit values in successive memory words
.ascii strStore the ASCII string str in memory. Strings are in double-quotes, i.e. "Computer Science"
.asciiz strStore the ASCII string str in memory and null terminate it. Strings are in double-quotes, i.e. "Computer Science"
.space nLeave an empty n-byte region of memory for later use
.align nAlign the next datum on a 2^n byte boundary. For example, .align 2 aligns the next value ona word boundary

Registers ​

Register NumberRegister NameDescription
0$zeroThe value 0
2-3$v0-$v1Values from expression evaluation and function results
4-7$a0-$a3(arguments) First four parameters for subroutine
8-15, 24-25$t0-$t9Temporary variables
16-23$s0-$s7Saved values representing final computed results
31$raReturn address

MARS(MIPS Assembler/Simulator) Tutorial ​

1. Input the Tutorial program

1.1) Open the MARS program and click from the file menu choose “File...New”. A black document will open which you can enter your assembly code into. Click “File...Save As” and save the file as “Tutorial1.asm ”.

1.2) Enter the code as shown below into the editor and save the file.

v
# Program File: Tutorial1.asm 
+# Written by:   MoSaad 
+# Date Created: 10/05/2023 
+# Description:  Tutorial program to introduce MARS simulator  including: breakpoints, single-
+stepping, and register and memory windows. 
+#----------------------------------------------------------- 
+#----------------------- 
+# Declare some constants 
+#----------------------- 
+.data 
+string1: .asciiz "Welcome to Hardware Lab at NIT Calicut\\n" 
+string2: .asciiz "Hello World \\n" 
+string3: .asciiz "\\nLoop #" 
+#------------------ 
+# Main program body 
+#------------------ 
+.text 
+main: 
+li $v0,4 
+la $a0,string1 
+syscall 
+la $a0,string2 
+syscall 
+li $t0, 1 
+loop: 
+li $v0, 4 
+la $a0,string3 
+syscall 
+li $v0,1 
+move $a0,$t0 
+syscall 
+addi $t0,$t0,1 
+bne  $t0,4,loop 
+#----- 
+# Halt  
+#----- 
+li $v0, 10 
+syscall

1.4) From the menu, choose “Run...Assemble”. The “Mars Messages” window at the bottom of the screen will indicate if any errors occurred. No errors should occur.

2. Simulate the tutorial program

2.1) From the menu, choose “Run...Go” to execute the program. The program will execute displaying two lines of text and three iterations of a loop to the Run /IO window.

2.2) The buttons at the top of the window can be used as shortcuts for the run menu. Use the “Reset” button to reset the program, and then try tracing through the program by clicking the step button.

2.3) You can adjust the speed the program runs by moving the slider to the right of the buttons. If you have an infinite loop in your program, it may be necessary to adjust (slow down) the speed of the simulator to prevent the MARS program from crashing.

',70),C=a("img",{src:e},null,-1),F=a("img",{src:t},null,-1),x=a("img",{src:i},null,-1),q=a("img",{src:p},null,-1),A=a("img",{src:l},null,-1),S=a("img",{src:r},null,-1),P=n('

3. Using the Debugging Tools

3.1) When a program does not work as expected you will need to use the debugging tools provided with the simulator.

3.2) One of the primary tools used to debug a program is setting a breakpoint. You can break before execution of an instruction by clicking on the checkbox associated with each instruction on the far left of the execute window. Set a breakpoint at the instruction: addi $t0,$t0,1

3.3) Run the program until the breakpoint by clicking “Run”. At this point in the program only the first loop iteration has been printed. (You will need to click back to the Run/IO window to see the output.)

3.4) Now use the “Trace Into” button to step through the loop that prints out the next line of text one character at a time. Step through the instructions until “Loop #2” is printed to the output window. Stop and find the value of the registers “t0” and “pc” at that point? Has the line of code that the program counter points to executed yet?

3.5) The simulator also allows you to view the memory contents. The memory window appears in the middle of the screen and is titled “Data Segment”. Remove the earlier breakpoint and add a breakpoint to line 33, “syscall”. Click the run button so that the program executes up until the new breakpoint. We are now in the code right before “Loop #” is about to be printed for the third iteration. Notice that the $a0 register is now a pointer to the address where the “Loop #” text is stored. What is the memory location the register is pointing to?

3.6) Now look in the data segment area, and find the address $a0 points to. This is the memory section where the characters of the text “Loop #” is stored. Using an ASCII table find the address where the ‘p’ in “Loop” is located?

3.7) Exercise: Can you find where the word “Welcome” is stored in the memory?

Integer Handling ​

Unlike NASM where numbers are stored as characters, MIPS can store single or multiple digit integers directly. This chapter describes how to read and print integers. Basic operations in integer handling (add, sub, mul, div) will also be covered.

1. Declaring an integer

Integers can be declared as constants in the ‘.data’ section as shown below:

Code to declare constants ‘x’ and ‘y’ with values 30 and 40 respectively:

v
.data 
+x: .word 30 
+y: .word 40

2. Loading an integer value into a register

Another way of using integers in MIPS is to read their values into temporary registers using ‘I’ type instructions. The two commonly used methods of reading integer values are:

  1. Loading a value into a temporary register.
  2. Adding the value of the zero register and any value into a temporary register.

Code to enter integer values 5 and 10 using add and load instructions respectively into temporary registers:

v
.text 
+addi  $t0, $0, 5 
+li $t1, 10

3. Reading integers as input from the user

Integers can be read from the user using syscall (system call) instructions. The system call code for reading an integer is ‘5’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The input is then stored in $v0.

Code to read an integer input from the user:

v
.text 
+li $v0, 5 
+syscall

4. Printing integers

Integers stored in registers can also be printed using syscall instructions. The system call code for printing an integer is ‘1’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The integer to be printed must be stored in the $a0 register.

Code to print the integer ‘5’ after storing it in a register:

v
.text 
+li $a0, 5 
+li $v0, 1 
+syscall

We have now learnt how to store single and multi digit integers and how to print their values. We shall now combine all of these into a single program for a more robust understanding of the covered concepts.

Code to declare a constant x with value 10, load values 20 and 30 into two registers and read an integer value from the user and print all these values:

v
.data 
+x: .word 10 
+.text 
+addi $t0, $0, 20   #load value 20 
+li $t1, 30    #load value 30 
+li $v0, 5     #read integer input
+syscall 
+move  $t2, $v0   #move integer input 
+lw $a0, x     #print x 
+li $v0, 1 
+syscall 
+move $a0, $t0    
+li $v0, 1     #print value of $t0  
+syscall    
+move $a0, $t1   #print value of $t1 
+li $v0, 1 
+syscall 
+move $a0, $t2   #print integer input 
+li $v0, 1 
+syscall 
+li $v0, 10    #exit program 
+syscall

Output:Assume the value ‘5’ is entered by the user as input.

v
5
+1020305
+-- program is finished running --

5. Adding integers

Integers can be added in two ways, either by adding fixed or immediate values to an integer value stored in a register, or by adding two integers that are both stored in registers. Both methods to add integers are demonstrated below:

Code to add integer values stored in registers:

v
.text 
+addi  $t0, $t1, 5   #t0=t1+5  
+add $t2, $t2, $t1   #t2=t2+t1 
+addi  $t1, $zero, 5   #t1=0+5 
+add   $t2, $zero, $t1    #t2=0+t1

6. Subtracting integers

Unlike addition, values can only be subtracted if they are stored in a register.

Code to subtract integer values stored in registers:

.text 
+sub $t2, $t2, $t1   #t2=t2-t1    
+sub   $t2, $zero, $t1    #t2=0-t1

7. Multiplying integers

MIPS allows you to multiply the values present in two registers and stores the 32 most significant bits in the HI special register and the 32 least significant bits in the LO special register.

The value obtained in the HI and LO registers can be accessed using the mfhi and mflo instructions respectively.

Code to multiply two integers values and access the result after multiplication:

.text 
+mult  $t0, $t1     #signed mult 
+mflo  $s0     #s0=t0*t1 
+multu $t2, $t3    #unsigned mult  
+mflo  $s1     #s1=t2*t3

8. Dividing integers

Division in MIPS is similar to multiplication except for a key difference, the HI special register stores the remainder while the LO special register will hold the quotient of the division.

Code to divide to integers and access the remainder and quotient after division:

.text 
+div $t1, $t2    #signed div 
+mfhi  $s0     #s0=t1%t2 
+mflo  $s1     #s1=t1/t2 
+divu  $t3, $t4    #unsigned div 
+mfhi  $s2     #s2=t3%t4 
+mflo  $s3      #s3=t3/t4

Points To Note ​

1. Entering number of size larger than 32 bits The largest integer that can be entered in 32 bit space is 2,147,483,647. Entering a number larger than that results in the following error:

\`\`\` Runtime exception at 0x0040002c: invalid integer input (syscall 5)\`\`\`
+

2. Changing the value of $zero register It is not possible to change the value of the $zero register, any instructions that attempt to alter the value have no effect.

3. Multiplying numbers of size 32 bits In MIPS, all integer values must be 32 bits. So if there is a valid answer, it must be contained in the lower 32 bits of the answer. Thus to implement multiplication in MIPS, the two numbers must be multiplied using the mult operator, and the valid result moved from the lo register.

4. Division by zero If the divisor is zero, then the MIPS divide instructions do not compute any result in the HI and LO registers. Division by zero is ignored and no exception is produced.

5. Meaning of the .word directive The .word directive allocates 4 bytes of space in the data region. The .word directive can then be given an integer value, and it will initialize the allocated space to that integer value. Be careful as it is incorrect to think of a the .word directive as a declaration for an integer, as this directive simply allocates and initializes 4 bytes of memory, it is not a data type. What is stored in this memory can be any type of data.

String Operations ​

Strings in MIPS can be declared as constant in the .data part of the program. They are often stored this way so that they can be used as user prompts or to format output of a program. Strings can also be entered by the user during the runtime of the program. Both methods of using strings in MIPS will be demonstrated below.

1. Entering string constants

Pre-determined strings enclosed by double quotes can be declared in the .data section.

Code to store the string “enter an element:” in memory under the name “message”:

.data 
+message: .asciiz “enter an element:”

2. Enter strings as input from the user

To enter strings as input, the syscall code to be used is 8. Apart from that, the address of the memory space into which the string must be entered, is loaded into the $a0 register. The maximum size of the string must also be loaded into the $a1 register before performing the syscall.

Code to read a string as input from the user:

.data 
+input: .space 100 
+inputsize: .word 100 
+.text 
+li $v0, 8 
+la $a0, input 
+lw $a1, inputsize 
+syscall

3. Printing strings stored in memory

To print the required string, the syscall to be used is 4. The address of the string has to be loaded into the $a0 register.

Code to print a string named ‘message’ stored in memory:

.text 
+li $v0, 4 
+la $a0, output 
+syscall

We have now learnt how to declare strings constants as well as how to store strings entered by the user. We shall now write a program combining both the concepts for a more robust understanding of basic string operations.

Code to read a string, with prompts instructing the user:

.text 
+main: 
+    # Prompt for the string to enter 
+    li $v0, 4 
+    la $a0, prompt 
+    syscall 
+ 
+    # Read the string.  
+    li $v0, 8 
+    la $a0, input 
+    lw $a1, inputSize  
+    syscall 
+     
+    # Output the text 
+    li $v0, 4 
+    la $a0, output 
+    syscall
+
+    # Output the number 
+    li $v0, 4 
+    la $a0, input 
+    syscall 
+ 
+    # Exit the program 
+    li $v0, 10 
+    syscall 
+ 
+.data 
+input:        .space 81 
+inputSize:    .word 80 
+prompt:       .asciiz "Please enter a string: " 
+output:       .asciiz "\\nYou typed the string: "

Points To Note ​

  • The .space directive allocates n bytes of memory in the data region of the program, where n=81 in this program. Since the size of a character is 1 byte, this is equivalent to saving 80 characters for data. 81 was used here because in MIPS a sequence of ASCII characters is terminated by a null value (byte containing 0). This is known as a null terminator.

  • If the string the user enters is larger than the maximum size of the string, it is truncated to the maximum size. This is to prevent the program from accessing memory not allocated to the string.

Floating Point Numbers ​

Floating point numbers are stored according to the IEEE 754 Standard. There are 2 types of floating point numbers, single precision and double precision.

Floating point number representation ​

According to IEE 754 Standard, floating point numbers follow the given representation.

Sign Exponent Fraction

  • The sign bit is 0 or 1, for positive or negative respectively.

  • The exponent stores the exponent of the number in scientific notation of its binary representation, plus a bias.

  • The fraction stores the fractional part of the binary representation of the number.

DataSingle PrecisionDouble Precision
Size32 bits64 bits
Exponent size8 bits11 bits
Fraction size23 bits52 bits
Bias1271023

Note

  • Since there are some numbers with non-ending decimal part in there binary representation ( For Example- ( 1 /3) 10 = (0.01 0011 0011 0011 ....) 2 ) and we have only limited bits to store the fraction part, there will be some slight inaccuracy while storing certain floating point numbers. Therefore, it is recommended to always use double, as it has a higher precision due to its increased no. of bits.

MIPS floating point architecture ​

In MIPS, all floating point calculations are computed in a separate processor, called co- processor 1.

The coprocessor contains 32 floating point registers, each of width 32 bits. The registers are numbered from $f 0 to $f3 1.

Each register is can store a single precision floating point number, while double precision is stored in 2 registers in an even-odd pair. For instructions concerning double precision numbers, the even numbered register is used in the instruction. Using an odd numbered register will throw an error.

In addition to the registers, there are 8 condition flags, which are used in floating point compare and branch instructions.

Floating point registers in MIPS ​

RegistersUsage
$f0 - $f3Used for results of floating point procedures
$f4 - $f11Temporary floating point registers, whose values are NOT preserved across procedure calls
$f12 - $f15Floating point parameters, whose values are NOT preserved across procedure calls
$f16 - $f19More temporary floating point registers, whose values are NOT preserved across procedure calls
$f20 - $f31Saved floating point registers, whose values are preserved across procedure calls

Among the 32 registers, only $f 4 - $f 11 , $f 16 - $f 19 and $f 20 - $f 31 can be used by the programmer for storing values, as the others are reserved for special purposes.

Note

  • Unlike the general purpose register $ 0 , $f 0 is not hardwired to be zero, and is used for storing results of procedures.

Declaring a Floating point number ​

.data
+  num1: .float 3.
+  num2: .double 4.5 3
+
+  .align 2 # Since float has 2^2 bytes
+  float_arr: .space 100 it has to be aligned to 2
+
+  .align 3 # Since double has 2^3 bytes it has to be aligned to 3
+  double_arr: .space 100

Reading and Printing Floating point numbers ​

Reading and printing a floating point number is similar to that of an integer, using syscall, only difference being in the $v0 value and parameter registers.

Single precision ​

The $v0 value for reading a single precision floating point number is 6 while that of printing is 2.

main: 
+  li $v0, 6 
+  syscall    # The number is stored in $f0 
+        
+  li $v0, 2 
+  mov.s $f12, $f0   # The number to be printed is moved to $f12 
+  syscall

Double precision ​

The $v0 value for reading a double precision floating point number is 7 while that of printing is 3.

main: 
+  li $v0, 7 
+  syscall    # The number is stored in $f0/$f1 
+        
+  li $v0, 3 
+  mov.d $f12, $f0   # The number to be printed is 
+  syscall     moved to $f12/$f13

Data Movement Instructions ​

InstructionSyntaxRemarks
Load single/doublel.s fdest, address l.d fdest, addressThe single/double floating-point stored in address is loaded onto register fdest
Store single/doubles.s fsrc, address s.d fsrc, addressThe single/double floating-point stored in register fsrc is stored to address
Move single/doublemov.s fdest, fsrc mov.d fdest, fsrcThe single/double floating-point stored in register fsrc is moved to register fdest
Move from coprocessor 1mfc1 dest, fsrcThe 32 - bit data from floating register fsrc is copied to general purpose register dest
Move to coprocessor 1mtc1 src, fdestThe 32 - bit data from general purpose register src is copied to floating point register fdest

Note

  • There is no load immediate for floating point. So if a constant is needed, it has to be stored in the data segment and loaded to the required register.
  • For the move to/from coprocessor 1 instructions, the first operand is a general purpose register and the second one is the floating point register.

Arithmetic Instructions ​

InstructionSyntaxRemarks
Additionadd.s fdest, fsrc1, fsrc2
add.d fdest, fsrc1, fsrc		The single/double floating-point numbers stored in fsrc1 and fsrc2
are added and stored in register fdest
Subtractionsub.s fdest, fsrc1, fsrc2
sub.d fdest, fsrc1, fsrc2		The single/double floating-point number stored in fsrc
subtracted from fsrc1 and stored in register fdest
Multiplicationmul.s fdest, fsrc1, fsrc2
mul.d fdest, fsrc1, fsrc2		The single/double floating-point numbers stored in fsrc1 and fsrc2
are multiplied and stored in register fdest
Divisiondiv.s fdest, fsrc1, fsrc2
div.d fdest, fsrc1, fsrc		The single/double floating-point number stored in fsrc1 is divided by fsrc2
and the quotient is stored in register fdest
Negationneg.s fdest, fsrc
neg.d fdest, fsrc		The single/double floating-point number stored in fsrc
is negated (Sign changed) and stored in register fdest
Absolute valueabs.s fdest, fsrc
abs.d fdest, fsrc		Absolute value (Magnitude) of the single/double floating-point number stored in fsrc
is stored in register fdest
Square rootsqrt.s fdest, fsrc
sqrt.d fdest, fsrc		Square root of the single/double floating-point number stored in fsrc
is stored in register fdest

Sample Question 1 ​

Given a temperature in Fahrenheit, convert it into Celsius (Input and output has to be floating point values).

Temperature in degrees Celsius = (Temperature in degrees Fahrenheit - 32 ) * 5 / 9.

data 
+  # Constants used for calculation 
+  const1: .double 32.0 
+  const2: .double 5.0 
+  const3: .double 9.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the temperature in Fahrenheit: " 
+  msg2: .asciiz "The temperature in Celsius is: " 
+ 
+
+.text 
+.globl main 
+main: 
+ 
+  li $v0, 4                    # Printing msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7                    # Reading user input 
+  syscall 
+  
+  mov.d $f12, $f0              # $f12 = User Input 
+  l.d $f14, const1             # $f12 = $f12 - 32 
+  sub.d $f12, $f12, $f14 
+  
+  l.d $f14, const2             # $f12 = $f12 * 5 
+  mul.d $f12, $f12, $f14 
+  
+  l.d $f14, const3             # $f12 = $f12 / 9 
+  div.d $f12, $f12, $f14 
+  
+  li $v0, 4                    # Printing msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 3                    # Printing final answer 
+  syscall 
+  
+  li $v0, 10                   # Exit 
+  syscall

Comparison/Branch Instructions ​

InstructionSyntaxRemarks
Compare equalc.eq.s cc, fsrc1, fsrc2
c.eq.s fsrc1, fsrc2
c.eq.d cc, fsrc1, fsrc2
c.eq.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the numbers in fsrc1
and fsrc2 are equal, 0 otherwise.
Compare less thanc.lt.s cc, fsrc1, fsrc2
c.lt.s fsrc1, fsrc2
c.lt.d cc, fsrc1, fsrc2
c.lt.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the number in fsrc1
is less than that in fsrc2, 0 otherwise.
Compare less than or equal toc.le.s cc, fsrc1, fsrc2
c.le.s fsrc1, fsrc2
c.le.d cc, fsrc1, fsrc2
c.le.d fsrc1, fsrc		Sets the condition flag cc as 1 if the number in fsrc1
is less thanor equal to that in fsrc2, 0 otherwise.
Branch if truebc1t cc, label
bc1t label		Jumps to label if the condition flag cc is set as 1
Branch if falsebc1f cc, label
bc1f label		Jumps to label if the condition flag cc is set as 0

Note

  • The condition flag can be omitted in the above instructions, in which case condition flag 0 is taken as default.
  • As there is no comparison instruction for “Not equal to”, it has to be implemented by reversing the required branch condition Ex. We need to branch to label if $f4 and $f6 are not equal. This can be written as
      c.eq.d $f4, $f6
+  bc1.f label
  • For greater than and greater than and equal to, it is simpler to reverse the input registers. Ex. We need to branch to label if $f4 if greater than $f6. This can be written as
      c.le.d $f6 , $f4
+  bc1.t label

Sample Question 2 ​

Given an array of floating numbers of size n, print the maximum and minimum element

data 
+  # Array 
+  .align 3 
+  arr: .space 1000 
+  
+  # Characters 
+  newline: .asciiz "\\n" 
+ 
+  # User Prompts 
+  msg1: .asciiz "Enter n: " 
+  msg2: .asciiz "Enter no. " 
+  msg3: .asciiz ": " 
+  msg4: .asciiz "The maximum no. is: " 
+  msg5: .asciiz "The minimum no. is: " 
+ 
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4    # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 5    # Read n 
+  syscall 
+  move $t0, $v0 
+  
+  li $t1, 0    # $t1 will be the loop variable  
+               # going from 0,1,2.. 
+  li $t2, 0    # $t2 will be the element indices 
+               # going from 0,8,16.. 
+  loop1:                      # Loop to read n elements 
+    beq $t0, $t1, end_loop1   # Termination condition 
+   
+    li $v0, 4                 # Print msg2 
+    la $a0, msg2 
+    syscall 
+   
+    li $v0, 1                 # Print position of                    
+    move $a0, $t1             # number to be inputted 
+    addi $a0, $a0, 1 
+    syscall 
+   
+    li $v0, 4                 # Print msg3 
+    la $a0, msg3 
+    syscall 
+   
+    li $v0, 7                 # Read input and  
+    syscall                   # store in arr 
+    s.d $f0, arr($t2) 
+   
+    addi $t1, $t1, 1   # Increamenting #t1  
+    addi $t2, $t2, 8   # and $t2 
+    j loop1 
+  
+  end_loop1: 
+  
+  li $t1, 0    # Resetting $t1 and $t2 
+  li $t2, 0 
+  l.d $f4, arr($zero)  # $f4 stores the max value 
+  l.d $f6, arr($zero)  # $f6 stores the min value
+
+  loop2:                        # Loop to compute max and min 
+    beq $t0, $t1, end_loop2     # Termination Condition 
+   
+    l.d $f8, arr($t2)           # Load a number from arr 
+   
+    c.lt.d $f4, $f8             # Compare if the number is  
+                                # greater than current max 
+    bc1f not_max  
+      mov.d $f4, $f8            # If yes then update new max 
+    not_max: 
+   
+    c.lt.d $f8, $f6             # Compare if the number is  
+                                # less than current min 
+    bc1f not_min 
+      mov.d $f6, $f8            # If yes then update new min 
+    not_min: 
+   
+    addi $t1, $t1, 1            # Incrementing $t1 and $t2 
+    addi $t2, $t2, 8 
+    j loop2 
+  
+  end_loop2: 
+  
+  li $v0, 4                      # Print msg4 
+  la $a0, msg4 
+  syscall 
+  
+  li $v0, 3                      # Print max number 
+  mov.d $f12, $f4 
+  syscall 
+
+  i $v0, 4    # Print newline 
+  la $a0, newline 
+  syscall 
+  
+  li $v0, 4    # Print msg5 
+  la $a0, msg5 
+  syscall 
+  
+  li $v0, 3    # Print min number 
+  mov.d $f12, $f6 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall

Data Conversion Instructions ​

Conversion within floating point ​

InstructionSyntaxRemarks
Convert single to doublecvt.d.s fdest, fsrcThe single floating-point stored in fsrc is converted to double and stored in fdest
Convert double to singlecvt.s.d fdest, fsrcThe double floating-point stored in fsrc is converted to single and stored in fdest

Conversion to integers ​

InstructionSyntaxRemarks
Convert single to integercvt.w.s fdest, fsrcThe single floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point)
and stored in 2 ’s compliment form in fdest
Convert double to integercvt.w.d fdest, fsrcThe double floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) and
stored in 2 ’s compliment form in fdest

Note

  • The output of the above two instructions is in 2 ’s compliment form, which should not be used with any other instructions other than mfc1. Other instructions always assume the data in registers are according to IEEE standards, which can cause errors.

Conversion from integers ​

InstructionSyntaxRemarks
Convert integer to singlecvt.s.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to single precision floating point and is stored in fdest
Convert integer to doublecvt.d.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to double precision floating point and is stored in fdest

Special Instructions ​

InstructionSyntaxRemarks
Ceilingceil.w.s fdest, fsrc
ceil.w.d fdest, fsrc		The smallest integer not greater than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form
Floorfloor.w.s fdest, fsrc
floor.w.d fdest, fsrc		The greatest integer not smaller than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form
Round to nearest integerround.w.s fdest, fsrc
round.w.d fdest, fsrc		The floating-point stored in fsrc is rounded off to
nearest integer and stored in fdest in 2 ’s compliment form

Sample Question 3 ​

Given a floating point number and an integer n, round off the floating point number to n digits.

Hint-

Multiplty then given number with 10^n, and round off using round.w.d instruction. Divide the result by 10^n to obtain the final result.

data 
+  # Constants used for calculation 
+  const1: .double 0.0 
+  const2: .double 1.0 
+  const3: .double 10.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the number : " 
+  msg2: .asciiz "Enter number of digits to round off to: " 
+  msg3: .asciiz "The rounded off number is: " 
+  
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4     # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7     # Read number to round off 
+  syscall 
+  
+  mov.d $f12, $f0    # $f12 = user input 
+  
+  li $v0, 4     # Print msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 7     # Read n 
+  syscall 
+
+  mov.d $f16, $f0    # $f16 = n 
+  l.d $f4, const1    # $f4 used as a loop varibale 
+                     # initialised to 0 
+  l.d $f6, const2    # $f6 used to store 10^n 
+  l.d $f8, const3    # $f8 used to store 10 for  
+                     # calculating power 
+  l.d $f10, const2   # $f10 used to store 1 for  
+                     # incrementing loop variable 
+  loop1:    # Loop to compute 10^n 
+    c.eq.d $f4, $f16  # Ternminaltion Condition 
+    bc1t end_loop1 
+  
+    mul.d $f6, $f6, $f8 # $f6 = $f6 * 10 
+    add.d $f4, $f4, $f10  # $f4 = $f4 + 1 
+  
+    j loop1 
+  end_loop1: 
+  
+  mul.d $f12, $f12, $f6  # $f12 = $f12 * (10^n) 
+  round.w.d $f12, $f12   # $f12 is rounded to nearest 
+                         # integer 
+  cvt.d.w $f12, $f12     # Output after rounding,  
+                         # which is a word, is  
+                         # converted back to double 
+  div.d $f12, $f12, $f6  # $f12 = $f12 / (10^n) 
+  
+  li $v0, 4    # Print msg3 
+  la $a0, msg3 
+  syscall  
+ 
+  li $v0, 3    # Print final answer 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall

Integer Arrays ​

An Integer Array is continuous storage block in memory in which each element is an integer. Each element of an array is accessed using the base address of the array and the index of the element we must access.

Declaration and Initialization ​

Integer arrays can be initialized using .word or an empty array can be declared using the .space keyword inside the .data section of the program

data: 
+arr: .word 3,4,-5,6    #initialized an array arr=[3,4,-5,6] 
+arr2: .space 40  # empty array with 40 bytes reserved for arr2

Array Traversal ​

Array traversal refers to accessing each element of the array using its index.

Each integer element of an array occupies a word (4 bytes). Therefore,4 bytes needed to be added to the current address to obtain the address of the following element.

Address of arr [k] = base address of arr + 4 * k

Eg: To access arr[3] and store it to $t

a $s0,arr   # base add address of array is stored in $s0 
+addi $s0,$s0,12    #  $s0 = address of arr[3] = arr + 4 * 3 
+lw $t2,0($s0)    # $t2=arr[3]

or

a $s0,arr   # base add address of array is stored in $s0 
+lw $t2,12($s0)  # $t2=value of (arr + 12)

Array Input ​

The elements of an integer array can be received from the user using the syscall for integer input and a for loop.

An empty array must be declared in the .data by allocating the necessary space as shown before.

Each integer element of an array occupies 4 bytes. Therefore, 4 bytes needed to be added to the current address after each insertion.

The following code segment can be used to create an array of size n by receiving inputs from the user:

Assume $s1 contains n, $s0 contains base address of an empty array and $t0 is the loop counter

for: 
+  beq $t0,$s1,exit      # loop termination condition 
+  sll $t1,$t0,2         # $t1=i*4 
+  add $t1,$t1,$s0   # $t1 = arr + i * 4         
+       
+  li $v0,5           # input integer and store in $t2 
+  syscall 
+  move $t2,$v0 
+  sw $t2,0($t1)      # $t2 = arr[i] 
+  addi $t0,$t0,1     # increment loop counter i 
+  j for

Printing an Integer Array ​

Integer Array can be printed by traversing each element by using array traversal rules (as discussed above) and integer printing (code 1 is loaded to $v0).

Consider the following code snippet to print the array created in the previous example in which every element is provided by the user:

la $s0,arr             # store base address of array in $s0 
+li $t0,0 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       # array traversal to access arr[i] 
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)       # $t2=arr[i] 
+  li $v0,1            # 1 is the syscall number to print integers 
+  move $a0,$t2         # print $t2   
+  syscall 
+    
+  li $a0, 32     # 32 is the ASCII code for space  
+  li $v0, 11          # syscall number for printing character 
+  syscall 
+  addi $t0,$t0,1 # increment loop counter 
+  j print 
+end:                         
+li $v0,10   #end program        
+syscall

Negative Numbers as Elements ​

All integer operations in MIPS support both positive and negative numbers. No changes are required to the program for the input and output of positive integers.

enter array element: -5 
+enter array element: -6 
+enter array element: 8 
+enter array element: -2 
+The elements of the array are: -5.0 -6.0 8.0 -2.0  
+-- program is finished running --

Floating Point Numbers as Elements ​

An array of floating-point numbers can be created by replacing all the integer operations with floating-point operations. The following changes need to be made to convert an integer array into an array of floating-point numbers:

  1. Replace the integer code loaded to $v0 by floating-point code
  2. Replace the load, store and move operation by l.s , s.s and mov.s where floating point data type is used
# program to input array 
+for: 
+  beq $t0,$s1,exit
+  sll $t1,$t0,2
+  add $t1,$t1,$s0  
+  li $v0,6          # code for floating point input 
+  syscall
+  s.s $f0,0($t1)    # arr[i]=$f0 
+  addi $t0,$t0,1 
+  j for  
+exit: 
+
+# print array 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       
+  add $t1,$t1,$s0 
+  l.s $f0,0($t1)       # $f0=arr[i] 
+  li $v0,2           # code for printing floating point 
+  mov.s $f12,$f0   
+  syscall 
+  li $a0, 32           
+  li $v0, 11           
+  syscall 
+  addi $t0,$t0,1  
+  j print 
+end

One Dimensional Arrays ​

To calculate the sum of n numbers in an n sized array ​

li $t0,0 
+la $s0,arr 
+li $t3,0        #t3 stores the sum 
+sum:          #for loop 
+  beq $t0,$s1,end     # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)      # $t2=arr[i] 
+  add $t3,$t3,$t2    # $t3=$t3+$t2 
+  addi $t0,$t0,1     # increment loop counter 
+  j sum 
+end:                 
+li $v0,1              # print sum 
+move $a0,$t3                 
+syscall

To find the largest element in an n sized array ​

la $s0,arr 
+li $t0,0 
+li $t3,-1000 # $t3=max 
+  # initialized to -1000   
+max: 
+  beq $t0,$s1,end # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)  # $t2=arr[i] 
+  ble $t2,$t3,inc_i  # if arr[i]<=max, jump to inc_count 
+  move $t3,$t2   # if arr[i]>max, max=arr[i] 
+  inc_count: 
+    addi $t0,$t0,1  # increment loop counter 
+    j max 
+end:  
+li $v0,1                  # print max 
+move $a0,$t3                 
+syscall

String Operations (Advanced) ​

Null Character and Newline ​

When strings are created by using user input (code 8 passed to $vo), it forms a sequence of ASCII characters that are terminated by a newline character, followed by a NULL character. The newline character is triggered by the pressing of enter key during user input.

The ASCII code for newline is 10. Hence beq, $t1,10,label can be used as a comparing instruction

MIPS treats NULL character as a zero. Hence beqz, $t1, label can be used as a comparing instruction

String Traversal ​

Strings are made up of characters, in which each character occupies a byte. Hence, unlike an Integer Array, each character must be traversed byte by byte.

Eg:

To find the length of a string (newline character need not be included)

# assume string is input to str1 
+li $s1,0 #loop counter (i) 
+  
+len: 
+  lb $t1,str1($s1)  # $t1=str[i] 
+  beq $t1,10,start  # termination condition 
+  addi $s1,$s1,1    # i=i+1 
+  j len 
+start: 
+  li $v0,1          # print len=i  
+  move $a0,$s1 
+  syscall

If the newline character needs to be included in the length, beq should be replaced with beqz

String Concatenation ​

Concatenation of two strings can be done using 2 loops. The presence of newline and null character at the end of each string should be considered.

Consider two strings, str1 and str2. The following is the pseudocode and the code snippet for concatenating str2 to str1:
Pseudo Code:

c
i=0
+
+j=0
+
+while str1[i]!='\\n'
+
+i++
+
+while str2[j]!='\\0'
+
+str1[i]=str2[j]
+
+i++
+
+j++

MIPS:

mips
i $s1,0           # i=0 
+li $s2,0           # j=0 
+loop1: 
+   lb $t1,str1($s1)  
+  beq $t1,10,loop2 
+  addi $s1,$s1,1           # i++ 
+  j loop1 
+loop2: 
+  lb $t1,str2($s2) 
+  beqz $t1,end 
+  sb $t1,str1($s1)    # str1[i]=str[j] 
+  addi $s1,$s1,1      # i++ 
+  addi $s2,$s2,1      # j++ 
+  j loop2 
+end:

Palindrome Checking ​

A palindrome sequence that reads the same backwards as forwards. Palindrome checking uses two pointer method.

Assume a string str, whole length is n. Length of the string is calculated by previous method and stored in $s1. The following code snippet shows the while loop necessary for checking whether the string is palindrome

addi $s1,$s1,-1 # j=n-1  
+li $s0,0        # i=0 
+for: 
+  lb $t1,str($s0)   
+  lb $t2,str($s1)   
+  bge $s0,$s1,true    # if i>=j,exit loop. return True 
+  bne $t1,$t2,false   # if str[i]!=str[j], return False 
+  addi $s0,$s0,1      #  i++ 
+  addi $s1,$s1,-1     #  j-- 
+  j for

Two Dimensional Arrays ​

2-DArrays/Matrices/Tables aren’t stored in memory the way it is normally visualized; rather it is stored as a single array in either row major form or column major form. Let’s see how a matrix is represented in memory in both the forms with a starting address of 1230. (Remember:In an array each element is 4 bytes long).

a) Row Major form : Here elements are stored row wise. First we store the first row, then the second and soon.

b) Column Major form: Here elements are stored column wise. First we store the first column, then the second and soon.

Row Major form ( starting address 1000 )

Column Major form ( starting address 1000 )

Sample code ​

->Insertion of elements and printing the 2D-array

**We are using row major form to input the elements as a string

**NOTE: all characters need to be space separated, the end of the sequence also need to have a space

Pseudo code-> ​

Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D array
+Print the matrix:
+- Loop through rows:
+- Loop through columns:
+- Print each element of the matrix
+- Print a space between elements
+- Print a newline after each row
+Exit the program

MIPS Code-> ​

.data
+newline: .asciiz "\\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+mat1: .space 100
+input: .space 100
+
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0         # $t0 = number of rows
+
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+
+  li $v0, 5
+  syscall
+  move $t1, $v0         # $t1 = number of columns
+
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+
+  li $t5, 0
+
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+# when a space is detected add the number calculated to the array and continue
+
+  beq $t4, $zero , end_input
+
+#In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+
+#This loop exist to calculate numbers that have more than one digit , since our input is a string.
+
+# We need to iterate and add the characters until we detect a space
+
+  sub $t6 , $t4, 48 # converts character to integer
+
+# for calculating the number
+  
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  
+  j input_loop
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+print_loop:
+  beq $t6 , $t0 , end_programme
+  li $t7 , 0 # Initialize column index
+
+print_column_loop:
+  lw $t9 , 0($t8) # Load number from array
+  li $v0, 1 # syscall for print_int
+  move $a0, $t9 # Load number to print
+  syscall
+
+  li $v0, 4 # syscall for print_str 
+  la $a0, space # Load address of space
+  syscall
+
+  addi $t7, $t7, 1 # Increment column index
+  addi $t8 , $t8 , 4 # Increment base address
+  blt $t7, $t1 , print_column_loop # Print all elements in the row
+
+# Print newline after each row
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+
+# Reset column index for next row
+  li $t7 , 0
+
+# Increment row index
+  addi $t6 , $t6 , 1
+
+  j print_loop
+  
+end_programme :
+  li $v0, 10 # syscall for exit
+  syscall

Output ​

  Enter number of rows:3
+  Enter number of columns:3
+  Enter matrix(row major form) : 1 2 3 4 5 6 7 8 9
+
+  1 2 3 
+  4 5 6 
+  7 8 9

->To find maximum and minimum element in a 2-D array ​

**We are using row major form to input the elements as a string

**same process of taking the input as the above

**NOTE: all characters need to be space separated, the end of the sequence also need to have a space

Pseudo code-> ​

Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D
+array
+Find minimum and maximum elements in the matrix:
+- Initialize minimum element to maximum possible value
+and maximum element to 0
+- Loop through each element of the matrix:
+- Update minimum and maximum elements if necessary
+Print the maximum element message:
+- Print "The maximum element is: "
+- Print the maximum element
+Print the minimum element message:
+- Print "The minimum element is: "
+- Print the minimum element
+Exit the program

MIPS Code-> ​

.data
+newline: .asciiz "\\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+maximum : .asciiz"The maximum element is : "
+minimum : .asciiz"The minimum element is :
+mat1: .space 100
+input: .space 100
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0 # $t0 = number of rows
+  
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+  
+  li $v0, 5
+  syscall 
+  move $t1, $v0 # $t1 = number of columns
+  
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+  
+  li $t5, 0
+  
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+  # when a space is detected add the number calculated to the array and continue
+  
+  beq $t4, $zero , end_input
+  
+  #In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+  
+  #This loop exist to calculate numbers that have more than one digit , since our input is a string
+  # we need to iterate and add the characters until we detect a space
+  
+  sub $t6 , $t4, 48 # converts character to integer
+
+  # for calculating the number
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  j input_loop
+
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+find_min_max:
+  li $t3 , 0 # Initialize max element to 0
+  li $t2 , 0xffffffff
+  li $t6 , 0 # Initialize row index to 0
+  la $a0 , mat1
+
+row_loop:
+  beq $t6, $t0 , end # If all rows have been checked, exit
+  
+  li $t7, 0 # Initialize column index to 0 
+
+column_loop:
+  beq $t7, $t1 , end_column_loop # If all columns have been checked, move to next row
+  
+  lw $t8, 0($a0) # Load current element from array
+
+# Compare current element with max element and the min element
+  bgt $t8, $t3, update_max # if element greater than max element , update max
+  
+  min :
+  blt $t8 , $t2 , update_min # if element smaller than min element, update min
+  
+  increment :
+  addi $a0, $a0, 4 # Move to next column
+  addi $t7, $t7, 1 # Increment column index
+  j column_loop
+
+update_max:
+  move $t3 , $t8 # Update max element
+  j min # control goes back to checking for the conditional statement of min element
+
+update_min:
+  move $t2 , $t8 # Update min element
+  j increment # control goes back to incrementing the looping values
+
+End_column_loop:
+  addi $t6, $t6, 1 # Increment row index
+  j row_loop
+
+end :
+  li $v0 , 4
+  la $a0 , maximum  
+  syscall
+  
+  li $v0 , 1
+  move $a0 , $t3 # printing the maximum element
+  syscall
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+  
+  li $v0 , 4
+  la $a0 , minimum # printing the minimum element
+  syscall
+
+  li $v0 , 1
+  move $a0 , $t2
+  syscall
+  
+  li $v0 , 10
+  syscall

Output ​

  Enter number of rows :3
+  Enter number of columns :3
+  Enter matrix ( row major form ) : 1 2 34 5 6 7 300 9 22
+
+  The maximum element is : 300
+  The minimum element is : 1

More Questions ​

->Searching in Matrix: Write a MIPS assembly program to search for a given element in a matrix and return its position if found.

->Matrix Addition: Write a MIPS program to add two matrices of the same size

->Transpose of a Matrix: Write a MIPS assembly program to find the transpose of a given matrix.

★ MIPS code for if statements ● Iftheconditionisanequalityusebeq,bne ● Iftheconditionisacomparisoncombinebeq/bnewithset-on-less-than

Why not blt or bge? While blt and bge (pseudo-instructions) are available in MIPS, beq and bne are favoured inconditional statements for their efficiency making them the common choice.

Example 1) Given,f:$s0, g:$s1, h:$s2, i:$s3, j:$s4

  if(i==j)
+    f = g + h;
+  else
+    f = g - h;

Solution 1 :- Corresponding MIPS code

  bne $s3, $s4, else
+  add $s0, $s1, $s2
+  j endif
+else: sub $s0, $s1, $s2
+endif: ...........

Example 2) Given,f:$s0 ,g:$s1 ,h:$s2 ,i:$s3 ,j:$s4

  if(i<j)
+    f=g+h;
+  else
+    f=g-h;

Solution 2 :- Corresponding MIPS code

  slt $to, $s3, $s4
+  beq $to, $zero, else
+  add $s0, $s1, $s2
+  j endif
+else:
+  sub $s0, $s1, $s2
+endif: .......

★ MIPS code for Loop statements

Although there are said to be 3 different types of loops in C namely, do/while, while and for loop, they are all functionally identical. In other words, you can take any for-loop and easily turn it into a while-loop.

asm
  int i;
+  for(i= 0 ;i< 10 ;i++){
+    loopbody;
+  }

or

asm
  inti=0;
+  while(i< 10 ){
+    loopbody;
+    i++;
+  }

Example 1) Given, i:$s3, k:$s

asm
  while(i < j)
+    i+=1;

Solution 1 :- Corresponding MIPS code

asm
loop:
+  slt $t0, $s3, $s4
+  beq $t0, $zero, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit: ...

Example 2) Given i:$t0, k is some integer

asm
  int i;
+  for(i = 0; i < k; i++){
+    // loop body
+  }

Solution 2 :- Corresponding MIPS code

asm
  add $t0, $zero, $zero # i is initialized to 0, $t0 = 0
+Loop: // loop body
+  addi $t0, $t0, 1 # i ++
+  slti $t1, $t0, 4 # $t1 = 1 if i < 4
+  bne $t1, $zero, Loop # go to Loop if i < 4

Example 3) Given, i:$s3, base address of arr:$s6, k:$s

asm
  while(arr[i] == k)
+    i+=3;

Solution 3 :- Corresponding MIPS code

asm
loop:
+  sll $t0, $s3, 3
+  add $t1, $t0, $s6
+  lw $t2, 0($t1)
+  bne $t2, $s5, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit:...

★ Procedures in MIPS

Understanding the memory layout and the way procedures are called is crucial for writing efficient and correct MIPS assembly code.

➢ Memory Layout

➢ Stack allocation (refer Recursion in MIPS(non-leaf procedure) for detailed explanation)

(a) before, (b) during, and (c) after a procedure call.

There are two types of procedure calling-

1) Leaf Procedures: These procedures do not call other procedures.

When a leaf procedure is called:

● There turn address is saved on the stack. ● A stack frame/procedure frame/activation record is setup to store local variables. ● Arguments may be passed in registers or on the stack. ● The procedure executes its code.

Upon completion,it restores the stack pointer and returns to the saved return address.

2) Non-leaf Procedures(NestedProcedures): These procedures call other procedures, eg.- Recursive Functions/Procedures.

In addition to the steps for leaf procedures, non-leaf procedures must manage:

● Saving and restoring additional registers beyond there turn address. ● Managing multiple levels of procedure calls and returns. ● Ensuring that data in registers is preserved a cross nested calls. ● Properly handling there turn value from called procedures.

★ Function (Procedure) calling in MIPS

In MIPS assembly language, passing parameters to functions involves using registers. Unlike high-level languages where parameters are often passed on the stack,MIPS typically uses specific registers for passing arguments.

● $a0 to $a3 :These are argument registers and are used to pass the first four arguments to a function. If a function has more than four parameters,additional parameters are typically passed on the stack.

● $v0 and $v1: These are value registers and are used to return values from functions. Functions can return up to two values using these registers.

(Note:-i) Register 1, called $at, is reserved for the assembler.
ii) Registers 26–27, called $k0–$k1 are reserved for the operating system.)

➢ Steps in calling a procedure (function)

In MIPS assembly language, procedure calling follows a similar structure to function calls in high-level languages like C.

The following steps typically occur in both leaf and non-leaf functions but there are some nuances in how they're implemented, especially regarding the handling of the stack:

● Arguments Passing :.Arguments to the function can be passed via registers or the stack, depending on the calling convention. In register-based passing, arguments are loaded in to designated argument registers like $a0-$a3. If there are more arguments than available registers, excess arguments are typically passed on the stack.

● Jump and Link (jal) :jal makes the control jump to the given address while storing there turn address at PC+4 in the $ra register This effectively sets up the return mechanism for the function call.

● Function Prologue (Non-leaf functions): Non-leaf functions need to setup a stack frame. This involves: Saving the return address($ra) on to the stack, saving any callee- saved registers on to the stack(these are typically $s0-$s7),setting up the frame pointer($fp) to establish a reference point for accessing local variables and saved registers.

● Function Execution :The function performs its task, accessing arguments, local variables, and performing computations.

● Function Epilogue (Non-leaf functions): Before returning, non-leaf functions need to cleanup the stack frame and restore the state of callee-saved registers.This involves restoring callee-saved registers from the stack, restoring the return address($ra) from the stack resetting the stack pointer($sp) to deallocate the stack frame, jumping back to the return address using the jr $ra instruction.

● Return: Upon completing its task, the function returns control to the caller. If it's a leaf function, it typically involves jumping back to the return address stored in $ra using the jr $ra instruction. For non-leaf functions, the return sequence includes restoring the stack frame and registers before jumping back to the caller.

(Note:-For simplicity we will only use $sp and extend the stack at procedure entry/exit)

Example 1) Calling a procedure which prints a string

asm
//code
+printFunction();
+a=a+2;
+//code

Solution 1 :- Corresponding MIPS code

asm
data
+hello_string: .asciiz "Hello, world!\\n" # String definition
+
+.text
+main:
+....previous code
+jal printFunction #jump to printFunction
+addi $s2, 2
+....further code
+li $v0, 10 # Set syscall code 10 for exit
+syscall # Perform syscall to exit the program
+
+printFunction:
+li $v0, 4 # Set syscall code 4 to print a string
+la $a0, hello_string # Load the address of the string
+syscall # Perform syscall to print
+jr $ra # Return control to PC + 4

● When jal is used, the control moves to the address specified in the instruction and the address of the next instruction is stored in $ra.

● When the procedure ends jr $ra is used to return control back to the next address from where it jumped.

● These procedures are usually placed after the “main” procedure to avoid instruction overlap.

Example 1) Calling a function with parameters

asm
//code
+result=addNumbers(5,7);
+//code

Solution 1 :- Corresponding MIPS code

asm
text
+main:
+  li $a0, 5 # Load first parameter (5) into $a0
+  li $a1, 7 # Load second parameter (7) into $a1
+  jal addNumbers # Jump to addNumbers function
+  move $s0, $v0 # Store the result returned by addNumbers in $s0
+  # Further code
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+addNumbers:
+  add $v0, $a0, $a1 # Add the values of $a0 and $a1 and store the result in $v0
+  jr $ra # Return control to the next instruction after jal

● In the main function, parameters are passed to the addNumbers function by loading values into registers $a0 and $a1.

● The jal instruction is used to jump to the addNumbers function.

● Inside the addNumbers function, the parameters are accessed from the $a0 and $a1 registers.

● The result of the addition is stored in register $v0, which is commonly used to return function results in MIPS.

● Finally, jr $ra is used to return control back to the instruction after the jal in the main function.

★ Recursion in MIPS (non-leaf procedure)

In MIPS assembly language, implementing recursion involves understanding function calls and stack manipulation.

The Stack in MIPS Assembly

● The stack is a crucial data structure used in MIPS assembly language for managing function calls, local variables, and return addresses. ● It operates based on the Last-In-First-Out (LIFO) principle, meaning the last item pushed onto the stack is the first item to be popped off.

Stack Operations:

Stack Pointer ($sp): ● The stack pointer register, $sp, points to the top of the stack. It keeps track of the current position in memory where new items are pushed onto or popped off the stack.

Push Operation: ● To push data onto the stack, the stack pointer is decremented to reserve space for the new item, and then the data is stored at the memory location pointed to by the stack pointer.

Pop Operation: ● To pop data off the stack,the data is retrieved from the memory location pointed to by the stack pointer, and then the stack pointer is incremented to remove the item from the stack.

Stack Usage in Function Calls:Function Prologue: ● When a function is called, the current contents of relevant registers (such as there turn address and callee-saved registers) are typically saved on the stack to ensure they are preserved. ● This process is often referred to as the function prologue.

Function Epilogue: ● Upon completion of the function, the saved values on the stack are restored to their original registers. ● This process is known as the function epilogue.

Example) Function Call and Stack Usage

● When main calls my Function using jal, the return address (the address of the instruction following the function call) is automatically saved in register $ra. ● Inside my Function, the function prologue allocates space on the stack to save the return address. ● The function body executes the desired operations. ● Finally, in the function epilogue, the return address is restored, and the stack space allocated in the prologue is deallocated before returning control to the caller.

To understand recursion in MIPS, a good understanding of the stack pointer and how it operates on memory is imperative. Recursion involves careful management of the function call stack, ensuring that return addresses and local variables are properly saved and restored. This example illustrates the process of calculating the factorial of a number using recursion in MIPS assembly language.

Example) Calculating the factorial of a number using recursion

asm
//code
+result = factorial(5);
+//code

Solution 1 :- Corresponding MIPS code

asm
text
+main:
+  li $a0, 5 # Load the value 5 (number whose factorial is to be calculated) into $a0
+  jal factorial # Jump to the factorial function
+  move $s0, $v0 # Store the result returned by factorial in $s0
+  
+  # Further code using the result stored in $s0
+  # ...
+
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+factorial:
+  # Function prologue
+  addi $sp, $sp, -4 # Allocate space on the stack for local variables
+  sw $ra, 0($sp) # Save the return address on the stack
+  
+  # Check for base case: if n <= 1, return 1
+  li $t0, 1 # Load the value 1 into $t0
+  ble $a0, $t0, base_case # Branch to base_case if $a0 (n) <= $t0 (1)
+
+  # Recursive case: n * factorial(n - 1)
+  addi $a0, $a0, -1 # Decrement $a0 (n) by 1
+  jal factorial # Recursive call to factorial function
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  mul $v0, $a0, $v0 # Multiply n by the result of factorial(n - 1)
+  jr $ra # Return control to the caller
+
+base_case:
+  # Base case: n <= 1, return 1
+  li $v0, 1 # Load the value 1 into $v0
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  jr $ra # Return control to the caller

● In the main function, the value 5 is loaded into register $a0 to calculate its factorial.
● The factorial function is then called using the jal instruction.
● Inside the factorial function, the base case checks if the input value n is less than or equal to 1.If so,it returns 1.
● Otherwise,the function decrements n by 1 and recursively calls itself with the decremented value.
● The result of the recursive call is then multiplied by n to compute the factorial. ● Finally,the result is returned to the caller using register $v0.

References ​

J.L.Hennessy and D.A.Patterson Computer Organization and Design:The Hardware/Software Interface, Fifth Edition
“Digital Logic and Computer Design” by M.Morris Mano “Digital Fundamentals” by Thomas L.Flyod http://www.cs.missouristate.edu/MARS/https://www.d.umn.edu/~gshute/mips/directives-registers.pdfhttps://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.htmlhttps://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.htmlhttps://riptutorial.com/mips/example/29993/mars-mips-simulatorhttps://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf

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If a breakpoint has been set the program will stop at the next breakpoint. "),C,s(" Trace (Step) Into. Executes a single instruction. If the instruction is a procedure call (jal) the simulator will stop at the first instruction of the procedure. "),F,s(" Backstep. Undo the last step taken in the code. "),x,s(" Pause the currently running program. Press the run button to continue execution. "),q,s(" Stop the currently running program. You will need to reset the simulator to execute the program again after stopping it. "),A,s(" Reset. Resets the simulator, reinitializing the registers, program counter, and memory. "),S,s(" Adjusts the speed that the simulator runs at. 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INTRODUCTION ​

Table of Contents ​

TopicPage
Introduction1
Verilog Syntax2
Basic Logic Gates3
Binary Adders and Subtractors4
Latches5
Flip Flops6
Multiplexers7
Demultiplexers8
Parity Generator9
Code converter10
Comparators11
Registers12
Counters13
Arithmetic Logic Unit14
Encoders15
Decoders16
How ro make a verilog program17
Bibliography18

Verilog is a Hardware Description Language (HDL). They resemble programming languages specifically oriented to describe hardware structures and their behavior. This language describes an interconnection of components. Such a structural description, a netlist, can be used as input to logic simulation just as a schematic is used.

A typical procedure is used in employing an HDL description as simulation input. The steps in the procedure are analysis, elaboration, and initialization, followed by the simulation.
Analysis checks the description for violations of the syntax and semantic rules for the HDL and produces an intermediate representation of the design.

Elaboration traverses the design hierarchy represented by the description; in this process, the design hierarchy is flattened to an interconnection of modules described only by their behaviors.
The result of the analysis and elaboration performed by the compiler is a simulation model of the original HDL description. This model is then passed to the simulator for execution. Initialization sets all of the variables in the simulation model to specified or default values.
Simulation executes the simulation model in either batch or interactive mode with inputs specified by the user.

The testbench is a description that includes the design to be tested, typically referred to as the Device Under Test (DUT). The testbench describes a collection of hardware and software functions that apply inputs to the DUT and analyze the outputs for correctness.
Verilog supports a design at many levels of abstraction. The primary three kinds of abstraction in Verilog are

  • Behavioral level
  • Register-transfer level
  • Gate level

Behavioral: ​

This is the highest level of abstraction provided by Verilog HDL. It describes the circuit using procedural statements (the "always" block, case, and if statements). At the behavioral level, the circuit is described using an algorithm consisting of a set of instructions executed one after the other sequentially.

Data-Flow: ​

This is the second highest level of abstraction. It specifies the circuit as a combination of operations and data transfer between the registers. In this approach, the 'assign' statement is used. An assign statement is a continuous statement where any signal changes on the right-hand side will update the output signal. Changes in the inputs are continuously monitored. Any synthesizable code is called RTL code. Gate-Level: This is the lowest level of abstraction. Here, the circuit is described by logical links and their timing properties. The module is implemented in terms of logic gates and interconnections between these gates. It resembles a schematic drawing with components connected with signals.

Functional Differences ​

Behavioral Level ​

Pros ​

  • Easy to write and understand, especially for complex algorithms and high-level functionality.
  • Portability: the same behavioral code can be synthesized into different hardware architectures.
  • Enables early verification, allowing designers to test system functionality before committing to a particular hardware architecture.

Cons ​

  • Less control over the hardware implementation details.
  • Can be less efficient in terms of area, power, and performance than lower levels of abstraction.
  • More difficult to optimize for timing and power.

Register Transfer Level (RTL) ​

Pros ​

  • Offers greater control over the hardware implementation details.
  • Can be optimized for timing, power, and area, allowing for more efficient designs.
  • Can be used for both simulation and synthesis. Cons
  • More difficult to write and understand than the behavioral level.
  • Can be less portable than the behavioral level, since the same code may not synthesize correctly across different architectures.
  • Can be more difficult to verify than the behavioral level, since the design is more complex.

Gate Level ​

Pros ​

  • Provides the most detailed view of the hardware implementation.
  • Highly optimized for area, power, and performance.
  • Ideal for final verification of the design. Cons
  • Very difficult to write and understand.
  • Not portable: The code is specific to a particular hardware architecture.
  • Verification can be very time-consuming and difficult, especially for complex designs.

VERILOG SYNTAX ​

CODE: ​

v
module half_adder(output s, c, input a, b);
+import{_ as e,c as t,o as i,a4 as a}from"./chunks/framework.DRnJpP2i.js";const s="/hwlabnitc.github.io/assets/image-0026.DNX3PK74.png",o="/hwlabnitc.github.io/assets/image-0027.DCQ2xQ9f.png",n="/hwlabnitc.github.io/assets/image-0031.B_mT3BDL.png",r="/hwlabnitc.github.io/assets/image-0032.ChKJiHmt.png",l="/hwlabnitc.github.io/assets/image-0035.BrUwU0Bp.png",h="/hwlabnitc.github.io/assets/image-0036.DCBkwOrC.png",c="data:image/png;base64,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",p="/hwlabnitc.github.io/assets/image-0040.DKdyuEGL.png",d="/hwlabnitc.github.io/assets/image-0041.CJRl9WSq.png",u="/hwlabnitc.github.io/assets/image-0042.ASAb8rKQ.png",g="/hwlabnitc.github.io/assets/image-0045.DKA8LCPF.png",b="/hwlabnitc.github.io/assets/image-0048.CXFSDcsL.png",m="/hwlabnitc.github.io/assets/image-0049.CaB_GLup.png",f="/hwlabnitc.github.io/assets/image-0052.CeZf0k_U.png",y="/hwlabnitc.github.io/assets/image-0055.BznlVoEq.png",k="/hwlabnitc.github.io/assets/image-0059.CDTcKoGy.png",w="/hwlabnitc.github.io/assets/image-0060.BTMDQZS7.png",E="/hwlabnitc.github.io/assets/image-0064.DEPkAGIj.png",T="/hwlabnitc.github.io/assets/image-0063.-T7xou76.png",A="/hwlabnitc.github.io/assets/image-0067.kRnoR35N.png",v="/hwlabnitc.github.io/assets/image-0068.BNfWNNPe.png",q="/hwlabnitc.github.io/assets/image-0072.CZUwEFTz.png",R="/hwlabnitc.github.io/asset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INTRODUCTION ​
Table of Contents ​
TopicPage
Introduction1
Verilog Syntax2
Basic Logic Gates3
Binary Adders and Subtractors4
Latches5
Flip Flops6
Multiplexers7
Demultiplexers8
Parity Generator9
Code converter10
Comparators11
Registers12
Counters13
Arithmetic Logic Unit14
Encoders15
Decoders16
How ro make a verilog program17
Bibliography18
Verilog is a Hardware Description Language (HDL). They resemble programming languages specifically oriented to describe hardware structures and their behavior. This language describes an interconnection of components. Such a structural description, a netlist, can be used as input to logic simulation just as a schematic is used.
A typical procedure is used in employing an HDL description as simulation input. The steps in the procedure are analysis, elaboration, and initialization, followed by the simulation.
 Analysis checks the description for violations of the syntax and semantic rules for the HDL and produces an intermediate representation of the design.
Elaboration traverses the design hierarchy represented by the description; in this process, the design hierarchy is flattened to an interconnection of modules described only by their behaviors.
 The result of the analysis and elaboration performed by the compiler is a simulation model of the original HDL description. This model is then passed to the simulator for execution. Initialization sets all of the variables in the simulation model to specified or default values.
 Simulation executes the simulation model in either batch or interactive mode with inputs specified by the user.
The testbench is a description that includes the design to be tested, typically referred to as the Device Under Test (DUT). The testbench describes a collection of hardware and software functions that apply inputs to the DUT and analyze the outputs for correctness.
 Verilog supports a design at many levels of abstraction. The primary three kinds of abstraction in Verilog are
  • Behavioral level
  • Register-transfer level
  • Gate level
Behavioral: ​
This is the highest level of abstraction provided by Verilog HDL. It describes the circuit using procedural statements (the "always" block, case, and if statements). At the behavioral level, the circuit is described using an algorithm consisting of a set of instructions executed one after the other sequentially.
Data-Flow: ​
This is the second highest level of abstraction. It specifies the circuit as a combination of operations and data transfer between the registers. In this approach, the 'assign' statement is used. An assign statement is a continuous statement where any signal changes on the right-hand side will update the output signal. Changes in the inputs are continuously monitored. Any synthesizable code is called RTL code. Gate-Level: This is the lowest level of abstraction. Here, the circuit is described by logical links and their timing properties. The module is implemented in terms of logic gates and interconnections between these gates. It resembles a schematic drawing with components connected with signals.
Functional Differences ​
Behavioral Level ​
Pros ​
  • Easy to write and understand, especially for complex algorithms and high-level functionality.
  • Portability: the same behavioral code can be synthesized into different hardware architectures.
  • Enables early verification, allowing designers to test system functionality before committing to a particular hardware architecture.
Cons ​
  • Less control over the hardware implementation details.
  • Can be less efficient in terms of area, power, and performance than lower levels of abstraction.
  • More difficult to optimize for timing and power.
Register Transfer Level (RTL) ​
Pros ​
  • Offers greater control over the hardware implementation details.
  • Can be optimized for timing, power, and area, allowing for more efficient designs.
  • Can be used for both simulation and synthesis. Cons
  • More difficult to write and understand than the behavioral level.
  • Can be less portable than the behavioral level, since the same code may not synthesize correctly across different architectures.
  • Can be more difficult to verify than the behavioral level, since the design is more complex.
Gate Level ​
Pros ​
  • Provides the most detailed view of the hardware implementation.
  • Highly optimized for area, power, and performance.
  • Ideal for final verification of the design. Cons
  • Very difficult to write and understand.
  • Not portable: The code is specific to a particular hardware architecture.
  • Verification can be very time-consuming and difficult, especially for complex designs.
VERILOG SYNTAX ​
CODE: ​
v
module half_adder(output s, c, input a, b);
     assign s = a ^ b;
     assign c = a & b;
 endmodule
module is always terminated by endmodule. Always specify output first and then input.
TESTBENCH: ​
v
module half_adder_test;
@@ -13,4 +13,4 @@ import{_ as e,c as t,o as a,a4 as i}from"./chunks/framework.CgMb17D3.js";const s
         #20;
         end
     end
-endmodule
reg: store input values
wire: store output values begin end is used to specify a block of code.
BASIC LOGIC GATES ​
Logic gates are basic building blocks of digital electronics circuits that perform logical operations on one or more binary inputs and produce a binary output. In other words, a logic gate is an electronic device that operates on logical signals (digital signals) to perform a Boolean function.
There are several types of logic gates, including:
AND gate: It has two or more input signals and produces a HIGH output only if all inputs are HIGH. The AND gate symbol is the dot or multiplication symbol.
OR gate: It has two or more input signals and produces a HIGH output if at least one input is HIGH. The OR gate symbol is the plus symbol.
NOT gate (Inverter): It has one input signal and produces the complement of the input signal at its output. The NOT gate symbol is a triangle with a circle at the output.
NAND gate: It is a combination of an AND gate and a NOT gate. It produces a LOW output only if all inputs are HIGH. The NAND gate symbol is an AND gate with a small circle at its output.
NOR gate: It is a combination of an OR gate and a NOT gate. It produces a HIGH output only if all inputs are LOW. The NOR gate symbol is an OR gate with a small circle at its output.
XOR gate: It has two input signals and produces a HIGH output if the two inputs are different (i.e., one input is HIGH and the other is LOW). The XOR gate symbol is the addition symbol with a circle around it.
XNOR gate: It is a combination of an XOR gate and a NOT gate. It produces a HIGH output if the two inputs are the same (i.e., both inputs are HIGH or both inputs are LOW). The XNOR gate symbol is an XOR gate with a small circle at its output.
Binary Adders and Subtractors ​
HALF ADDER ​
A half-adder is an arithmetic circuit that generates the sum of two binary digits. The circuit has two inputs and two outputs. The input variables are the augend and addend bits to be added, and the output variables produce the sum and carry.
The Boolean functions for the two outputs, easily obtained from the truth table, are
S = XY + XY = X ⊕ Y
C = XY
xyCS
0000
0101
1001
1110
FULL ADDER ​
A full adder is a combinational circuit that forms the arithmetic sum of three input bits. Two input variables, denoted by X and Y, represent the two significant bits to be added. The third input, Z, represents the carry from the previous lower significant position.
 The simplified sum-of-product functions for the two outputs are :
S = XYZ + XYZ + XY Z + XYZ
C = XY + XZ + YZ
S = (X ⊕ Y) ⊕ Z
C = XY + Z(X ⊕ Y)
RIPPLE CARRY ADDER ​
A parallel binary adder is a digital circuit that produces the arithmetic sum of two binary numbers using only combinational logic. The parallel adder uses n full adders in parallel, with all input bits applied simultaneously to produce the sum.
 The full adders are connected in cascade, with the carry output from one full adder connected to the carry input of the next full adder. Since a 1 carry may appear near the least significant bit of the adder and yet propagate through many full adders to the most significant bit, just as a wave ripples outward from a pebble dropped in a pond, the parallel adder is referred to as a ripple carry adder.
CARRY LOOK AHEAD ADDER ​
Define two new binary variables
Pi = Ai XOR Bi
Gi = Ai AND Bi
the output sum and carry can respectively be expressed as
Si = Pi XOR Ci
Ci+1 = Gi + (Pi AND Ci)
Each sum output requires two exclusive-OR gates. The output of the first exclusive-OR gate generates the Pi variable, and the AND gate generates the Gi variable. The carries are propagated through the carry lookahead generator and applied as inputs to the second exclusive-OR gate. All output carries are generated after a delay through two levels of gates. Thus, outputs S1 through S3 have equal propagation delay times.
HALF SUBTRACTOR ​
A half subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) and produces two output bits: the difference (D) and the borrow (B). The half subtractor is called "half" because it can only subtract two single-bit binary numbers, unlike a full subtractor that can subtract two multi-bit binary numbers. D= A XOR B B’ = Abar AND B
 
FULL SUBTRACTOR ​
A full subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) along with a borrow (Bin) and produces two output bits: the difference (D) and the borrow (Bout). The full subtractor is an extension of the half subtractor, which can only subtract two single-bit binary numbers.
D = A XOR B XOR Bin
 B’ = Abar AND B OR ((A XOR B)bar)Bin
BINARY ADDER AND SUBTRACTOR ​
M-N where M-minuend and N is subtrahend When performing a subtraction we complement the subtrahend N, and when performing an addition we do not complement N.
The 2s complement can be obtained by taking the 1s complement and adding 1 to the least significant bit. The 1s complement can be implemented easily with inverter circuits, and we can add 1 to the sum by making the input carry of the parallel adder equal to 1. The input carry C0 must be equal to 1. The operation that is performed becomes A plus the 1s complement of B plus 1. This is equal to A plus the 2s complement of B. For unsigned numbers, it gives A - B if A >= B or the 2s complement of B - A if A []( B
LATCHES ​
SR LATCH ​
The SR latch is a circuit constructed from two cross- coupled NOR gates. The latch has two inputs, labeled S for set and R for reset, and two useful states. When output Q = 1 and Q = 0, the latch is said to be in the set state. When Q = 0 and Q = 1, it is in the reset state. Outputs Q and Q are normally the complements of each other. When both inputs are equal to 1 at the same time, an undefined state with both outputs equal to 0 occurs.
S̅R̅ LATCH ​
The SR latch with two cross- coupled NAND gates. It operates with both inputs normally at 1, unless the state of the latch has to be changed. The application of a 0 to the S input causes output Q to go to 1, putting the latch in the set state. When the S input goes back to 1, the circuit remains in the set state. With both inputs at 1, the state of the latch is changed by placing a 0 on the R input. This causes the circuit to go to the reset state and stay there, even after both inputs return to 1. The condition that is undefined for this NAND latch is when both inputs are equal to 0 at the same time, an input combination that should be avoided. When the NAND latch requires a 0 signal to change its state, it is referred to as an SR latch.
SR LATCH WITH CONTROL INPUT ​
It consists of the basic NAND latch and two additional NAND gates. The control input C acts as an enable signal for the other two inputs. The output of the NAND gates stays at the logic- 1 level as long as the control input remains at 0.
 When the control input goes to 1, information from the S and R inputs is allowed to affect the S R latch. The set state is reached with S = 1, R = 0, and C = 1. To change to the reset state, the inputs must be S = 0, R = 1, and C = 1. In either case, when C returns to 0, the circuit remains in its current state. Control input C = 0 disables the circuit so that the state of the output does not change, regardless of the values of S and R. Moreover, when C = 1 and both the S and R inputs are equal to 0, the state of the circuit does not change.An undefined state occurs when all three inputs are equal to 1. This condition places 0s on both inputs of the basic S R latch, giving an undefined state.
D LATCH ​
One way to eliminate the undesirable undefined state in the SR latch is to ensure that inputs S and R are never equal to 1 at the same time. This is done in the D latch, shown in Figure 4-8. This latch has only two inputs: D (data) and C (control). The complement of the D input goes directly to the S input, and D is applied to the R input.
 As long as the control input is 0, the S R latch has both inputs at the 1 level, and the circuit cannot change state regardless of the value of D. The D input is sampled when C = 1. If D is 1, the Q output goes to 1, placing the circuit in the set state. If D is 0, output Q goes to 0, placing the circuit in the reset state. The D latch receives its designation from its ability to hold data in its internal storage. The binary information present at the data input of the D latch is transferred to the Q output when the control input is enabled (1). The output follows changes in the data input, as long as the control input is enabled. When the control input is disabled (0), the binary information that was present at the data input at the time the transition in C occurred is retained at the Q output until the control input C is enabled again.
FLIP FLOPS ​
There are basically 4 types of flip-flops:
  1. SR Flip-Flop
  2. JK Flip-Flop
  3. D Flip-Flop
  4. T Flip-Flop
SR FLIP-FLOP ​
SR flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, SR latch operates with an enable signal. The circuit diagram of SR flip-flop is shown in the following figure.This circuit has two inputs S & R and two outputs QN and Qn+1, present and next state respectively. The operation of the SR flip-flop is similar to SR Latch. But, this flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. Qn+1 = S + R’Qn
JK FLIP-FLOP ​
JK flip-flop is the modified version of SR flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has two inputs J & K and two outputs Qn and Qn+1, present and next state respectively, JK flip-flop can be used for one of these four functions such as Hold, Reset, Set & Complement of present state based on the input conditions, when positive transition of clock signal is applied.
Qn+1 = J(Qn)’ + K’(Qn)
D FLIP-FLOP ​
D flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, D latch operates with an enable signal. That means, the output of D flip-flop is insensitive to the changes in the input, D except for active transition of the clock signal. This circuit has single input D and two outputs Qn and Qn+1. This flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. D flip-flop always holds the information, which is available on data input, D of earlier positive transition of clock signal. Next state of D flip-flop is always equal to data input, D for every positive transition of the clock signal.
Qn+1 = D
T FLIP-FLOP ​
T flip-flop is the simplified version of JK flip-flop. It is obtained by connecting the same input ‘T’ to both inputs of JK flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has single input T and two outputs Qn and Qn+1. The operation of the T flip-flop is the same as that of the JK flip-flop. Here, we considered the inputs of JK flip-flop as J = T and K = T in order to utilize the modified JK flip-flop for 2 combinations of inputs. So, we eliminated the other two combinations of J & K, for which those two values complement each other in a T flip-flop.
Qn+1 = T’Q(n) + (Q(n))’T = T XOR Q(n)
MULTIPLEXERS ​
2-1 MUX ​
It selects binary information from one of many input lines and directs the information to a single output line. The selection of a particular input line is controlled by a set of input variables, called selection inputs. there are 2^n input lines and n selection inputs whose bit combinations determine which input is selected. , if the select input S = 0, the output of the multiplexer takes on the values of I 0 , and, if input S = 1, the output of the multiplexer takes on the values of I 1 . Thus, S selects either input I 0 or input I 1 to appear at output Y.
 We can see that the equation for the 2–to–1-line multiplexer output Y is
 Y = S’I0 + SI1
4-1 MUX ​
The function Y depends on four inputs I 0 , I 1 , I 2 , and I 3 and two select inputs S1 and S0 . By placing the values of I 0 through I 3 in the Y column. Since there are six variables, and only S1 and S0 are fixed, this single row represents 16 rows of the corresponding full truth table. From the table, we can write the equation for Y as
 Y = S1’S0’ I0 + S1’S0 I1 + S1S0’I2 + S1S0 I3
S1S2Y
00I0
01I1
10I2
11I3
DEMULTIPLEXERS ​
1:2 DEMUX ​
A 1-to-2 demultiplexer consists of one input line, two output lines and one select line. The signal on the select line helps to switch the input to one of the two outputs. When the select input is LOW, then the input will be passed to Y0 and if the select input is HIGH, then the input will be passed to Y1
 Y0 = S’ D
 Y1 = S D
PARITY GENERATOR ​
Many systems use a parity bit as a means for bit error detection. Any group of bits contains either an even or an odd number of 1s. A parity bit is attached to a group of bits to make the total number of 1s in a group always even or always odd. An even parity bit makes the total number of 1s even, and an odd parity bit makes the total odd. A parity bit provides for the detection of a single bit error (or any odd number of errors, which is very unlikely) but cannot check for two errors in one group. For instance, let’s assume that we wish to transmit the BCD code 0101. (Parity can be used with any number of bits; we are using four for illustration.) The total code transmitted, including the even parity bit, is
Now let’s assume that an error occurs in the third bit from the left (the 1 becomes a 0)
When this code is received, the parity check circuitry determines that there is only a single 1 (odd number), when there should be an even number of 1s. Because an even number of 1s does not appear in the code when it is received, an error is indicated.
CODE CONVERTER ​
BCD to Binary Code converter ​
The binary numbers representing the weights of the BCD bits are summed to produce the total binary number. The binary equivalent of each BCD bit is a binary number representing the weight of that bit within the total BCD number.
Binary to Gray ​
Conversion between binary code and Gray code is sometimes useful. The following rules explain how to convert from a binary number to a Gray code word:
  1. The most significant bit (left-most) in the Gray code is the same as the corresponding MSB in the binary number.
  2. Going from left to right, add each adjacent pair of binary code bits to get the next Gray code bit. Discard carries
Gray to Binary ​
To convert from Gray code to binary, use a similar method; however, there are some differences. The following rules apply:
  1. The most significant bit (left-most) in the binary code is the same as the corresponding bit in the Gray code.
  2. Add each binary code bit generated to the Gray code bit in the next adjacent position. Discard carries.
COMPARATORS ​
The exclusive-NOR gate can be used as a basic comparator because its output is a 0 if the two input bits are not equal and a 1 if the input bits are equal. The basic comparator can be expanded to any number of bits. The AND gate sets the condition that all corresponding bits of the two numbers must be equal if the two numbers themselves are equal. To determine an inequality of binary numbers A and B, you first examine the highest order bit in each number. The following conditions are possible: 1. If A3 = 1 and B3 = 0, number A is greater than number B. 2. If A3 = 0 and B3 = 1, number A is less than number B. 3. If A3 = B3, then you must examine the next lower bit position for an inequality. These three operations are valid for each bit position in the numbers. The general procedure used in a comparator is to check for an inequality in a bit position, starting with the highest-order bits (MSBs). When such an inequality is found, the relationship of the two numbers is established, and any other inequalities in lower-order bit positions must be ignored because it is possible for an opposite indication to occur; the highest-order indication must take precedence.
Registers ​
A register is a group of flip‐flops, each one of which shares a common clock and is capable of storing one bit of information. An n ‐bit register consists of a group of n flip‐flops capable of storing n bits of binary information. In addition to the flip‐flops, a register may have combinational gates that perform certain data‐processing tasks.
Four‐bit register ​
The common clock input triggers all flip‐flops on the positive edge of each pulse, and the binary data available at the four inputs are transferred into the register. The value of (I3 , I2 , I1 , I0) immediately before the clock edge determines the value of (A3 , A2 , A1 , A0) after the clock edge. The four outputs can be sampled at any time to obtain the binary information stored in the register. The input Clear_b goes to the active‐low R (reset) input of all four flip‐flops. When this input goes to 0, all flip‐flops are reset asynchronously. The Clear_b input is useful for clearing the register to all 0’s prior to its clocked operation. The R inputs must be maintained at logic 1 (i.e., de-asserted) during normal clocked operation. Note that, depending on the flip‐flop, either Clear, Clear_b, reset, or reset_b can be used to indicate the transfer of the register to an all 0’s state.
Four bit register with parallel load**Gi = Ai AND Bi ** ​
A four‐bit data‐storage register with a load control input that is directed through gates and into the D inputs of the flip‐flops. The additional gates implement a two‐channel mux whose output drives the input to the register with either the data bus or the output of the register. The load input to the register determines the action to be taken with each clock pulse.
SHIFT REGISTERS ​
SERIAL IN/SERIAL OUT REGISTERS ​
The serial in/serial out shift register accepts data serially—that is, one bit at a time on a single line. It produces the stored information on its output also in serial form .
Serial In/Parallel Out Shift Registers ​
Data bits are entered serially (least-significant bit first) into a serial in/parallel out shift register in the same manner as in serial in/serial out registers. The difference is the way in which the data bits are taken out of the register; in the parallel output register, the output of each stage is available. Once the data is stored, each bit appears on its respective output line, and all bits are available simultaneously, rather than on a bit-by-bit basis as with the serial output.
Parallel In/Serial Out Shift Registers ​
For a register with parallel data inputs, the bits are entered simultaneously into their respective stages on parallel lines rather than on a bit-by-bit basis on one line as with serial data inputs.
Parallel In/Parallel Out Shift Registers ​
Parallel entry and parallel output of data have been discussed. The parallel in/parallel out register employs both methods. Immediately following the simultaneous entry of all data bits, the bits appear on the parallel outputs.
COUNTERS ​
A register that goes through a prescribed sequence of states upon the application of input pulses is called a counter. The input pulses may be clock pulses, or they may originate from some external source and may occur at a fixed interval of time or at random. The sequence of states may follow the binary number sequence or any other sequence of states.
BINARY RIPPLE COUNTER ​
A binary ripple counter consists of a series connection of complementing flip‐flops, with the output of each flip‐flop connected to the C input of the next higher order flip‐flop. The flip‐flop holding the least significant bit receives the incoming count pulses. A complementing flip‐flop can be obtained from a JK flip‐flop with the J and K inputs tied together or from a T flip‐flop. A third possibility is to use a D flip‐flop with the complement output connected to the D input.The output of each flip‐flop is connected to the C input of the next flip‐flop in sequence. The flip‐flop holding the least significant bit receives the incoming count pulses. The bubble in front of the dynamic indicator symbol next to C indicates that the flip‐flops respond to the negative‐edge transition of the input. The negative transition occurs when the output of the previous flip‐flop to which C is connected goes from 1 to 0.
BCD RIPPLE COUNTER ​
A decimal counter follows a sequence of 10 states and returns to 0 after the count of 9. Such a counter must have at least four flip‐flops to represent each decimal digit, since a decimal digit is represented by a binary code with at least four bits. The sequence of states in a decimal counter is dictated by the binary code used to represent a decimal digit. The four outputs are designated by the letter symbol Q, with a numeric subscript equal to the binary weight of the corresponding bit in the BCD code. Note that the output of Q1 is applied to the C inputs of both Q2 and Q8 and the output of Q2 is applied to the C input of Q4. The J and K inputs are connected either to a permanent 1 signal or to outputs of other flip‐flops.
4 BIT SYNCHRONOUS BINARY COUNTER ​
The flip‐flop in the least significant position is complemented with every pulse. A flip‐flop in any other position is complemented when all the bits in the lower significant positions are equal to 1 . Synchronous binary counters have a regular pattern and can be constructed with complementing flip‐flops and gates. The C inputs of all flip‐flops are connected to a common clock. The counter is enabled by Count_enable. If the enable input is 0, all J and K inputs are equal to 0 and the clock does not change the state of the counter. The first stage, A0, has its J and K equal to 1 if the counter is enabled. The other J and K inputs are equal to 1 if all previous least significant stages are equal to 1 and the count is enabled. The chain of AND gates generates the required logic for the J and K inputs in each stage. The counter can be extended to any number of stages, with each stage having an additional flip‐flop and an AND gate that gives an output of 1 if all previous flip‐flop outputs are 1. Note that the flip‐flops trigger on the positive edge of the clock.
FOUR BIT UP-DOWN BINARY COUNTER ​
The two operations can be combined in one circuit to form a counter capable of counting either up or down. It has an up control input and a down control input. When the up input is 1, the circuit counts up, since the T inputs receive their signals from the values of the previous normal outputs of the flip‐flops.
BINARY COUNTER WITH PARALLEL LOAD ​
When equal to 1, the input load control disables the count operation and causes a transfer of data from the four data inputs into the four flip‐flops. If both control inputs are 0, clock pulses do not change the state of the register. The carry output becomes a 1 if all the flip‐flops are equal to 1 while the count input is enabled. This is the condition for complementing the flip‐flop that holds the next significant bit. The carry output is useful for expanding the counter to more than four bits. The speed of the counter is increased when the carry is generated directly from the outputs of all four flip‐flops, because the delay to generate the carry bit is reduced. A counter with a parallel load can be used to generate any desired count sequence.the Count control is set to 1 to enable the count through the CLK input. Also, recall that the Load control inhibits the count and that the clear operation is independent of other control inputs.
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ARITHMETIC LOGIC UNIT (ALU) ​
The ALU, or arithmetic logic unit, is a crucial component of the CPU (central processing unit) in a computer system. It is responsible for carrying out arithmetic and logic operations. Also referred to as the integer unit (IU), it is an integrated circuit found in both CPUs and GPUs. The ALU is the final stage in the processor where calculations are performed. It possesses the capability to handle various tasks related to arithmetic and logic operations, including addition, subtraction, shifting operations, as well as Boolean comparisons such as XOR, OR, AND, and NOT operations. It operates on binary numbers and can execute mathematical and bitwise operations. The ALU consists of two units: the arithmetic unit (AU) and the logic unit (LU). By utilizing operands and codes, the ALU determines which operations to perform based on the input data provided. Once the ALU completes processing the input, the resulting information is sent to the computer's memory.
Here are the main functions of an ALU:
Arithmetic Operations: The ALU performs various arithmetic operations on binary numbers, such as addition, subtraction, multiplication, and division. It uses binary addition and subtraction circuits to handle these operations efficiently.
Logical Operations: The ALU executes logical operations on binary data, including AND, OR, XOR (exclusive OR), and NOT. These operations manipulate individual bits or binary values to determine logical relationships and produce logical results.
Comparison Operations: The ALU performs comparison operations to determine the relationship between two binary values. It can compare if two values are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other. The result of these comparisons is typically represented by setting specific flags or registers in the CPU.
Bitwise Operations: The ALU carries out bitwise operations, which manipulate individual bits in binary numbers. These operations include shifting the bits left or right, rotating bits, and masking operations. Bitwise operations are commonly used in tasks such as data manipulation, encryption, and signal processing.
Conditional Operations: The ALU supports conditional operations, enabling the CPU to execute different instructions based on certain conditions. For example, it can perform conditional branching, where the CPU jumps to a specific instruction address based on the result of a comparison operation.
Data Movement: The ALU may also handle data movement operations within the CPU. This involves transferring data between registers, memory, and other CPU components.
ENCODER ​
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n (or fewer) input lines and n output lines.
PRIORITY ENCODER ​
A priority encoder is an encoder circuit that includes the priority function. The operation of the priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence. In addition to the two outputs x and y , the circuit has a third output designated by V ; this is a valid bit indicator that is set to 1 when one or more inputs are equal to 1. If all inputs are 0, there is no valid input and V is equal to 0. The other two outputs are not inspected when V equals 0 and are specified as don’t-care conditions.
x = D2+ D3
 y = D3 + D1 D 2
 V = D0 + D1 + D2 + D3
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DECODER ​
A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines.The decoders presented here are called n -to- m -line decoders, where m … 2^n.
3-8 LINE DECODER ​
The three inputs are decoded into eight outputs, each representing one of the minterms of the three input variables. The three inverters provide the complement of the inputs, and each one of the eight AND gates generates one of the minterms.
2-4 LINE DECODER WITH ENABLE INPUT ​
The circuit operates with complemented outputs and a complement enable input. The decoder is enabled when E is equal to 0 (i.e., active-low enable). As indicated by the truth table, only one output can be equal to 0 at any given time; all other outputs are equal to 1. The output whose value is equal to 0 represents the minterm selected by inputs A and B . The circuit is disabled when E is equal to 1, regardless of the values of the other two inputs. When the circuit is disabled, none of the outputs are equal to 0 and none of the minterms are selected.
HOW TO MAKE A VERILOG PROGRAM ​
Create a New Project in your own version of Quartus Prime. ​
Select an appropriate directory for your Verilog project files and create an empty project file template. ​
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Use the 10M50DAF484C7G Board from the MAX 10 Family. ​
Set ModelSim as your Simulation Tool (ModelSim must be installed prior) and finish the initialization of the project. ​
Click on the file icon in the top left corner and create a new Verilog HDL file. ​
When you wish to save your program, simply use Ctrl+S or click the Save icon in the top left corner. ​
Before running your program, you must first set a testbench for it. Do this by going into the Assignments menu and clicking Settings. ​
Create a new Test Bench if you are creating one for a new program that has not been made before. ​
Name your Test Bench appropriately (usually just the name of the test bench file) and add it to the list of Test Benches. ​
After setting your testbench, you can now run and compile your program by clicking on the third play button. ​
You will be able to view your circuit design and how it is structured, and simulate results using the test bench by going to the Tools menu. ​
BIBLIOGRAPHY ​
  1. Digital Design, 5th Edition by M Morris Mano and Michael Ciletti
  2. Digital Fundamentals by Floyd and Jain
  3. electronicshub.org/demultiplexerdemux
  4. tutorialspoint.com/digital_circuits/digital_circuits_flip_flops
  5. tutorialspoint.com/digital_circuits/digital_circuits_demultiplexers
',232),de=[ce];function ue(me,ge,fe,be,ye,ke){return a(),t("div",null,de)}const Te=e(pe,[["render",ue]]);export{we as __pageData,Te as default};
+endmodule

reg: store input values
wire: store output values begin end is used to specify a block of code.

BASIC LOGIC GATES ​

Logic gates are basic building blocks of digital electronics circuits that perform logical operations on one or more binary inputs and produce a binary output. In other words, a logic gate is an electronic device that operates on logical signals (digital signals) to perform a Boolean function.

There are several types of logic gates, including:

AND gate: It has two or more input signals and produces a HIGH output only if all inputs are HIGH. The AND gate symbol is the dot or multiplication symbol.

OR gate: It has two or more input signals and produces a HIGH output if at least one input is HIGH. The OR gate symbol is the plus symbol.

NOT gate (Inverter): It has one input signal and produces the complement of the input signal at its output. The NOT gate symbol is a triangle with a circle at the output.

NAND gate: It is a combination of an AND gate and a NOT gate. It produces a LOW output only if all inputs are HIGH. The NAND gate symbol is an AND gate with a small circle at its output.

NOR gate: It is a combination of an OR gate and a NOT gate. It produces a HIGH output only if all inputs are LOW. The NOR gate symbol is an OR gate with a small circle at its output.

XOR gate: It has two input signals and produces a HIGH output if the two inputs are different (i.e., one input is HIGH and the other is LOW). The XOR gate symbol is the addition symbol with a circle around it.

XNOR gate: It is a combination of an XOR gate and a NOT gate. It produces a HIGH output if the two inputs are the same (i.e., both inputs are HIGH or both inputs are LOW). The XNOR gate symbol is an XOR gate with a small circle at its output.

Binary Adders and Subtractors ​

HALF ADDER ​

A half-adder is an arithmetic circuit that generates the sum of two binary digits. The circuit has two inputs and two outputs. The input variables are the augend and addend bits to be added, and the output variables produce the sum and carry.

The Boolean functions for the two outputs, easily obtained from the truth table, are

S = XY + XY = X ⊕ Y

C = XY

xyCS
0000
0101
1001
1110

FULL ADDER ​

A full adder is a combinational circuit that forms the arithmetic sum of three input bits. Two input variables, denoted by X and Y, represent the two significant bits to be added. The third input, Z, represents the carry from the previous lower significant position.
The simplified sum-of-product functions for the two outputs are :

S = XYZ + XYZ + XY Z + XYZ
C = XY + XZ + YZ

S = (X ⊕ Y) ⊕ Z
C = XY + Z(X ⊕ Y)

RIPPLE CARRY ADDER ​

A parallel binary adder is a digital circuit that produces the arithmetic sum of two binary numbers using only combinational logic. The parallel adder uses n full adders in parallel, with all input bits applied simultaneously to produce the sum.
The full adders are connected in cascade, with the carry output from one full adder connected to the carry input of the next full adder. Since a 1 carry may appear near the least significant bit of the adder and yet propagate through many full adders to the most significant bit, just as a wave ripples outward from a pebble dropped in a pond, the parallel adder is referred to as a ripple carry adder.

CARRY LOOK AHEAD ADDER ​

Define two new binary variables

Pi = Ai XOR Bi
Gi = Ai AND Bi

the output sum and carry can respectively be expressed as

Si = Pi XOR Ci
Ci+1 = Gi + (Pi AND Ci)

Each sum output requires two exclusive-OR gates. The output of the first exclusive-OR gate generates the Pi variable, and the AND gate generates the Gi variable. The carries are propagated through the carry lookahead generator and applied as inputs to the second exclusive-OR gate. All output carries are generated after a delay through two levels of gates. Thus, outputs S1 through S3 have equal propagation delay times.

HALF SUBTRACTOR ​

A half subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) and produces two output bits: the difference (D) and the borrow (B). The half subtractor is called "half" because it can only subtract two single-bit binary numbers, unlike a full subtractor that can subtract two multi-bit binary numbers. D= A XOR B B’ = Abar AND B

FULL SUBTRACTOR ​

A full subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) along with a borrow (Bin) and produces two output bits: the difference (D) and the borrow (Bout). The full subtractor is an extension of the half subtractor, which can only subtract two single-bit binary numbers.

D = A XOR B XOR Bin
B’ = Abar AND B OR ((A XOR B)bar)Bin

BINARY ADDER AND SUBTRACTOR ​

M-N where M-minuend and N is subtrahend When performing a subtraction we complement the subtrahend N, and when performing an addition we do not complement N.

The 2s complement can be obtained by taking the 1s complement and adding 1 to the least significant bit. The 1s complement can be implemented easily with inverter circuits, and we can add 1 to the sum by making the input carry of the parallel adder equal to 1. The input carry C0 must be equal to 1. The operation that is performed becomes A plus the 1s complement of B plus 1. This is equal to A plus the 2s complement of B. For unsigned numbers, it gives A - B if A >= B or the 2s complement of B - A if A []( B

LATCHES ​

SR LATCH ​

The SR latch is a circuit constructed from two cross- coupled NOR gates. The latch has two inputs, labeled S for set and R for reset, and two useful states. When output Q = 1 and Q = 0, the latch is said to be in the set state. When Q = 0 and Q = 1, it is in the reset state. Outputs Q and Q are normally the complements of each other. When both inputs are equal to 1 at the same time, an undefined state with both outputs equal to 0 occurs.

S̅R̅ LATCH ​

The SR latch with two cross- coupled NAND gates. It operates with both inputs normally at 1, unless the state of the latch has to be changed. The application of a 0 to the S input causes output Q to go to 1, putting the latch in the set state. When the S input goes back to 1, the circuit remains in the set state. With both inputs at 1, the state of the latch is changed by placing a 0 on the R input. This causes the circuit to go to the reset state and stay there, even after both inputs return to 1. The condition that is undefined for this NAND latch is when both inputs are equal to 0 at the same time, an input combination that should be avoided. When the NAND latch requires a 0 signal to change its state, it is referred to as an SR latch.

SR LATCH WITH CONTROL INPUT ​

It consists of the basic NAND latch and two additional NAND gates. The control input C acts as an enable signal for the other two inputs. The output of the NAND gates stays at the logic- 1 level as long as the control input remains at 0.
When the control input goes to 1, information from the S and R inputs is allowed to affect the S R latch. The set state is reached with S = 1, R = 0, and C = 1. To change to the reset state, the inputs must be S = 0, R = 1, and C = 1. In either case, when C returns to 0, the circuit remains in its current state. Control input C = 0 disables the circuit so that the state of the output does not change, regardless of the values of S and R. Moreover, when C = 1 and both the S and R inputs are equal to 0, the state of the circuit does not change.An undefined state occurs when all three inputs are equal to 1. This condition places 0s on both inputs of the basic S R latch, giving an undefined state.

D LATCH ​

One way to eliminate the undesirable undefined state in the SR latch is to ensure that inputs S and R are never equal to 1 at the same time. This is done in the D latch, shown in Figure 4-8. This latch has only two inputs: D (data) and C (control). The complement of the D input goes directly to the S input, and D is applied to the R input.
As long as the control input is 0, the S R latch has both inputs at the 1 level, and the circuit cannot change state regardless of the value of D. The D input is sampled when C = 1. If D is 1, the Q output goes to 1, placing the circuit in the set state. If D is 0, output Q goes to 0, placing the circuit in the reset state. The D latch receives its designation from its ability to hold data in its internal storage. The binary information present at the data input of the D latch is transferred to the Q output when the control input is enabled (1). The output follows changes in the data input, as long as the control input is enabled. When the control input is disabled (0), the binary information that was present at the data input at the time the transition in C occurred is retained at the Q output until the control input C is enabled again.

FLIP FLOPS ​

There are basically 4 types of flip-flops:

  1. SR Flip-Flop
  2. JK Flip-Flop
  3. D Flip-Flop
  4. T Flip-Flop

SR FLIP-FLOP ​

SR flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, SR latch operates with an enable signal. The circuit diagram of SR flip-flop is shown in the following figure.This circuit has two inputs S & R and two outputs QN and Qn+1, present and next state respectively. The operation of the SR flip-flop is similar to SR Latch. But, this flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. Qn+1 = S + R’Qn

JK FLIP-FLOP ​

JK flip-flop is the modified version of SR flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has two inputs J & K and two outputs Qn and Qn+1, present and next state respectively, JK flip-flop can be used for one of these four functions such as Hold, Reset, Set & Complement of present state based on the input conditions, when positive transition of clock signal is applied.

Qn+1 = J(Qn)’ + K’(Qn)

D FLIP-FLOP ​

D flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, D latch operates with an enable signal. That means, the output of D flip-flop is insensitive to the changes in the input, D except for active transition of the clock signal. This circuit has single input D and two outputs Qn and Qn+1. This flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. D flip-flop always holds the information, which is available on data input, D of earlier positive transition of clock signal. Next state of D flip-flop is always equal to data input, D for every positive transition of the clock signal.

Qn+1 = D

T FLIP-FLOP ​

T flip-flop is the simplified version of JK flip-flop. It is obtained by connecting the same input ‘T’ to both inputs of JK flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has single input T and two outputs Qn and Qn+1. The operation of the T flip-flop is the same as that of the JK flip-flop. Here, we considered the inputs of JK flip-flop as J = T and K = T in order to utilize the modified JK flip-flop for 2 combinations of inputs. So, we eliminated the other two combinations of J & K, for which those two values complement each other in a T flip-flop.

Qn+1 = T’Q(n) + (Q(n))’T = T XOR Q(n)

MULTIPLEXERS ​

2-1 MUX ​

It selects binary information from one of many input lines and directs the information to a single output line. The selection of a particular input line is controlled by a set of input variables, called selection inputs. there are 2^n input lines and n selection inputs whose bit combinations determine which input is selected. , if the select input S = 0, the output of the multiplexer takes on the values of I 0 , and, if input S = 1, the output of the multiplexer takes on the values of I 1 . Thus, S selects either input I 0 or input I 1 to appear at output Y.
We can see that the equation for the 2–to–1-line multiplexer output Y is
Y = S’I0 + SI1

4-1 MUX ​

The function Y depends on four inputs I 0 , I 1 , I 2 , and I 3 and two select inputs S1 and S0 . By placing the values of I 0 through I 3 in the Y column. Since there are six variables, and only S1 and S0 are fixed, this single row represents 16 rows of the corresponding full truth table. From the table, we can write the equation for Y as
Y = S1’S0’ I0 + S1’S0 I1 + S1S0’I2 + S1S0 I3

S1S2Y
00I0
01I1
10I2
11I3

DEMULTIPLEXERS ​

1:2 DEMUX ​

A 1-to-2 demultiplexer consists of one input line, two output lines and one select line. The signal on the select line helps to switch the input to one of the two outputs. When the select input is LOW, then the input will be passed to Y0 and if the select input is HIGH, then the input will be passed to Y1
Y0 = S’ D
Y1 = S D

PARITY GENERATOR ​

Many systems use a parity bit as a means for bit error detection. Any group of bits contains either an even or an odd number of 1s. A parity bit is attached to a group of bits to make the total number of 1s in a group always even or always odd. An even parity bit makes the total number of 1s even, and an odd parity bit makes the total odd. A parity bit provides for the detection of a single bit error (or any odd number of errors, which is very unlikely) but cannot check for two errors in one group. For instance, let’s assume that we wish to transmit the BCD code 0101. (Parity can be used with any number of bits; we are using four for illustration.) The total code transmitted, including the even parity bit, is

Now let’s assume that an error occurs in the third bit from the left (the 1 becomes a 0)

When this code is received, the parity check circuitry determines that there is only a single 1 (odd number), when there should be an even number of 1s. Because an even number of 1s does not appear in the code when it is received, an error is indicated.

CODE CONVERTER ​

BCD to Binary Code converter ​

The binary numbers representing the weights of the BCD bits are summed to produce the total binary number. The binary equivalent of each BCD bit is a binary number representing the weight of that bit within the total BCD number.

Binary to Gray ​

Conversion between binary code and Gray code is sometimes useful. The following rules explain how to convert from a binary number to a Gray code word:

  1. The most significant bit (left-most) in the Gray code is the same as the corresponding MSB in the binary number.
  2. Going from left to right, add each adjacent pair of binary code bits to get the next Gray code bit. Discard carries

Gray to Binary ​

To convert from Gray code to binary, use a similar method; however, there are some differences. The following rules apply:

  1. The most significant bit (left-most) in the binary code is the same as the corresponding bit in the Gray code.
  2. Add each binary code bit generated to the Gray code bit in the next adjacent position. Discard carries.

COMPARATORS ​

The exclusive-NOR gate can be used as a basic comparator because its output is a 0 if the two input bits are not equal and a 1 if the input bits are equal. The basic comparator can be expanded to any number of bits. The AND gate sets the condition that all corresponding bits of the two numbers must be equal if the two numbers themselves are equal. To determine an inequality of binary numbers A and B, you first examine the highest order bit in each number. The following conditions are possible: 1. If A3 = 1 and B3 = 0, number A is greater than number B. 2. If A3 = 0 and B3 = 1, number A is less than number B. 3. If A3 = B3, then you must examine the next lower bit position for an inequality. These three operations are valid for each bit position in the numbers. The general procedure used in a comparator is to check for an inequality in a bit position, starting with the highest-order bits (MSBs). When such an inequality is found, the relationship of the two numbers is established, and any other inequalities in lower-order bit positions must be ignored because it is possible for an opposite indication to occur; the highest-order indication must take precedence.

Registers ​

A register is a group of flip‐flops, each one of which shares a common clock and is capable of storing one bit of information. An n ‐bit register consists of a group of n flip‐flops capable of storing n bits of binary information. In addition to the flip‐flops, a register may have combinational gates that perform certain data‐processing tasks.

Four‐bit register ​

The common clock input triggers all flip‐flops on the positive edge of each pulse, and the binary data available at the four inputs are transferred into the register. The value of (I3 , I2 , I1 , I0) immediately before the clock edge determines the value of (A3 , A2 , A1 , A0) after the clock edge. The four outputs can be sampled at any time to obtain the binary information stored in the register. The input Clear_b goes to the active‐low R (reset) input of all four flip‐flops. When this input goes to 0, all flip‐flops are reset asynchronously. The Clear_b input is useful for clearing the register to all 0’s prior to its clocked operation. The R inputs must be maintained at logic 1 (i.e., de-asserted) during normal clocked operation. Note that, depending on the flip‐flop, either Clear, Clear_b, reset, or reset_b can be used to indicate the transfer of the register to an all 0’s state.

Four bit register with parallel load**Gi = Ai AND Bi ** ​

A four‐bit data‐storage register with a load control input that is directed through gates and into the D inputs of the flip‐flops. The additional gates implement a two‐channel mux whose output drives the input to the register with either the data bus or the output of the register. The load input to the register determines the action to be taken with each clock pulse.

SHIFT REGISTERS ​

SERIAL IN/SERIAL OUT REGISTERS ​

The serial in/serial out shift register accepts data serially—that is, one bit at a time on a single line. It produces the stored information on its output also in serial form .

Serial In/Parallel Out Shift Registers ​

Data bits are entered serially (least-significant bit first) into a serial in/parallel out shift register in the same manner as in serial in/serial out registers. The difference is the way in which the data bits are taken out of the register; in the parallel output register, the output of each stage is available. Once the data is stored, each bit appears on its respective output line, and all bits are available simultaneously, rather than on a bit-by-bit basis as with the serial output.

Parallel In/Serial Out Shift Registers ​

For a register with parallel data inputs, the bits are entered simultaneously into their respective stages on parallel lines rather than on a bit-by-bit basis on one line as with serial data inputs.

Parallel In/Parallel Out Shift Registers ​

Parallel entry and parallel output of data have been discussed. The parallel in/parallel out register employs both methods. Immediately following the simultaneous entry of all data bits, the bits appear on the parallel outputs.

COUNTERS ​

A register that goes through a prescribed sequence of states upon the application of input pulses is called a counter. The input pulses may be clock pulses, or they may originate from some external source and may occur at a fixed interval of time or at random. The sequence of states may follow the binary number sequence or any other sequence of states.

BINARY RIPPLE COUNTER ​

A binary ripple counter consists of a series connection of complementing flip‐flops, with the output of each flip‐flop connected to the C input of the next higher order flip‐flop. The flip‐flop holding the least significant bit receives the incoming count pulses. A complementing flip‐flop can be obtained from a JK flip‐flop with the J and K inputs tied together or from a T flip‐flop. A third possibility is to use a D flip‐flop with the complement output connected to the D input.The output of each flip‐flop is connected to the C input of the next flip‐flop in sequence. The flip‐flop holding the least significant bit receives the incoming count pulses. The bubble in front of the dynamic indicator symbol next to C indicates that the flip‐flops respond to the negative‐edge transition of the input. The negative transition occurs when the output of the previous flip‐flop to which C is connected goes from 1 to 0.

BCD RIPPLE COUNTER ​

A decimal counter follows a sequence of 10 states and returns to 0 after the count of 9. Such a counter must have at least four flip‐flops to represent each decimal digit, since a decimal digit is represented by a binary code with at least four bits. The sequence of states in a decimal counter is dictated by the binary code used to represent a decimal digit. The four outputs are designated by the letter symbol Q, with a numeric subscript equal to the binary weight of the corresponding bit in the BCD code. Note that the output of Q1 is applied to the C inputs of both Q2 and Q8 and the output of Q2 is applied to the C input of Q4. The J and K inputs are connected either to a permanent 1 signal or to outputs of other flip‐flops.

4 BIT SYNCHRONOUS BINARY COUNTER ​

The flip‐flop in the least significant position is complemented with every pulse. A flip‐flop in any other position is complemented when all the bits in the lower significant positions are equal to 1 . Synchronous binary counters have a regular pattern and can be constructed with complementing flip‐flops and gates. The C inputs of all flip‐flops are connected to a common clock. The counter is enabled by Count_enable. If the enable input is 0, all J and K inputs are equal to 0 and the clock does not change the state of the counter. The first stage, A0, has its J and K equal to 1 if the counter is enabled. The other J and K inputs are equal to 1 if all previous least significant stages are equal to 1 and the count is enabled. The chain of AND gates generates the required logic for the J and K inputs in each stage. The counter can be extended to any number of stages, with each stage having an additional flip‐flop and an AND gate that gives an output of 1 if all previous flip‐flop outputs are 1. Note that the flip‐flops trigger on the positive edge of the clock.

FOUR BIT UP-DOWN BINARY COUNTER ​

The two operations can be combined in one circuit to form a counter capable of counting either up or down. It has an up control input and a down control input. When the up input is 1, the circuit counts up, since the T inputs receive their signals from the values of the previous normal outputs of the flip‐flops.

BINARY COUNTER WITH PARALLEL LOAD ​

When equal to 1, the input load control disables the count operation and causes a transfer of data from the four data inputs into the four flip‐flops. If both control inputs are 0, clock pulses do not change the state of the register. The carry output becomes a 1 if all the flip‐flops are equal to 1 while the count input is enabled. This is the condition for complementing the flip‐flop that holds the next significant bit. The carry output is useful for expanding the counter to more than four bits. The speed of the counter is increased when the carry is generated directly from the outputs of all four flip‐flops, because the delay to generate the carry bit is reduced. A counter with a parallel load can be used to generate any desired count sequence.the Count control is set to 1 to enable the count through the CLK input. Also, recall that the Load control inhibits the count and that the clear operation is independent of other control inputs.

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ARITHMETIC LOGIC UNIT (ALU) ​

The ALU, or arithmetic logic unit, is a crucial component of the CPU (central processing unit) in a computer system. It is responsible for carrying out arithmetic and logic operations. Also referred to as the integer unit (IU), it is an integrated circuit found in both CPUs and GPUs. The ALU is the final stage in the processor where calculations are performed. It possesses the capability to handle various tasks related to arithmetic and logic operations, including addition, subtraction, shifting operations, as well as Boolean comparisons such as XOR, OR, AND, and NOT operations. It operates on binary numbers and can execute mathematical and bitwise operations. The ALU consists of two units: the arithmetic unit (AU) and the logic unit (LU). By utilizing operands and codes, the ALU determines which operations to perform based on the input data provided. Once the ALU completes processing the input, the resulting information is sent to the computer's memory.

Here are the main functions of an ALU:

Arithmetic Operations: The ALU performs various arithmetic operations on binary numbers, such as addition, subtraction, multiplication, and division. It uses binary addition and subtraction circuits to handle these operations efficiently.

Logical Operations: The ALU executes logical operations on binary data, including AND, OR, XOR (exclusive OR), and NOT. These operations manipulate individual bits or binary values to determine logical relationships and produce logical results.

Comparison Operations: The ALU performs comparison operations to determine the relationship between two binary values. It can compare if two values are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other. The result of these comparisons is typically represented by setting specific flags or registers in the CPU.

Bitwise Operations: The ALU carries out bitwise operations, which manipulate individual bits in binary numbers. These operations include shifting the bits left or right, rotating bits, and masking operations. Bitwise operations are commonly used in tasks such as data manipulation, encryption, and signal processing.

Conditional Operations: The ALU supports conditional operations, enabling the CPU to execute different instructions based on certain conditions. For example, it can perform conditional branching, where the CPU jumps to a specific instruction address based on the result of a comparison operation.

Data Movement: The ALU may also handle data movement operations within the CPU. This involves transferring data between registers, memory, and other CPU components.

ENCODER ​

An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n (or fewer) input lines and n output lines.

PRIORITY ENCODER ​

A priority encoder is an encoder circuit that includes the priority function. The operation of the priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence. In addition to the two outputs x and y , the circuit has a third output designated by V ; this is a valid bit indicator that is set to 1 when one or more inputs are equal to 1. If all inputs are 0, there is no valid input and V is equal to 0. The other two outputs are not inspected when V equals 0 and are specified as don’t-care conditions.

x = D2+ D3
y = D3 + D1 D 2
V = D0 + D1 + D2 + D3

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DECODER ​

A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines.The decoders presented here are called n -to- m -line decoders, where m … 2^n.

3-8 LINE DECODER ​

The three inputs are decoded into eight outputs, each representing one of the minterms of the three input variables. The three inverters provide the complement of the inputs, and each one of the eight AND gates generates one of the minterms.

2-4 LINE DECODER WITH ENABLE INPUT ​

The circuit operates with complemented outputs and a complement enable input. The decoder is enabled when E is equal to 0 (i.e., active-low enable). As indicated by the truth table, only one output can be equal to 0 at any given time; all other outputs are equal to 1. The output whose value is equal to 0 represents the minterm selected by inputs A and B . The circuit is disabled when E is equal to 1, regardless of the values of the other two inputs. When the circuit is disabled, none of the outputs are equal to 0 and none of the minterms are selected.

HOW TO MAKE A VERILOG PROGRAM ​

Create a New Project in your own version of Quartus Prime. ​

Select an appropriate directory for your Verilog project files and create an empty project file template. ​

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Use the 10M50DAF484C7G Board from the MAX 10 Family. ​

Set ModelSim as your Simulation Tool (ModelSim must be installed prior) and finish the initialization of the project. ​

Click on the file icon in the top left corner and create a new Verilog HDL file. ​

When you wish to save your program, simply use Ctrl+S or click the Save icon in the top left corner. ​

Before running your program, you must first set a testbench for it. Do this by going into the Assignments menu and clicking Settings. ​

Create a new Test Bench if you are creating one for a new program that has not been made before. ​

Name your Test Bench appropriately (usually just the name of the test bench file) and add it to the list of Test Benches. ​

After setting your testbench, you can now run and compile your program by clicking on the third play button. ​

You will be able to view your circuit design and how it is structured, and simulate results using the test bench by going to the Tools menu. ​

BIBLIOGRAPHY ​

  1. Digital Design, 5th Edition by M Morris Mano and Michael Ciletti
  2. Digital Fundamentals by Floyd and Jain
  3. electronicshub.org/demultiplexerdemux
  4. tutorialspoint.com/digital_circuits/digital_circuits_flip_flops
  5. tutorialspoint.com/digital_circuits/digital_circuits_demultiplexers
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Single Cycle Processor ​

Table of Contents ​

Sl No.TopicPage No.
1Overview1
2Prerequisites2
3Theory- Control Unit3
4Theory- Datapath8
5Implementation22
1Top Level Module22
2Data Memory24
3Instruction Memory25
4Microprocessor Top Level (MIPS)27
5Controller29
6Main Decoder31
7ALU Decoder33
8Datapath35
9Register File38
10Other Functional Units41
6How to Run Instructions?44
7Test Cases for Various Instructions46
8References53

1. Overview ​

Till now you have learned to design sequential and combinational logic, in this section you will learn how to create a single cycle processor, specifically the MIPS microprocessor.

This section combines almost every concept covered so far. Abstraction of block diagrams and Verilog HDLis used to describe the arrangement of each component. We exploit regularity and modularity by reusing already created blocks such as ALUs, multiplexers and register files. The microarchitecture is partitioned into datapath and control units. The MIPS microprocessor datapath uses the register file, ALU, memory unit, and instruction decoder to execute instructions. The register file stores data and instructions, the ALU performs operations, the memory unit accesses and stores data, and the instruction decoder controls data flow. The control unit of a MIPS microprocessor generates control signals that direct the flow of data between components in the datapath, ensuring that instructions are executed correctly. It receives instructions from the decoder, directs data flow to the correct components, and controls instruction timing.
Together, the datapath and control units work to execute instructions in the MIPS microprocessor.
We will focus on the single-cycle implementation of a subset of MIPS instructions. Additionally, we will compare single-cycle, multicycle, and pipelined microarchitectures for the MIPS processor.

2. Prerequisites ​

To create a Verilog MIPS single cycle processor, you should have a strong understanding of digital logic design, computer architecture, and Verilog programming.

Some of the specific prerequisites include-

  • Knowledge of digital logic design concepts, such as combinational and sequential circuits, logic gates, flip-flops, and registers and implementing these in Verilog HDL.

  • Understanding of computer architecture principles, including datapath and control unit design, memory organisation, instruction decoding, and input/output interfaces. These are also covered once more in the “Theory” section of our module.

  • Experience with Verilog programming, including the ability to write and understand Verilog code, testbenches, and simulation results.

  • Ability to use simulation and synthesis tools, such as ModelSim, Quartus, to simulate and synthesise Verilog code.

  • Knowledge of computer organisation and assembly language programming is also beneficial, as it provides context for understanding the MIPS single cycle processor and its operation.

Additionally, it would be helpful if you were familiar with the MIPS instruction set architecture, including its various instruction formats, opcode values, and functionality.

3. Control Unit ​

This section covers an implementation of our MIPS subset, which is created by adding a basic control function to the datapath discussed in the previous section. Support for load word (lw), store word (sw), branch equal (beq), and arithmetic-logical instructions like add, sub, AND, OR, and set on less than are all included in this version. It is implemented in 2 parts: the main control Unit and ALU Control Unit. Firstly we look at the instruction format.

CU

Instruction Format ​

The 32 bit MIPS instruction can be broken down into the following parts

fig 2

The op field, called the opcode, is always contained in bits 31:26. We will refer to this field as Op[5:0] by standard notation.

  • The two registers to be read are always specified by the rs and rt fields, at positions 25:21 and 20:16. This is true for the R-type instructions, branch equal, and store.

  • The base register for load and store instructions is always in bit positions 25:21 (rs).

  • The 16-bit offset for branch equal, load, and store is always in positions 15:0.

  • The destination register is in one of two places. For a load, it is in bit positions 20:16 (rt), while for an R-type instruction it is in bit positions 15:11 (rd). Thus, we will need to add a multiplexor to select which field of the instruction is used to indicate the register number to be written.

Main Control Unit (Main Decoder) ​

The control unit computes the control ignals based on the opcode and funct fields of the instruction, [31:26] and [5:0].

Most of the control information comes from the opcode, but R-type instructions also use the funct field to determine the ALU operation. The majority of the outputs from the opcode are computed by the main decoder. The 6 bits of the opcode are decoded into various control signals of the Main Decoder as shown in Fig. 3.

Simple PLA Implementation

Fig 3. Simple PLA Implementation

Table 1 explains each of the control signals in detail with all the important information. These nine control (two from ALUOp which are explained later) signals are set on the basis of six input signals to the control unit, which are the opcode bits 31 to 26.

Control SignalsDeassertedAsserted
RegDstThe write register number comes from the rt field (20:16)The write register number comes from the rd field (15:11)
RegWrite-The register on the write register input is written with the value of the Write data input.
ALUSrcSecond ALU Operand is the second register file output.Second ALU Operand is the sign extended offset (16 bit to 32 bits)
PCSrcPC = PC + 4 (For sequential exec.)PC is replaced by branch target.
MemRead-Data memory contents designated by address input are put in Read Data Output.
MemWrite-Data memory contents designated by address input are put in Write Data Output.
MemtoRegWrite Data is fed input from ALU.Write Data is fed input from Data Memory.

Table 1. Different Control Signals for the different MUXs

With the exception of the PCSrc control line, the control unit can set all of the control signals based only on the opcode field of the instruction. If the instruction is branch on equal and the ALU's Zero output is asserted, then the PCSrc control line should also be asserted. We must AND the Zero signal from the ALU with the Branch signal from the control unit in order to produce the PCSrc signal.

ALU Control Unit (ALU Decoder) ​

Depending on the instruction class, the ALU will need to perform one of these functions.

Table 2. ALU Control Lines

The main decoder determines a 2-bit ALUOp signal which is used as input for ALU Decoder along with the 6-bit funct (or function) field in the low-order bits of the instruction. The 4 bit output signal of the ALU Control Unit represents the operation to be carried out by the ALU. Fig 4. ALU Hardware Implementation

The 2 bit ALUOp sent by the Control Unit indicates whether the operation to be performed should be add (00) for loads and stores, subtract (01) for beq, or determined by the operation encoded in the funct field (10).

Understanding the optimal implementation: ​

Using multiple levels of control can reduce the size of the main control unit. Using several smaller control units may also potentially increase the speed of the control unit. Such optimizations are important, since the speed of the control unit is often critical to clock cycle time

ALU Control Truth Table ​

Input-Output Truth Table ​

4. Datapath ​

A datapath is the part of a computer processor that performs arithmetic and logic operations on data. It is a digital circuit that consists of registers, an arithmetic logic unit (ALU), and multiplexers.

The datapath receives instructions and data from the processor's memory and performs the necessary operations specified by the instructions. The ALU performs arithmetic and logical operations on the data, and the registers store intermediate and final results.

The datapath also includes multiplexers that allow the selection of different input values based on control signals. The control signals are generated by the control unit, which coordinates the operations of the datapath to execute instructions.

The datapath operates on words of data. MIPS is a 32-bit architecture, so we will use a 32-bit datapath. The datapath first decodes the instruction for the control unit which then sets the different multiplexers thereby fixing the datapath. We will split the datapath into different state elements and try to learn them one by one and finally piece them together to create a complete datapath.

State elements ​

There are 5 main state elements required for building the datapath.

a Instruction Memory ​

The program counter contains the address of the instruction to be executed. The first step is to read this instruction from the element called instruction memory. The instruction memory takes the address in PC as the input and fetches the 32 bit instruction, labelled instr.

The processor’s actions depend on the specific instruction that was fetched.

b Register File ​

The register file contains all the available registers. It has two read ports and one write port. Since MIPS architecture contains 32 registers, each register is identified by a unique 5 bit number (log2 32). This unique 5 bit number is given as the input in both read and write ports. The contents of the registers specified via the read ports are given as the output. If the control signal RegWrite is set, the data given in the data port is written into the register given in the write port.

c) ALU ​

ALU performs different arithmetic operations on the data depending on the signal received from the control unit. It has two data input ports and an input from the control unit which specifies the operation to be performed. The final result is output through ALU result and zero port is set to 1 if the result is zero.

d Data Memory ​

The memory unit is a state element with inputs for the address and the write data, and a single output for the read result.There are separate read and write controls, called MemRead and MemWrite. Only one of these may be asserted at a time.

  • If MemRead is set then value at the address given is fetched and outputted through the read data port.
  • If MemWrite is set then the value at the address is changed to write data.

e) Sign extension ​

To understand what sign extension is, let’s take an example. Consider the 4 bit number 1100. If we were to sign extend it to an 8 bit number, we take the MSB which in this case is 1 and extend it to make the upper half of the 8 bit number keeping the lower same as the initial 4 bits which gives us 1111 1100. Similarly, this element sign extends a 16 bit number into a 32 bit number.

Now that we have seen the different state elements involved in a datapath, let's see the datapath followed by different MIPS instructions. Since we are considering MIPS microprocessor, each instruction is 32 bits long.

  • add It is an R-type instruction of the form add $rd,$rs,$rt The R-type instruction format is

The datapath for add instruction is as follows :

  1. Grab the instruction address from the PC.

PC

  1. Decode instruction.

Decoder

  1. Pass rs,rt and rd into read register and write register ports.

Register

  1. Retrieve data from read register 1 and register 2 (rs and rt).

  1. Pass contents of rs and rt into the ALU as operands for the addition operation. The only difference between different arithmetic operations is in the ALU operation performed.

  1. Return back the ALU result to the register file as the Write data argument. The data will be written into the Write register specified by the rd field.

  1. Increment the value of PC to PC+4 to move on to the next instruction.

  • lw(load word)
    The lw instruction is of the form lw $rt immediate($rs). It has an I-type instruction format.

lw

The load word instruction copies the data stored at the address ‘immediate+value(rs)’ and stores it into the register rt.
The datapath for lw instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. The control unit examines the most significant five bits of the instruction to determine the necessary datapath configuration.

  3. The register file receives the two register numbers rs and rt, with rs connected to the read port and rt to the write port. Read data 1 port outputs the data stored in rs.

  4. This output is then added to the sign-extended immediate using ALU.

  5. The ALU result is sent to the data memory unit, which reads the data stored at the address specified by the ALU result.

  6. Finally, the data read from the memory is returned to the register file, which writes it into register rt.

  7. PC is incremented to PC+4.

lw

  • sw(store word) sw instruction is of the form

    v
    sw $rt immediate($rs)

    The instruction format is again of the form I-type with an opcode 43.

The store word instruction writes the data stored in the register rt into the memory address ‘value(rs)+immediate ’.

The datapath for sw instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five bits and determines the necessary datapath configuration by setting the multiplexers.

  3. The register file receives two register numbers rs and rt, with rs connected to read port1 and rt connected to read port2. The data stored in registers rs and rt is output through the read data port1 and read data port2 respectively.

  4. The read data1 is then added to the sign-extended immediate using ALU.

  5. The ALU result along with read data2 (which contains the value stored in register rt) is sent to the data memory unit, which writes the read data2 into the address specified by the ALU result.

  6. PC is incremented to PC+4.

sw

  • beq(branch if equal)

The beq instruction is of the form

mips
    beq $rs ,$rt ,immediate

It has an I-type instruction format.

I-type

It compares the contents of rs and rt to check if they are equal and uses the 16-bit immediate field to compute the target address of the branch relative to the current address.

The datapath for beq instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five its and determines the necessary datapath configuration.

  3. The register file receives two register numbers rs and rt in the read register port and outputs the contents in rs and rt.

  4. ALU subtracts the value of rs from rt and sets the zero port to 1 if the result is 0.

  5. The immediate value is sign extended and then shifted left by 2 bits.

  6. PC is incremented to PC+4 and is added with the immediate value to give the branch target.

  7. PC is changed to the branch target if zero port was set to 1.

beq

  • j (jump)

The jump instruction is of the form j targaddr. It has a J-type instruction format with opcode 2.

This instruction uses the 26 bit targaddr to compute jump address and updates the value of PC to jump address.

J-type

The datapath for j instruction is as follows :-

  1. The instruction memory reads the PC and outputs the instruction.

  2. Control unit examines the most significant five bits and determines the necessary datapath configuration.

  3. The 26 bit targaddr is shifted left by 2 bits to create a 28 bit result

  4. Concatenate the result with the upper 4 bits of PC+4 to get the jump address.

  5. Finally, the PC gets updated to the jump address.

j

The Final Datapath ​

Final

Fig 4. Simple datapath with control unit (for R-type and I-type)

Here, the input to the control unit is the 6-bit opcode field from the instruction. The outputs are the control signals which serve various purposes :-

  • RegDst, ALUSrc, MemtoReg - 1-bit signals that control the multiplexors.

  • RegWrite, MemRead, MemWrite - Signals that control reads and writes in the data memory and register file.

  • Branch - Signal used in checking if a branch is required.

  • ALUOp - 2-bit control signal for the ALU.

Note that here, the AND gate is used to combine the Branch control signal with the Zero output from the ALU. This is responsible for the selection of the next PC.

Role of Multiplexors ​

As seen above, there are 4 multiplexors required at various stages of the datapath. They are needed in order to implement both R-type and I-type instructions using the same datapath. Their roles are explained below :-

  1. MUX 1 - This MUX determines which register needs to be written into using the RegDst control signal. If it’s 0, the write register number comes from the rt field (in the case of I-type), whereas if it’s 1, the write register number comes from the rd field (for R-type instructions)

  2. MUX 2 - This MUX is placed at the ALU input with ALUSrc as the select line. When it’s 0, an arithmetic-logical instruction is taking place, and the second ALU operand is the data read from the second register. When it’s 1, a memory instruction is taking place, with the second ALU operand being the sign-extended 16-bit immediate field from instruction.

  3. MUX 3 - It chooses which value is stored in the destination register using the MemtoReg control signal. This value comes from the ALU (for an R-type instruction) or the memory (for a load).

  4. MUX 4 - The final MUX is used to select if the PC moves onto the sequentially following instruction address (PC + 4) or branches to a target address. The control signal that achieves this is the output of the AND gate which is 1 in case of a branch instruction and 0 otherwise.

Final

Fig 4. Datapath with Jump implementation

Additionally to implement the Jump instruction in the same datapath, an additional MUX, controlled by the jump control signal, is used to determine whether to move to the jump target address or the next consequent instruction. This jump target is obtained by shifting the lower 26 bits of the jump instruction left 2 bits (ie. multiplying by 4) and then concatenating the upper 4 bits of PC + 4 as the high-order bits, thus yielding a 32-bit address.

5. Implementation ​

1. Top level module ​

Top

v
module top (input clk, reset, 
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Single Cycle Processor ​
Table of Contents ​
Sl No.TopicPage No.
1Overview1
2Prerequisites2
3Theory- Control Unit3
4Theory- Datapath8
5Implementation22
1Top Level Module22
2Data Memory24
3Instruction Memory25
4Microprocessor Top Level (MIPS)27
5Controller29
6Main Decoder31
7ALU Decoder33
8Datapath35
9Register File38
10Other Functional Units41
6How to Run Instructions?44
7Test Cases for Various Instructions46
8References53
1. Overview ​
Till now you have learned to design sequential and combinational logic, in this section you will learn how to create a single cycle processor, specifically the MIPS microprocessor.
This section combines almost every concept covered so far. Abstraction of block diagrams and Verilog HDLis used to describe the arrangement of each component. We exploit regularity and modularity by reusing already created blocks such as ALUs, multiplexers and register files. The microarchitecture is partitioned into datapath and control units. The MIPS microprocessor datapath uses the register file, ALU, memory unit, and instruction decoder to execute instructions. The register file stores data and instructions, the ALU performs operations, the memory unit accesses and stores data, and the instruction decoder controls data flow. The control unit of a MIPS microprocessor generates control signals that direct the flow of data between components in the datapath, ensuring that instructions are executed correctly. It receives instructions from the decoder, directs data flow to the correct components, and controls instruction timing.
 Together, the datapath and control units work to execute instructions in the MIPS microprocessor.
 We will focus on the single-cycle implementation of a subset of MIPS instructions. Additionally, we will compare single-cycle, multicycle, and pipelined microarchitectures for the MIPS processor.
2. Prerequisites ​
To create a Verilog MIPS single cycle processor, you should have a strong understanding of digital logic design, computer architecture, and Verilog programming.
Some of the specific prerequisites include-
  • Knowledge of digital logic design concepts, such as combinational and sequential circuits, logic gates, flip-flops, and registers and implementing these in Verilog HDL.
  • Understanding of computer architecture principles, including datapath and control unit design, memory organisation, instruction decoding, and input/output interfaces. These are also covered once more in the “Theory” section of our module.
  • Experience with Verilog programming, including the ability to write and understand Verilog code, testbenches, and simulation results.
  • Ability to use simulation and synthesis tools, such as ModelSim, Quartus, to simulate and synthesise Verilog code.
  • Knowledge of computer organisation and assembly language programming is also beneficial, as it provides context for understanding the MIPS single cycle processor and its operation.
Additionally, it would be helpful if you were familiar with the MIPS instruction set architecture, including its various instruction formats, opcode values, and functionality.
3. Control Unit ​
This section covers an implementation of our MIPS subset, which is created by adding a basic control function to the datapath discussed in the previous section. Support for load word (lw), store word (sw), branch equal (beq), and arithmetic-logical instructions like add, sub, AND, OR, and set on less than are all included in this version. It is implemented in 2 parts: the main control Unit and ALU Control Unit. Firstly we look at the instruction format.
CU
Instruction Format ​
The 32 bit MIPS instruction can be broken down into the following parts
fig 2
The op field, called the opcode, is always contained in bits 31:26. We will refer to this field as Op[5:0] by standard notation.
  • The two registers to be read are always specified by the rs and rt fields, at positions 25:21 and 20:16. This is true for the R-type instructions, branch equal, and store.
  • The base register for load and store instructions is always in bit positions 25:21 (rs).
  • The 16-bit offset for branch equal, load, and store is always in positions 15:0.
  • The destination register is in one of two places. For a load, it is in bit positions 20:16 (rt), while for an R-type instruction it is in bit positions 15:11 (rd). Thus, we will need to add a multiplexor to select which field of the instruction is used to indicate the register number to be written.
Main Control Unit (Main Decoder) ​
The control unit computes the control ignals based on the opcode and funct fields of the instruction, [31:26] and [5:0].
Most of the control information comes from the opcode, but R-type instructions also use the funct field to determine the ALU operation. The majority of the outputs from the opcode are computed by the main decoder. The 6 bits of the opcode are decoded into various control signals of the Main Decoder as shown in Fig. 3.
Simple PLA Implementation 
Fig 3. Simple PLA Implementation
Table 1 explains each of the control signals in detail with all the important information. These nine control (two from ALUOp which are explained later) signals are set on the basis of six input signals to the control unit, which are the opcode bits 31 to 26.
Control SignalsDeassertedAsserted
RegDstThe write register number comes from the rt field (20:16)The write register number comes from the rd field (15:11)
RegWrite-The register on the write register input is written with the value of the Write data input.
ALUSrcSecond ALU Operand is the second register file output.Second ALU Operand is the sign extended offset (16 bit to 32 bits)
PCSrcPC = PC + 4 (For sequential exec.)PC is replaced by branch target.
MemRead-Data memory contents designated by address input are put in Read Data Output.
MemWrite-Data memory contents designated by address input are put in Write Data Output.
MemtoRegWrite Data is fed input from ALU.Write Data is fed input from Data Memory.
Table 1. Different Control Signals for the different MUXs
With the exception of the PCSrc control line, the control unit can set all of the control signals based only on the opcode field of the instruction. If the instruction is branch on equal and the ALU's Zero output is asserted, then the PCSrc control line should also be asserted. We must AND the Zero signal from the ALU with the Branch signal from the control unit in order to produce the PCSrc signal.
ALU Control Unit (ALU Decoder) ​
Depending on the instruction class, the ALU will need to perform one of these functions.
 Table 2. ALU Control Lines
The main decoder determines a 2-bit ALUOp signal which is used as input for ALU Decoder along with the 6-bit funct (or function) field in the low-order bits of the instruction. The 4 bit output signal of the ALU Control Unit represents the operation to be carried out by the ALU.  Fig 4. ALU Hardware Implementation
The 2 bit ALUOp sent by the Control Unit indicates whether the operation to be performed should be add (00) for loads and stores, subtract (01) for beq, or determined by the operation encoded in the funct field (10).
Understanding the optimal implementation: ​
Using multiple levels of control can reduce the size of the main control unit. Using several smaller control units may also potentially increase the speed of the control unit. Such optimizations are important, since the speed of the control unit is often critical to clock cycle time
ALU Control Truth Table ​
Input-Output Truth Table ​
4. Datapath ​
A datapath is the part of a computer processor that performs arithmetic and logic operations on data. It is a digital circuit that consists of registers, an arithmetic logic unit (ALU), and multiplexers.
The datapath receives instructions and data from the processor's memory and performs the necessary operations specified by the instructions. The ALU performs arithmetic and logical operations on the data, and the registers store intermediate and final results.
The datapath also includes multiplexers that allow the selection of different input values based on control signals. The control signals are generated by the control unit, which coordinates the operations of the datapath to execute instructions.
The datapath operates on words of data. MIPS  is a 32-bit architecture, so we will use a 32-bit datapath. The datapath first decodes the instruction for the control unit which then sets the different multiplexers thereby fixing the datapath. We will split the datapath into different state elements and try to learn them one by one and finally piece them together to create a complete datapath.
State elements ​
There are 5 main state elements required for building the datapath.
a Instruction Memory ​
The program counter contains the address of the instruction to be executed. The first step is to read this instruction from the element called instruction memory. The instruction memory takes the address in PC as the input and fetches the 32 bit instruction, labelled instr.
The processor’s actions depend on the specific instruction that was fetched.
b Register File ​
The register file contains all the available registers. It has two read ports and one write port. Since MIPS architecture contains 32 registers, each register is identified by a unique 5 bit number (log2 32). This unique 5 bit number is given as the input in both read and write ports. The contents of the registers specified via the read ports are given as the output. If the control signal RegWrite is set, the data given in the data port is written into the register given in the write port.
c) ALU ​
ALU performs different arithmetic operations on the data depending on the signal received from the control unit. It has two data input ports and an input from the control unit which specifies the operation to be performed. The final result is output through ALU result and zero port is set to 1 if the result is zero.
d Data Memory ​
The memory unit is a state element with inputs for the address and the write data, and a single output for the read result.There are separate read and write controls, called MemRead and MemWrite. Only one of these may be asserted at a time.
  • If MemRead is set then value at the address given is fetched and outputted through the read data port.
  • If MemWrite is set then the value at the address is changed to write data.
e) Sign extension ​
To understand what sign extension is, let’s take an example. Consider the 4 bit number 1100. If we were to sign extend it to an 8 bit number, we take the MSB which in this case is 1 and extend it to make the upper half of the 8 bit number keeping the lower same as the initial 4 bits which gives us 1111 1100. Similarly, this element sign extends a 16 bit number into a 32 bit number.
Now that we have seen the different state elements involved in a datapath, let's see the datapath followed by different MIPS instructions. Since we are considering MIPS microprocessor, each instruction is 32 bits long.
  • add It is an R-type instruction of the form add $rd,$rs,$rt The R-type instruction format is
The datapath for add instruction is as follows :
  1. Grab the instruction address from the PC.
PC
  1. Decode instruction.
Decoder
  1. Pass rs,rt and rd into read register and write register ports.
Register
  1. Retrieve data from read register 1 and register 2 (rs and rt).
  1. Pass contents of rs and rt into the ALU as operands for the addition operation. The only difference between different arithmetic operations is in the ALU operation performed.
  1. Return back the ALU result to the register file as the Write data argument. The data will be written into the Write register specified by the rd field.
  1. Increment the value of PC to PC+4 to move on to the next instruction.
  • lw(load word)
     The lw instruction is of the form lw $rt immediate($rs). It has an I-type instruction format.
lw
The load word instruction copies the data stored at the address ‘immediate+value(rs)’ and stores it into the register rt.
 The datapath for lw instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. The control unit examines the most significant five bits of the instruction to determine the necessary datapath configuration.
  3. The register file receives the two register numbers rs and rt, with rs connected to the read port and rt to the write port. Read data 1 port outputs the data stored in rs.
  4. This output is then added to the sign-extended immediate using ALU.
  5. The ALU result is sent to the data memory unit, which reads the data stored at the address specified by the ALU result.
  6. Finally, the data read from the memory is returned to the register file, which writes it into register rt.
  7. PC is incremented to PC+4.
lw
  •  sw(store word) sw instruction is of the form
    v
    sw $rt immediate($rs)
    The instruction format is again of the form I-type with an opcode 43.
The store word instruction writes the data stored in the register rt into the memory address ‘value(rs)+immediate ’.
The datapath for sw instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five bits and determines the necessary datapath configuration by setting the multiplexers.
  3. The register file receives two register numbers rs and rt, with rs connected to read port1 and rt connected to read port2. The data stored in registers rs and rt is output through the read data port1 and read data port2 respectively.
  4. The read data1 is then added to the sign-extended immediate using ALU.
  5. The ALU result along with read data2 (which contains the value stored in register rt) is sent to the data memory unit, which writes the read data2 into the address specified by the ALU result.
  6. PC is incremented to PC+4.
sw
  • beq(branch if equal)
The beq instruction is of the form
mips
    beq $rs ,$rt ,immediate
It has an I-type instruction format.
I-type
It compares the contents of rs and rt to check if they are equal and uses the 16-bit immediate field to compute the target address of the branch relative to the current address.
The datapath for beq instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five its and determines the necessary datapath configuration.
  3. The register file receives two register numbers rs and rt in the read register port and outputs the contents in rs and rt.
  4. ALU subtracts the value of rs from rt and sets the zero port to 1 if the result is 0.
  5. The immediate value is sign extended and then shifted left by 2 bits.
  6. PC is incremented to PC+4 and is added with the immediate value to give the branch target.
  7. PC is changed to the branch target if zero port was set to 1.
beq
  • j (jump)
The jump instruction is of the form j targaddr. It has a J-type instruction format with opcode 2.
This instruction uses the 26 bit targaddr to compute jump address and updates the value of PC to jump address.
J-type
The datapath for j instruction is as follows :-
  1. The instruction memory reads the PC and outputs the instruction.
  2. Control unit examines the most significant five bits and determines the necessary datapath configuration.
  3. The 26 bit targaddr is shifted left by 2 bits to create a 28 bit result
  4. Concatenate the result with the upper 4 bits of PC+4 to get the jump address.
  5. Finally, the PC gets updated to the jump address.
j
The Final Datapath ​
Final
Fig 4. Simple datapath with control unit (for R-type and I-type)
Here, the input to the control unit is the 6-bit opcode field from the instruction. The outputs are the control signals which serve various purposes :-
  • RegDst, ALUSrc, MemtoReg - 1-bit signals that control the multiplexors.
  • RegWrite, MemRead, MemWrite - Signals that control reads and writes in the data memory and register file.
  • Branch - Signal used in checking if a branch is required.
  • ALUOp - 2-bit control signal for the ALU.
Note that here, the AND gate is used to combine the Branch control signal with the Zero output from the ALU. This is responsible for the selection of the next PC.
Role of Multiplexors ​
As seen above, there are 4 multiplexors required at various stages of the datapath. They are needed in order to implement both R-type and I-type instructions using the same datapath. Their roles are explained below :-
  1. MUX 1 - This MUX determines which register needs to be written into using the RegDst control signal. If it’s 0, the write register number comes from the rt field (in the case of I-type), whereas if it’s 1, the write register number comes from the rd field (for R-type instructions)
  2. MUX 2 - This MUX is placed at the ALU input with ALUSrc as the select line. When it’s 0, an arithmetic-logical instruction is taking place, and the second ALU operand is the data read from the second register. When it’s 1, a memory instruction is taking place, with the second ALU operand being the sign-extended 16-bit immediate field from instruction.
  3. MUX 3 - It chooses which value is stored in the destination register using the MemtoReg control signal. This value comes from the ALU (for an R-type instruction) or the memory (for a load).
  4. MUX 4 - The final MUX is used to select if the PC moves onto the sequentially following instruction address (PC + 4) or branches to a target address. The control signal that achieves this is the output of the AND gate which is 1 in case of a branch instruction and 0 otherwise.
Final
Fig 4. Datapath with Jump implementation
Additionally to implement the Jump instruction in the same datapath, an additional MUX, controlled by the jump control signal, is used to determine whether to move to the jump target address or the next consequent instruction. This jump target is obtained by shifting the lower 26 bits of the jump instruction left 2 bits (ie. multiplying by 4) and then concatenating the upper 4 bits of PC + 4 as the high-order bits, thus yielding a 32-bit address.
5. Implementation ​
1. Top level module ​
Top
v
module top (input clk, reset, 
     output [31:0] writedata, dataadr, 
     output memwrite); 
     wire [31:0] pc, instr, readdata; 
diff --git a/docs/.vitepress/dist/assets/Verilog_SingleCycle.md.7mWeb3Kr.lean.js b/docs/.vitepress/dist/assets/Verilog_SingleCycle.md.7mWeb3Kr.lean.js
new file mode 100644
index 0000000..9ace8bb
--- /dev/null
+++ b/docs/.vitepress/dist/assets/Verilog_SingleCycle.md.7mWeb3Kr.lean.js
@@ -0,0 +1 @@
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deleted file mode 100644
index f732951..0000000
--- a/docs/.vitepress/dist/assets/Verilog_SingleCycle.md.DvYIvDh1.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.CgMb17D3.js";const n="/assets/singlecycle-0013.D6xsb9Bh.png",e="/assets/singlecycle-0017.CsR-Gwit.png",l="/assets/singlecycle-0020.XlAfVWge.png",h="/assets/singlecycle-0023.z1LVUBzF.png",p="/assets/singlecycle-0026.C6JaUoQ9.png",k="/assets/singlecycle-0027.ChN4ySyT.png",r="/assets/singlecycle-0030.BEZcafmD.png",d="/assets/singlecycle-0033.C-B0skUE.png",E="/assets/singlecycle-0036.hCbdKgzO.png",o="/assets/singlecycle-0037.DN7JwD_b.png",c="/assets/singlecycle-0040.DzuCZnH4.png",g="/assets/singlecycle-0041.DguRb9xh.png",y="/assets/singlecycle-0044.Bh4VFCKF.png",u="/assets/singlecycle-0045.Bts3iwtV.png",F="/assets/singlecycle-0046.DMG-WAVD.png",m="/assets/singlecycle-0049.Bb3hbLru.png",C="/assets/singlecycle-0050.C0OQvrsm.png",b="/assets/singlecycle-0053.riT0reSK.png",f="/assets/singlecycle-0054.DtcVKxV5.png",B="/assets/singlecycle-0057._jB5dNCX.png",w="/assets/singlecycle-0058.kZmqGpg9.png",A="/assets/singlecycle-0061.DLiLLvpn.png",v="/assets/singlecycle-0065.P3xu36xq.png",D="/assets/singlecycle-0066.StzZ_r5K.png",x="/assets/singlecycle-0069.sFli2F5X.png",_="/assets/singlecycle-0072.CUr1uECj.png",q="/assets/singlecycle-0073.CxG6ZJA4.png",T="/assets/singlecycle-0076.C5bAn5jN.png",P="/assets/singlecycle-0079.gNbxYTcc.png",U="/assets/singlecycle-0082.DQiZ0qVK.jpg",I="/assets/singlecycle-0088.BSYfCwJb.jpg",L="/assets/singlecycle-0092.ChkEmr9X.jpg",M="/assets/singlecycle-0097.D48mp-L4.jpg",S="/assets/singlecycle-0102.NMndrpRj.jpg",$="/assets/singlecycle-0122._9sweLFO.jpg",R="/assets/singlecycle-0110.B09az6UL.png",O="/assets/singlecycle-0113.al9_Q5p9.png",W="/assets/singlecycle-0125.BY3On3Mc.png",j="/assets/singlecycle-0134.Qjaml-am.png",ss=JSON.parse('{"title":"Single Cycle Processor","description":"","frontmatter":{},"headers":[],"relativePath":"Verilog/SingleCycle.md","filePath":"Verilog/SingleCycle.md"}'),V={name:"Verilog/SingleCycle.md"},N=t("",279),z=[N];function H(X,Y,Z,J,G,K){return a(),i("div",null,z)}const is=s(V,[["render",H]]);export{ss as __pageData,is as default};
diff --git a/docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.js b/docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.js
similarity index 76%
rename from docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.js
rename to docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.js
index 02f8083..6f28a5e 100644
--- a/docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.js
+++ b/docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.js
@@ -1 +1 @@
-import{_ as e,c as r,o as t,a4 as o}from"./chunks/framework.CgMb17D3.js";const f=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the Verilog Guide","text":"","tagline":"This course covers the following topics : "},"features":[{"title":"Introduction To Verilog","details":"Learn the Basics of Verilog HDL and implement various circuits using Verilog.","link":"#introduction-to-verilog"},{"title":"Finite State Machines","details":"Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.","link":"#finite-state-machines"},{"title":"MIPS Single Cycle Processor","details":"Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.","link":"#single-cycle-mips-processor"}]},"headers":[],"relativePath":"Verilog/index.md","filePath":"Verilog/index.md"}'),a={name:"Verilog/index.md"},n=o('
​
Introduction to Verilog ​
Theory :
Documentation: Link to Main Documentation
 Video Explanation of Theory:
  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS) 
  2. Theory Vid Part 2 (PARITY-TILL END) 
Implementation :
 How to Run Verilog Files in Quartus: How to Run ? 
 Sample Codes: Link to Sample Codes 
 Video Explanation of Select Codes:
  1. Verilog Syntax 
  2. Adder Subtractor 
  3. DEMUX 
  4. Counter 
  5. Decoder 
     Assignment 1: Download Here
Finite State Machines ​
Theory :
 Documentation: Link to Main Documentation :simple-googledrive:
 Video Explanation of Concept:
  1.  Main Concept 
  2.  Syntax (Optional) 
Implementation :
Video Explanation of Code (From Documentation):
 Examples of FSM along with Code explanation 
Code Bank:  Link to Sample Codes 
Assignment 2:  Download Here 
Single Cycle MIPS Processor ​
Theory :
Documentation: Link to Main Documentation Video Explanation of Concept:
  1.  Control Unit Theory 
  2.  Datapath Theory 
Implementation :
 Video Explanation of Code (From Documentation) :
  1. Code Modules 1 to 5 explained 
  2. Code Modules 6 to 10 explained 
  3. All Testbenches explained 
     Code Bank:
     Link to Sample Codes 
     Assignment 3:  Download Here 
',22),i=[n];function l(s,h,c,p,g,d){return t(),r("div",null,i)}const b=e(a,[["render",l]]);export{f as __pageData,b as default};
+import{_ as e,c as r,o as t,a4 as o}from"./chunks/framework.DRnJpP2i.js";const f=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the Verilog Guide","text":"","tagline":"This course covers the following topics : "},"features":[{"title":"Introduction To Verilog","details":"Learn the Basics of Verilog HDL and implement various circuits using Verilog.","link":"#introduction-to-verilog"},{"title":"Finite State Machines","details":"Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.","link":"#finite-state-machines"},{"title":"MIPS Single Cycle Processor","details":"Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.","link":"#single-cycle-mips-processor"}]},"headers":[],"relativePath":"Verilog/index.md","filePath":"Verilog/index.md"}'),a={name:"Verilog/index.md"},n=o('
​
Introduction to Verilog ​
Theory :
Documentation: Link to Main Documentation
 Video Explanation of Theory:
  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS) 
  2. Theory Vid Part 2 (PARITY-TILL END) 
Implementation :
 How to Run Verilog Files in Quartus: How to Run ? 
 Sample Codes: Link to Sample Codes 
 Video Explanation of Select Codes:
  1. Verilog Syntax 
  2. Adder Subtractor 
  3. DEMUX 
  4. Counter 
  5. Decoder 
     Assignment 1: Download Here
Finite State Machines ​
Theory :
 Documentation: Link to Main Documentation :simple-googledrive:
 Video Explanation of Concept:
  1.  Main Concept 
  2.  Syntax (Optional) 
Implementation :
Video Explanation of Code (From Documentation):
 Examples of FSM along with Code explanation 
Code Bank:  Link to Sample Codes 
Assignment 2:  Download Here 
Single Cycle MIPS Processor ​
Theory :
Documentation: Link to Main Documentation Video Explanation of Concept:
  1.  Control Unit Theory 
  2.  Datapath Theory 
Implementation :
 Video Explanation of Code (From Documentation) :
  1. Code Modules 1 to 5 explained 
  2. Code Modules 6 to 10 explained 
  3. All Testbenches explained 
     Code Bank:
     Link to Sample Codes 
     Assignment 3:  Download Here 
',22),i=[n];function l(s,h,c,p,g,d){return t(),r("div",null,i)}const b=e(a,[["render",l]]);export{f as __pageData,b as default};
diff --git a/docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.lean.js b/docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.lean.js
similarity index 88%
rename from docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.lean.js
rename to docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.lean.js
index 8df49ef..34fe7b3 100644
--- a/docs/.vitepress/dist/assets/Verilog_index.md.BmIHPG-w.lean.js
+++ b/docs/.vitepress/dist/assets/Verilog_index.md.CgSFKGIP.lean.js
@@ -1 +1 @@
-import{_ as e,c as r,o as t,a4 as o}from"./chunks/framework.CgMb17D3.js";const f=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the Verilog Guide","text":"","tagline":"This course covers the following topics : "},"features":[{"title":"Introduction To Verilog","details":"Learn the Basics of Verilog HDL and implement various circuits using Verilog.","link":"#introduction-to-verilog"},{"title":"Finite State Machines","details":"Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.","link":"#finite-state-machines"},{"title":"MIPS Single Cycle Processor","details":"Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.","link":"#single-cycle-mips-processor"}]},"headers":[],"relativePath":"Verilog/index.md","filePath":"Verilog/index.md"}'),a={name:"Verilog/index.md"},n=o("",22),i=[n];function l(s,h,c,p,g,d){return t(),r("div",null,i)}const b=e(a,[["render",l]]);export{f as __pageData,b as default};
+import{_ as e,c as r,o as t,a4 as o}from"./chunks/framework.DRnJpP2i.js";const f=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"home","hero":{"name":"Welcome to the Verilog Guide","text":"","tagline":"This course covers the following topics : "},"features":[{"title":"Introduction To Verilog","details":"Learn the Basics of Verilog HDL and implement various circuits using Verilog.","link":"#introduction-to-verilog"},{"title":"Finite State Machines","details":"Design a Verilog-based FSM that enhances your circuits with efficient sequential control and decision-making capabilities.","link":"#finite-state-machines"},{"title":"MIPS Single Cycle Processor","details":"Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.","link":"#single-cycle-mips-processor"}]},"headers":[],"relativePath":"Verilog/index.md","filePath":"Verilog/index.md"}'),a={name:"Verilog/index.md"},n=o("",22),i=[n];function l(s,h,c,p,g,d){return t(),r("div",null,i)}const b=e(a,[["render",l]]);export{f as __pageData,b as default};
diff --git a/docs/.vitepress/dist/assets/about.md.CY5iuE6T.js b/docs/.vitepress/dist/assets/about.md.Dzg05ABX.js
similarity index 97%
rename from docs/.vitepress/dist/assets/about.md.CY5iuE6T.js
rename to docs/.vitepress/dist/assets/about.md.Dzg05ABX.js
index 255d016..2ee7dfa 100644
--- a/docs/.vitepress/dist/assets/about.md.CY5iuE6T.js
+++ b/docs/.vitepress/dist/assets/about.md.Dzg05ABX.js
@@ -1 +1 @@
-import{_ as e,c as a,o as r,a4 as t}from"./chunks/framework.CgMb17D3.js";const f=JSON.parse('{"title":"About Us","description":"","frontmatter":{},"headers":[],"relativePath":"about.md","filePath":"about.md"}'),i={name:"about.md"},o=t('
About Us ​
Welcome to the Hardware Lab at Computer Science and Engineering Department of National Institute of Technology, Calicut. We are a team of dedicated individuals who have come together to create a comprehensive resource for students studying computer hardware in the department.
Our Philosophy ​
Our mission is to provide students with a valuable tool that enhances their learning experience in the hardware lab course. We aim to simplify complex concepts, offer practical tips, and provide step-by-step guides to help students excel in their studies.
The Computer Science Department ​
The Computer Science Department of NITC is a leading academic department that fosters innovation, research, and excellence in the field of computer science. Our department offers a wide range of courses and programs designed to equip students with the knowledge and skills required to thrive in the ever-evolving world of technology.For more information visit https://minerva.nitc.ac.in/
The Hardware Lab Course Guide Team ​
Faculty :fontawesome-solid-computer: ​
The MIPS Team :simple-linkedin: ​
The Verilog Team :simple-linkedin: ​
Web and Repository Maintenance :simple-github: ​
Join Our Team ​
We are always looking to expand our team and welcome individuals who share our passion for computer hardware education. If you are interested in contributing to the Hardware Lab Course Guide or have any suggestions, we would love to hear from you. Please reach out to us at hwlab_csed@nitc.ac.in :octicons-mail-16:
Thank you for visiting the Computer Science Department's Hardware Lab Course Guide. We hope this resource serves as a valuable tool for your studies and contributes to your success in the fascinating world of computer hardware.
',18),n=[o];function l(s,h,c,d,u,m){return r(),a("div",null,n)}const b=e(i,[["render",l]]);export{f as __pageData,b as default};
+import{_ as e,c as a,o as r,a4 as t}from"./chunks/framework.DRnJpP2i.js";const f=JSON.parse('{"title":"About Us","description":"","frontmatter":{},"headers":[],"relativePath":"about.md","filePath":"about.md"}'),i={name:"about.md"},o=t('
About Us ​
Welcome to the Hardware Lab at Computer Science and Engineering Department of National Institute of Technology, Calicut. We are a team of dedicated individuals who have come together to create a comprehensive resource for students studying computer hardware in the department.
Our Philosophy ​
Our mission is to provide students with a valuable tool that enhances their learning experience in the hardware lab course. We aim to simplify complex concepts, offer practical tips, and provide step-by-step guides to help students excel in their studies.
The Computer Science Department ​
The Computer Science Department of NITC is a leading academic department that fosters innovation, research, and excellence in the field of computer science. Our department offers a wide range of courses and programs designed to equip students with the knowledge and skills required to thrive in the ever-evolving world of technology.For more information visit https://minerva.nitc.ac.in/
The Hardware Lab Course Guide Team ​
Faculty :fontawesome-solid-computer: ​
The MIPS Team :simple-linkedin: ​
The Verilog Team :simple-linkedin: ​
Web and Repository Maintenance :simple-github: ​
Join Our Team ​
We are always looking to expand our team and welcome individuals who share our passion for computer hardware education. If you are interested in contributing to the Hardware Lab Course Guide or have any suggestions, we would love to hear from you. Please reach out to us at hwlab_csed@nitc.ac.in :octicons-mail-16:
Thank you for visiting the Computer Science Department's Hardware Lab Course Guide. We hope this resource serves as a valuable tool for your studies and contributes to your success in the fascinating world of computer hardware.
',18),n=[o];function l(s,h,c,d,u,m){return r(),a("div",null,n)}const b=e(i,[["render",l]]);export{f as __pageData,b as default};
diff --git a/docs/.vitepress/dist/assets/about.md.CY5iuE6T.lean.js b/docs/.vitepress/dist/assets/about.md.Dzg05ABX.lean.js
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+import{_ as e,c as a,o as r,a4 as t}from"./chunks/framework.DRnJpP2i.js";const f=JSON.parse('{"title":"About Us","description":"","frontmatter":{},"headers":[],"relativePath":"about.md","filePath":"about.md"}'),i={name:"about.md"},o=t("",18),n=[o];function l(s,h,c,d,u,m){return r(),a("div",null,n)}const b=e(i,[["render",l]]);export{f as __pageData,b as default};
diff --git a/docs/.vitepress/dist/assets/app.BVAsbgWq.js b/docs/.vitepress/dist/assets/app.BfUHQ1UT.js
similarity index 90%
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--- a/docs/.vitepress/dist/assets/app.BVAsbgWq.js
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LOGIC GATES"]},"53":{"title":"Registers","titles":["BASIC LOGIC GATES"]},"54":{"title":"Four‐bit register","titles":["BASIC LOGIC GATES","Registers"]},"55":{"title":"Four bit register with parallel load**Gi = Ai AND Bi  **","titles":["BASIC LOGIC GATES","Registers"]},"56":{"title":"SHIFT REGISTERS","titles":["BASIC LOGIC GATES","Registers"]},"57":{"title":"SERIAL IN/SERIAL OUT REGISTERS","titles":["BASIC LOGIC GATES","Registers","SHIFT REGISTERS"]},"58":{"title":"Serial In/Parallel Out Shift Registers","titles":["BASIC LOGIC GATES","Registers","SHIFT REGISTERS"]},"59":{"title":"Parallel In/Serial Out Shift Registers","titles":["BASIC LOGIC GATES","Registers","SHIFT REGISTERS"]},"60":{"title":"Parallel In/Parallel Out Shift Registers","titles":["BASIC LOGIC GATES","Registers","SHIFT REGISTERS"]},"61":{"title":"COUNTERS","titles":["BASIC LOGIC GATES"]},"62":{"title":"BINARY RIPPLE COUNTER","titles":["BASIC LOGIC GATES","COUNTERS"]},"63":{"title":"BCD RIPPLE COUNTER","titles":["BASIC LOGIC GATES","COUNTERS"]},"64":{"title":"4 BIT SYNCHRONOUS BINARY COUNTER","titles":["BASIC LOGIC GATES","COUNTERS"]},"65":{"title":"FOUR BIT UP-DOWN BINARY COUNTER","titles":["BASIC LOGIC GATES","COUNTERS"]},"66":{"title":"BINARY COUNTER WITH PARALLEL LOAD","titles":["BASIC LOGIC GATES","COUNTERS"]},"67":{"title":"ARITHMETIC LOGIC UNIT (ALU)","titles":["BASIC LOGIC GATES"]},"68":{"title":"ENCODER","titles":["BASIC LOGIC GATES"]},"69":{"title":"PRIORITY ENCODER","titles":["BASIC LOGIC GATES","ENCODER"]},"70":{"title":"DECODER","titles":["BASIC LOGIC GATES"]},"71":{"title":"3-8 LINE DECODER","titles":["BASIC LOGIC GATES","DECODER"]},"72":{"title":"2-4 LINE DECODER WITH ENABLE INPUT","titles":["BASIC LOGIC GATES","DECODER"]},"73":{"title":"HOW TO MAKE A VERILOG PROGRAM","titles":[]},"74":{"title":"Create a New Project in your own version of Quartus Prime.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"75":{"title":"Select an appropriate directory for your Verilog project files and create an empty project file template.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"76":{"title":"Use the 10M50DAF484C7G Board from the MAX 10 Family.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"77":{"title":"Set ModelSim as your Simulation Tool (ModelSim must be installed prior) and finish the initialization of the project.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"78":{"title":"Click on the file icon in the top left corner and create a new Verilog HDL file.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"79":{"title":"When you wish to save your program, simply use Ctrl+S or click the Save icon in the top left corner.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"80":{"title":"Before running your program, you must first set a testbench for it. Do this by going into the Assignments menu and clicking Settings.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"81":{"title":"Change the NativeLink Setting to Compile Test Bench and select the Test Bench file for your program.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"82":{"title":"Create a new Test Bench if you are creating one for a new program that has not been made before.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"83":{"title":"Name your Test Bench appropriately (usually just the name of the test bench file) and add it to the list of Test Benches.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"84":{"title":"After setting your testbench, you can now run and compile your program by clicking on the third play button.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"85":{"title":"You will be able to view your circuit design and how it is structured, and simulate results using the test bench by going to the Tools menu.","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"86":{"title":"BIBLIOGRAPHY","titles":["HOW TO MAKE A VERILOG PROGRAM"]},"87":{"title":"Introduction to Verilog","titles":[]},"88":{"title":"Finite State Machines","titles":[]},"89":{"title":"Single Cycle MIPS Processor","titles":[]},"90":{"title":"MIPS","titles":[]},"91":{"title":"Setting up the MARS Code Editor","titles":["MIPS"]},"92":{"title":"Introduction to MARS Simulator","titles":["MIPS","Setting up the MARS Code Editor"]},"93":{"title":"Setting up JAVA SDK","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS Simulator"]},"94":{"title":"Downloading Java SDK on MacOS:","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS Simulator","Setting up JAVA SDK"]},"95":{"title":"Downloading Java SDK on Windows:","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS Simulator","Setting up JAVA SDK"]},"96":{"title":"Downloading Java SDK on Windows:","titles":["MIPS","Setting up the MARS Code Editor","Introduction to 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Arrays"]},"144":{"title":"To calculate the sum of n numbers in an n sized array","titles":["MIPS","Integer Arrays","One Dimensional Arrays"]},"145":{"title":"To find the largest element in an n sized array","titles":["MIPS","Integer Arrays","One Dimensional Arrays"]},"146":{"title":"String Operations (Advanced)","titles":["MIPS"]},"147":{"title":"Null Character and Newline","titles":["MIPS","String Operations (Advanced)"]},"148":{"title":"String Traversal","titles":["MIPS","String Operations (Advanced)"]},"149":{"title":"String Concatenation","titles":["MIPS","String Operations (Advanced)"]},"150":{"title":"Palindrome Checking","titles":["MIPS","String Operations (Advanced)"]},"151":{"title":"Two Dimensional Arrays","titles":["MIPS"]},"152":{"title":"Sample code","titles":["MIPS","Two Dimensional Arrays"]},"153":{"title":"Pseudo code->","titles":["MIPS","Two Dimensional Arrays"]},"154":{"title":"MIPS Code->","titles":["MIPS","Two Dimensional Arrays"]},"155":{"title":"Output","titles":["MIPS","Two Dimensional Arrays"]},"156":{"title":"->To find maximum and minimum element in a 2-D array","titles":["MIPS","Two Dimensional Arrays"]},"157":{"title":"Pseudo code->","titles":["MIPS","Two Dimensional Arrays","->To find maximum and minimum element in a 2-D array"]},"158":{"title":"MIPS Code->","titles":["MIPS","Two Dimensional Arrays"]},"159":{"title":"Output","titles":["MIPS","Two Dimensional Arrays"]},"160":{"title":"More Questions","titles":["MIPS","Two Dimensional Arrays"]},"161":{"title":"References","titles":["MIPS","Two Dimensional Arrays"]},"162":{"title":"About Us","titles":[]},"163":{"title":"Our Philosophy","titles":["About Us"]},"164":{"title":"The Computer Science Department","titles":["About Us"]},"165":{"title":"The Hardware Lab Course Guide Team","titles":["About Us"]},"166":{"title":"Faculty :fontawesome-solid-computer:","titles":["About Us"]},"167":{"title":"The MIPS Team :simple-linkedin:","titles":["About Us","Faculty :fontawesome-solid-computer:"]},"168":{"title":"The Verilog Team :simple-linkedin:","titles":["About Us","Faculty :fontawesome-solid-computer:"]},"169":{"title":"Web and Repository Maintenance :simple-github:","titles":["About Us","Faculty :fontawesome-solid-computer:"]},"170":{"title":"Join Our Team","titles":["About Us"]},"171":{"title":"Single Cycle Processor","titles":[]},"172":{"title":"Table of Contents","titles":["Single Cycle Processor"]},"173":{"title":"1. Overview","titles":["Single Cycle Processor"]},"174":{"title":"2. Prerequisites","titles":["Single Cycle Processor"]},"175":{"title":"3. Control Unit","titles":["Single Cycle Processor"]},"176":{"title":"Instruction Format","titles":["Single Cycle Processor","3. Control Unit"]},"177":{"title":"Main Control Unit (Main Decoder)","titles":["Single Cycle Processor","3. Control Unit"]},"178":{"title":"ALU Control Unit (ALU Decoder)","titles":["Single Cycle Processor","3. Control Unit"]},"179":{"title":"Understanding the optimal implementation:","titles":["Single Cycle Processor","3. Control Unit","ALU Control Unit (ALU Decoder)"]},"180":{"title":"ALU Control Truth Table","titles":["Single Cycle Processor","3. Control Unit","ALU Control Unit (ALU Decoder)"]},"181":{"title":"Input-Output Truth Table","titles":["Single Cycle Processor","3. Control Unit","ALU Control Unit (ALU Decoder)"]},"182":{"title":"4. Datapath","titles":["Single Cycle Processor"]},"183":{"title":"State elements","titles":["Single Cycle Processor","4. Datapath"]},"184":{"title":"a Instruction Memory","titles":["Single Cycle Processor","4. Datapath","State elements"]},"185":{"title":"b Register File","titles":["Single Cycle Processor","4. Datapath","State elements"]},"186":{"title":"c) ALU","titles":["Single Cycle Processor","4. Datapath","State elements"]},"187":{"title":"d Data Memory","titles":["Single Cycle Processor","4. Datapath","State elements"]},"188":{"title":"e) Sign extension","titles":["Single Cycle Processor","4. Datapath","State elements"]},"189":{"title":"The Final Datapath","titles":["Single Cycle Processor","4. Datapath"]},"190":{"title":"Role of Multiplexors","titles":["Single Cycle Processor","4. Datapath","The Final Datapath"]},"191":{"title":"5. Implementation","titles":["Single Cycle Processor"]},"192":{"title":"1. Top level module","titles":["Single Cycle Processor","5. Implementation"]},"193":{"title":"Inputs","titles":["Single Cycle Processor","5. Implementation","1. Top level module"]},"194":{"title":"Outputs","titles":["Single Cycle Processor","5. Implementation","1. Top level module"]},"195":{"title":"2. Data Memory","titles":["Single Cycle Processor","5. Implementation"]},"196":{"title":"Inputs-","titles":["Single Cycle Processor","5. Implementation","2. Data Memory"]},"197":{"title":"Output-","titles":["Single Cycle Processor","5. Implementation","2. Data Memory"]},"198":{"title":"3. Instruction Memory","titles":["Single Cycle Processor","5. Implementation"]},"199":{"title":"4.MIPS","titles":["Single Cycle Processor","5. Implementation"]},"200":{"title":"5. Controller","titles":["Single Cycle Processor","5. Implementation"]},"201":{"title":"Working","titles":["Single Cycle Processor","5. Implementation","5. Controller"]},"202":{"title":"6. Main Decoder","titles":["Single Cycle Processor","5. 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Some Other Functional Units"]},"213":{"title":"5. 2 WAY MUX MODULE (with variable width)","titles":["Single Cycle Processor","10. Some Other Functional Units"]},"214":{"title":"6. 32 BIT ALU MODULE","titles":["Single Cycle Processor","10. Some Other Functional Units"]},"215":{"title":"6. How to Run Instructions","titles":["Single Cycle Processor"]},"216":{"title":"7. Test cases for Various Instructions","titles":["Single Cycle Processor"]},"217":{"title":"1. add","titles":["Single Cycle Processor","7. Test cases for Various Instructions"]},"218":{"title":"2. sub","titles":["Single Cycle Processor","7. Test cases for Various Instructions"]},"219":{"title":"3. sw","titles":["Single Cycle Processor","7. Test cases for Various Instructions"]},"220":{"title":"4. lw","titles":["Single Cycle Processor","7. Test cases for Various Instructions"]},"221":{"title":"5. beq","titles":["Single Cycle Processor","7. Test cases for Various Instructions"]},"222":{"title":"8. References","titles":["Single Cycle Processor"]},"223":{"title":"Introduction To Finite State Machines","titles":[]},"224":{"title":"Basic Definition And Formulations:","titles":["Introduction To Finite State Machines"]},"225":{"title":"State Table","titles":["Introduction To Finite State Machines","Basic Definition And Formulations:"]},"226":{"title":"State Equations","titles":["Introduction To Finite State Machines","Basic Definition And Formulations:"]},"227":{"title":"State Diagram","titles":["Introduction To Finite State Machines","Basic Definition And Formulations:"]},"228":{"title":"Types of Finite State Machines:","titles":["Introduction To Finite State Machines"]},"229":{"title":"Mealy Model","titles":["Introduction To Finite State Machines","Types of Finite State Machines:"]},"230":{"title":"Moore Model","titles":["Introduction To Finite State Machines","Types of Finite State Machines:"]},"231":{"title":"Pre-Requisite Verilog Commands:","titles":["Introduction To Finite State 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Machines in Verilog:","titles":["Introduction To Finite State Machines"]},"241":{"title":"Mealy Machine Implementations","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"242":{"title":"Verilog Code:","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"243":{"title":"TestBench:","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"244":{"title":"Simulation Waveform:","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"245":{"title":"Moore Machine Implememtation","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"246":{"title":"Verilog Code:","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"247":{"title":"Testbench:","titles":["Introduction To Finite State 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of Implementing State Machines in Verilog:"]},"255":{"title":"TestBench:","titles":["Introduction To Finite State Machines","Examples of Implementing State Machines in Verilog:"]},"256":{"title":"References","titles":["Introduction To Finite State Machines"]},"257":{"title":"Welcome to the Hardware Lab Guide","titles":[]},"258":{"title":"Course Layout","titles":["Welcome to the Hardware Lab Guide"]},"259":{"title":"Welcome to the MIPS Guide","titles":[]},"260":{"title":"Introduction to MIPS","titles":["Welcome to the MIPS Guide"]},"261":{"title":"Basic Integer and String Handling","titles":["Welcome to the MIPS Guide"]},"262":{"title":"Floating Point Handling","titles":["Welcome to the MIPS Guide"]},"263":{"title":"Integer Array Handling","titles":["Welcome to the MIPS Guide"]},"264":{"title":"2-D Integer Array Handling","titles":["Welcome to the MIPS Guide"]},"265":{"title":"String Handling (advanced)","titles":["Welcome to the MIPS Guide"]},"266":{"title":"Introduction To Registers","titles":[]},"267":{"title":"Registers","titles":["Introduction To Registers"]},"268":{"title":"Register Files","titles":["Introduction To Registers"]},"269":{"title":"Shift Registers","titles":["Introduction To Registers"]},"270":{"title":"Some useful short notes","titles":["Introduction To Registers"]},"271":{"title":"References","titles":["Introduction To Registers"]},"272":{"title":"MIPS","titles":[]},"273":{"title":"Setting up the MARS Code Editor","titles":["MIPS"]},"274":{"title":"Introduction to MARS Simulator","titles":["MIPS","Setting up the MARS Code Editor"]},"275":{"title":"Setting up JAVA SDK","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS Simulator"]},"276":{"title":"Downloading Java SDK on MacOS:","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS Simulator","Setting up JAVA SDK"]},"277":{"title":"Downloading Java SDK on Windows:","titles":["MIPS","Setting up the MARS Code Editor","Introduction to MARS 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diff --git a/docs/.vitepress/dist/assets/chunks/framework.CgMb17D3.js b/docs/.vitepress/dist/assets/chunks/framework.DRnJpP2i.js
similarity index 74%
rename from docs/.vitepress/dist/assets/chunks/framework.CgMb17D3.js
rename to docs/.vitepress/dist/assets/chunks/framework.DRnJpP2i.js
index 9df7c15..97cba11 100644
--- a/docs/.vitepress/dist/assets/chunks/framework.CgMb17D3.js
+++ b/docs/.vitepress/dist/assets/chunks/framework.DRnJpP2i.js
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wm81MLSOKFqGXyWuERe5id3S3Xq+fmpr62XQr35emp6f7dH3V9dXpeelpJ9OKzxe3trcaDIZfkJbEs9r+82zOs7V945HvMzzCb7/hlm6gfAV82idR3eQ5nQAAAABJRU5ErkJggg==",V="data:image/png;base64,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diff --git a/docs/.vitepress/dist/assets/chunks/theme.B6pbfA9S.js b/docs/.vitepress/dist/assets/chunks/theme.CpY-xi-5.js
similarity index 99%
rename from docs/.vitepress/dist/assets/chunks/theme.B6pbfA9S.js
rename to docs/.vitepress/dist/assets/chunks/theme.CpY-xi-5.js
index 73e6c4e..e1ff7db 100644
--- a/docs/.vitepress/dist/assets/chunks/theme.B6pbfA9S.js
+++ b/docs/.vitepress/dist/assets/chunks/theme.CpY-xi-5.js
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diff --git a/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.js b/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.js
new file mode 100644
index 0000000..d5d2be9
--- /dev/null
+++ b/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.js
@@ -0,0 +1,451 @@
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Basic Definition And Formulations: ​
An FSM is a digital sequential circuit that can follow a number of predefined states under the control of one or more inputs. Each state is a stable entity that the machine can occupy. It can move from this state to another state under the control of an outside-world input.
Some FSMs have a clock input and are called synchronous FSMs, i.e. those that do not belong to a type of FSM called asynchronous FSMs. Each state of the FSM needs to be identifiable. This is achieved by using a number of internal (to the FSM block) flip-flops. An FSM with four states would require two flip-flops, since two flip-flops can store 22 =4 state numbers. Each state has a unique state number, and states are usually assigned numbers as s0 (state 0), s1, s2, and s3 (for the four-state example). The rule here is
Number of states = 2(number of flip-flops) or Number of flip-flops = log2(number of states)
State Table ​
The time sequence of inputs, outputs, and flip-flop states may be enumerated in a state table. The state table for the circuit of Fig. 1.2 is shown in Table 1.1. It consists of three sections labeled present state, next state, and output. The present state designates the states of flip-flops before the occurrence of a clock pulse. The next state shows the states of flip-flops after the application of a clock pulse, and the output section lists the values of the output variables during the present state. Both the next state and output sections have two columns, one for x = 0 and the other for x = 1.
State Equations ​
A state equation (also known as an application equation) is an algebraic expression that specifies the conditions for a flip-flop state transition. The left side of the equation denotes the next state of a flip-flop and the right side, a Boolean function that specifies the present state conditions that make the next state equal to 1. A state equation is similar in form to a flip-flop characteristic equation, except that it specifies the next state conditions in terms of external input variables and other flip-flop values. The state equation is derived directly from a state table. For example, the state equation for flip-flop A is derived from inspection of Table 1-1. From the next state columns, we note that flip- flop A goes to the 1 state four times: when x = 0 and AB = 01 or 10 or 11, or when x = 1 and AB = 11. This can be expressed algebraically in a state equation as follows:
A(t + 1) = (A′B + AB′ + AB) x′ + Abx
State Diagram ​
The information available in a state table may be represented graphically in a state diagram. In this diagram, a state is represented by a circle, and the transition between states is indicated by directed lines connecting the circles. The state diagram of the sequential circuit give in the Section 1.1 is shown below. The binary number inside each circle identifies the state the circle represents. The directed lines are labeled with two binary numbers separated by a /. The input value that causes the state transition is labeled first; the number after the symbol / gives the value of the output during the present state. For example, the directed line from state 00 to 01 is labeled 1/0, meaning that the sequential circuit is in a present state 00 while x = 1 and x = 0, and that on the termination of the next clock pulse, the circuit goes to next state 01. A directed line connecting a circle with itself indicates that no change of state occurs. The state diagram provides the same information as the state table and is obtained directly from table in Section 1.1
Types of Finite State Machines: ​
Mealy Model ​
n this model, the FSM has a number of inputs that connect to the Next State Decoder (combinational) logic. The Q outputs of the memory element Flip- Flops connect to the Output Decoder logic, which in turn connects to the Outside World Outputs. The Flip-Flops outputs are used as Next State inputs to the Next State Decoder, and it is these that determine the next state that the FSM will move to. Once the FSM has moved to this Next State, its Flip-Flops acquire a new Present State, as dictated by the Next State Decoder. Note that some of the Outside World Inputs connect directly to the Output Decoder logic. This is the main feature of the Mealy-type FSM.
Moore Model ​
Another architectural form for an FSM is the Moore FSM. The Moore FSM Section 2.2 differs from the Mealy FSM in that it does not have the feed-forward paths. This type of FSM is very common. Note that the Outside World Outputs are a function of the Flip-Flops outputs only (unlike the Mealy FSM architecture, where the Outside World Outputs are a function of Flip-Flops outputs and some Outside World Inputs).
Pre-Requisite Verilog Commands: ​
Initial ​
A set of Verilog statements are usually executed sequentially in a simulation. These statements are placed inside a procedural block. Initial is one of the two main types of procedural block statements. An initial block is not synthesizable and hence cannot be converted into a hardware schematic with digital elements. Hence initial blocks do not serve much purpose than to be used in simulations. These blocks are primarily used to initialize variables and drive design ports with specific values.This block will be executed only once during the entire simulation. Execution of an initial block finishes once all the statements within the block are executed.
 The syntax is shown below:
v
initial
+  [single statement]
+
+initial begin
+  [multiple statement]
+end
Always ​
An always block is one of the procedural blocks in Verilog. Statements inside an always block are executed sequentially. The always block is executed at some particular event defined in the sensitivity list. A sensitivity list is the expression that defines when the always block should be executed and is specified after the @ operator within parentheses ( ) . This list may contain either one or a group of signals whose value change will execute the always block. An always block can be used to realize combinational or sequential elements. A sequential element like flip flop becomes active when it is provided with a clock and reset. Similarly, a combinational block becomes active when one of its nput values change. These hardware blocks are all working concurrently independent of each other. The connection between each is what determines the flow of data. To model this behavior, an always block is made as a continuous process that gets triggered and performs some action when a signal within the sensitivity list becomes active. The syntax is displayed in Section 2.2
v
always @ (event)
+  [statement]
+
+always @ (event) begin
+  [multiple statement]
+end
Begin..End ​
Statements are wrapped using begin and end keywords and will be executed sequentially in the given order, one after the other. Delay values are treated relative to the time of execution of the previous statement. After all the statements within the block are executed control may be passed elsewhere. The syntax is shown in Section 3.3
v
begin : name_seq
+  [statements]
+end
Fork..Join ​
Statements are launched in parallel by wrapping them within the join and fork keywords. A parallel block can execute statements concurrently and delay control can be used to provide time-ordering of the assignments. The syntax is shown in Section 3.4
v
fork : name_fork
+  [statements]
+join
Blocking Statements ​
Blocking assignment statements are assigned using = and are executed one after the other in a procedural block. However, this will not prevent execution of statments that run in a parallel block. For eg
v
module tb;
+  reg[7:0] a, b, c, d, e;
+
+  initial begin
+    a = 8'hDA;
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+
+    b = 8'hF1;
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+
+    c = 8'h30
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+  end
+
+  initial begin
+    d = 8'hAA;
+    $display("[%0t] d=0x0%h e=0x0%h", $time, d, e);
+
+    e = 8'h55;
+    $display("[%0t] d=0x0%h e=0x0%h", $time, d, e);
+  end
+endmodule
In the above example, there are two initial blocks which are executed in parallel when simulation starts. Statements are executed sequentially in each block and both blocks finish at time 0ns. To be more specific, variable a gets assigned first, followed by the display statement which is then followed by all other statements.
Non-Blocking Statements ​
Non-blocking assignment allows assignments to be scheduled without blocking the execution of following statements and is specified by a <= symbol. It's interesting to note that the same symbol is used as a relational operator in expressions, and as an assignment operator in the context of a non-blocking assignment. The following code snippet is written by replacing all the blocking statements in the previous example by non blocking statements. Try out for yourself and compare the difference in the outputs 😃 .
v
module tb;
+  reg[7:0] a, b, c, d, e;
+
+  initial begin
+    a <= 8'hDA;
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+
+    b <= 8'hF1;
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+
+    c <= 8'h30
+    $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time);
+  end
+
+  initial begin
+    d <= 8'hAA;
+    $display("[%0t] d=0x0%h e=0x0%h", $time, d, e);
+
+    e <= 8'h55;
+    $display("[%0t] d=0x0%h e=0x0%h", $time, d, e);
+  end
+endmodule
Posedge and Negedge ​
Simply speaking, posedge means the transition from 0 to 1 negedge the oposit transition from 1 to 0 In synchronous sequential circuits, changes in flip-flops occur only in response to a transition of a clock pulse. The transition may be either a positive edge or a negative edge of the clock, but not both. Verilog HDL takes care of these conditions by providing these two keywords viz. posedge and negedge. The syntax is shown in Section 3.7
v
always@(posedge clock, negedge reset);
Case Statement ​
The case statement checks if the given expression matches one of the other expressions in the list and branches accordingly. It is typically used to implement a multiplexer. The if-else construct may not be suitable if there are many conditions to be checked and would synthesize into a priority encoder instead of a multiplexer.
v
// Here 'expression' should match one of the lines
+case(<expression>)
+  case_item1  : <single statement>
+  case_item2,
+  case_item3  : begin
+                <multiple statement>
+              end
+  default     : <statement>
+endcase
The syntax is shown in Section 3.8. A Verilog case statement starts with the keyword case and ends with the endcase keyword. The expression within parantheses will be evaluated exactly once and is compared with the list of alternatives in the order they are written and the statements for which the alternative matches the given expression are executed. A block of multiple statements must be grouped and be within begin and end. If none of the case items match the given expression, statements within the default item is executed. The statement is optional, and there can be only one default statement in a case statement.
Examples of Implementing State Machines in Verilog: ​
Now that we are all set and armed with the required amunition of verilog commands, let’s dive headfirst into implementing state machines using verilog. This section will consist of four examples. Each example will consist of the problem statement, the state diagram, the verilog code and testbench and finally,the output of the code. Try implementing these problems on your own first without referring to this manual. If yoou get stuck at any point, you can come back and take a peek 😉 Remember, the key lies in understanding the state diagram thoroughly!!
Mealy Machine Implementations ​
Let’s start our dive with a simple example of implementing a mealy machine. Recall that in a Mealy machine, the output is a function of both, the present state as well as the input. Let’s consider the example of a Mealy Zero Detector shown in Section 4.1
Verilog Code: ​
v
module mealy_zero_det(
+  output reg y_out,
+  input x_in,clk,reset);
+
+  reg [1:0] state,next_state;
+  parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11;
+
+  always@(posedge clk,negedge reset)
+    if (reset==0) state <= S0;
+    else state<=next_state;
+
+  always @ (state, x_in)
+    case (state)
+      S0: 
+        if (x_in) next_state = S1; else next_state =S0; 
+      S1:
+        if (x_in) next_state = S3; else next_state =S0;
+      S2: 
+        if (~x_in) next_state = S0; else next_state = S2
+      S3: 
+        if (x_in) next_state = S2; else next_state=S0
+    endcase
+
+  always @ (state, x_in)
+    case (state)
+      S0:
+        y_out = 0;
+      S1, S2, S3: 
+        y_out = ~x_in;
+    endcase
+
+endmodule
TestBench: ​
v
module mealy_zero_det_tb();
+  wire t_y_out;
+  reg t_x_in,t_clock,t_reset;  
+  mealy_zero_det uut(t_y_out,t_x_in,t_clock,t_reset);initial #200 $finish;
+  initial 
+    begin 
+      $dumpfile("dump.vcd");
+      $dumpvars(1);
+      t_clock = 0; 
+      forever #5 t_clock = ~t_clock; 
+    end
+  initial 
+    fork
+      t_reset = 0;
+      #2 t_reset = 1;
+      #87 t_reset = 0;
+      #89 t_reset = 1;
+      #10 t_x_in = 1;
+      #30 t_x_in = 0;
+      #40 t_x_in = 1;
+      #50 t_x_in = 0;
+      #52 t_x_in = 1;
+      #54 t_x_in = 0;
+      #70 t_x_in = 1;
+      #80 t_x_in = 1;
+      #70 t_x_in = 0;
+      #90 t_x_in = 1;
+      #100 t_x_in = 0;
+      #120 t_x_in = 1;
+      #160 t_x_in = 0;
+      #170 t_x_in = 1;
+    join
+endmodule
Simulation Waveform: ​
Moore Machine Implememtation ​
Let’s try implementing the above example in Moore Model. The state diagram needs to be modified as in the Moore Model, the output depends only on the initial state. The state diagram will be as shown in Section 4.2
Verilog Code: ​
v
module moore_zero_det (   
+  output [1:0] y_out,
+  input x_in, clock, reset
+  );
+
+  reg [1:0] state;
+  parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11;
+
+  always @ (posedge clock, negedge reset)
+    if (reset == 0)
+      state <= S0;
+    else
+      case (state)
+        S0: 
+          if (~x_in)
+            state <= S1;
+          else
+            state <= S0;
+        S1: 
+          if (x_in)
+            state <= S2; 
+          else               
+            state <= S3;
+        S2: 
+          if (~x_in)               
+            state <= S3;          
+          else               
+            state <= S2;
+        S3: 
+          if (~x_in)               
+            state <= S0;          
+          else               
+            state <= S3;
+      endcase
+      
+  assign y_out = state;
+endmodule
Testbench: ​
v
module moore_zero_det_tb();
+wire [1:0] t_y_out;
+reg t_x_in,t_clock,t_reset;  
+moore_zero_det uut(t_y_out,t_x_in,t_clock,t_reset);initial #200 $finish;
+initial 
+  begin 
+    // Dump waves
+    $dumpfile("dump.vcd");
+    $dumpvars(1);
+    t_clock = 0; 
+    forever #5 t_clock = ~t_clock;
+  end
+    initial 
+      fork
+        t_reset = 0;
+        #2 t_reset = 1;
+        #87 t_reset = 0;
+        #89 t_reset = 1;
+        #10 t_x_in = 1;
+        #30 t_x_in = 0;
+        #40 t_x_in = 1;
+        #50 t_x_in = 0;
+        #52 t_x_in = 1;
+        #54 t_x_in = 0;
+        #70 t_x_in = 1;
+        #80 t_x_in = 1;
+        #70 t_x_in = 0;
+        #90 t_x_in = 1;
+        #100 t_x_in = 0;
+        #120 t_x_in = 1;
+        #160 t_x_in = 0;
+        #170 t_x_in = 1;
+      join
+endmodule
Simulation Waveform: ​
Chess Clock Controller ​
Background: At the start of a new game, the Reset input is asserted to initialize the system and clear both timers to zero time. This is achieved by means of the Clr output of the Chess Clock FSM being driven high, thereby asserting the reset (rst) input of both timers. Each chess player has a push-button, which when pressed applies a logic 1 to their respective inputs, Pa and Pb, of the Chess Clock FSM. After resetting the timers, the player who is not making the first move presses their push-button in order to enable the other player’s timer to commence timing.
 For example, if Player-A is to make the first move, then Player-B starts the game by pressing their push-button. This has the effect of activating the Ta output of the Chess Clock FSM block in order to enable TIMER-A to record the time taken by Player-A to make the first move. Once Player-A completes the first move, Player-A’s button is pressed in order to stop their own timer and start Player-B’s timer (Ta is negated and Tb is asserted)
 The state diagram of this machine is given in Section 4.3

 As shown, the FSM makes use of four states having the names shown in the upper half of the state circles. The states of the FSM outputs Ta, Tb and Clr are listed in the lower half of every state circle; those outputs preceded by ‘/’ are forced to logic 0, whereas those without ‘/’ are forced to logic 1. The presence of the output states within each of the state circles indicates that the Chess Clock FSM is of the Moore variety. The values of the inputs, Pa and Pb, are shown alongside each corresponding state transition path (arrow) using a format similar to that used to show the state of the outputs. The movement from one state to another occurs on the rising edge of the Clock input. Where the number of transitions shown originating from a given state is less than the total number possible, the remaining input conditions result in a so-called sling, i.e. the next state is the same as the current state.
Verilog Code: ​
v
module chess_clk_cntrl(
+  output time_a,time_b,clr,
+  input player_a,player_b,clk,reset);
+  
+  localparam run_a=0,run_b=1,stop=2,Wait=3;
+  reg [1:0] state;
+  always@(posedge clk,posedge reset)
+    begin
+      if(reset)
+        state<=stop;
+      else
+        case(state)
+          run_a:
+            casex({player_a,player_b})
+              2'b0x: state<=run_a;
+              2'b10: state<=run_b;
+              2'b11: state<=Wait;
+            endcase
+          run_b:
+            casex({player_a,player_b})
+              2'bx0: state<=run_b;
+              2'b01: state<=run_a;
+              2'b11: state<=Wait;
+            endcase
+          stop:
+            case({player_a,player_b})
+              2'b00: state<=stop;
+              2'b01: state<=run_a;
+              2'b10: state<=run_b;
+              2'b11: state<=Wait;
+            endcase
+          Wait:
+            if(player_a==player_b) 
+              state<=Wait;
+          	else 
+              if(player_a==1'b1)
+                state<=run_b;
+          	  else
+                state<=run_a;
+        endcase
+    end
+  assign time_a=state==run_a;
+  assign time_b=state==run_b;
+  assign clr=state==stop;
+endmodule
Testbench: ​
v
module chess_clk_cntrl_tb();
+  wire time_a,time_b,clr;
+  reg player_a,player_b,clk,reset;
+  chess_clk_cntrl 	uut(time_a,time_b,clr,player_a,player_b,clk,reset);
+  initial
+    begin
+      $dumpfile("dump.vcd");
+	  $dumpvars(1);
+      clk=1'b0;
+      forever 
+        #50 clk=~clk;
+    end
+  
+  initial
+    begin
+      reset=1'b1;player_a=1'b0;player_b=1'b0;
+      #100 reset=1'b0;
+      #101 player_a=1'b1;
+      #167 player_a=1'b0;
+      #215 player_b=1'b1;
+      #289 player_b=1'b0;
+      #350 player_a=1'b1;player_b=1'b1;
+      #478 player_a=1'b0;player_b=1'b0;
+      #513 player_b=1'b1;
+      #550 $stop;
+    end
+endmodule
Simulation Waveform: ​
Vending Machine ​
Our vending machine is based on the following state diagram:

 The machine has the following states: •State 1: Reset •State 2: Five •State 3: Ten •State 4: Fifteen •State 5: Twenty •State 6: Twenty Five The machine only accepts the following coins •Rs. 5 (nickel) •Rs. 10 (dime) •Rs. 25 (quarter) Whenever we get a coin we jump to the next state. So for example, if we get a coin from the reset state, say a Rs. 5 coin, then we jump to the next state Five . Otherwise we stay in the same state. When we get Extra amount we come back to the reset state and the difference is given back to the user.
Verilog Code ​
v
module vending_machine(
+  output reg vend,
+  output reg [2:0] change,state,
+  input [2:0] coin,
+  input clk,rst);
+  
+  parameter [2:0]rs_5= 3'b001;
+  parameter [2:0]rs_10= 3'b010;
+  parameter [2:0]rs_15= 3'b011;
+  parameter [2:0]rs_20= 3'b100;
+  parameter [2:0]rs_25= 3'b101;
+  
+  parameter [2:0]idle= 3'b000;
+  parameter [2:0]five= 3'b001;
+  parameter [2:0]ten= 3'b010;
+  parameter [2:0]fifteen= 3'b011;
+  parameter [2:0]twenty= 3'b100;
+  parameter [2:0]twenty_five=3'b101;
+  
+  reg[2:0] next_state;
+  
+  always@(coin or state)
+    begin
+      next_state=0;
+      case(state)
+        idle:
+          case(coin)
+            rs_5: next_state=five;
+            rs_10: next_state=ten;
+            rs_25: next_state=twenty_five;
+            default: next_state=idle;
+          endcase
+        five:
+          case(coin)
+            rs_5: next_state= ten;
+            rs_10: next_state=fifteen;
+            rs_25: next_state=twenty_five;
+            default: next_state=five;
+          endcase
+        ten:
+          case(coin)
+            rs_5: next_state=fifteen;
+            rs_10: next_state=twenty;
+            rs_25: next_state=twenty_five;
+            default: next_state=ten;
+          endcase
+        fifteen:
+          case(coin)
+            rs_5: next_state=twenty;
+            rs_10: next_state=twenty_five;
+            rs_25: next_state=twenty_five;
+            default: next_state=fifteen;
+          endcase
+        twenty:
+          case(coin)
+            rs_5: next_state=twenty_five;
+            rs_10: next_state=twenty_five;
+            rs_25: next_state=twenty_five;
+            default: next_state=twenty;
+          endcase
+        twenty_five:
+          next_state=idle;
+        default: next_state=idle;
+      endcase
+    end
+  
+  always@(clk)
+    begin
+      if(rst)
+        begin
+          change<=3'b000;
+          vend<=1'b0;
+          state<=idle;
+        end
+      else
+        state<=next_state;
+      case(state)
+        idle:
+          begin
+            vend<=1'b0;
+            change<=3'd0;
+          end
+        five:
+          begin
+            vend<=1'b0;
+            if(coin==rs_25)
+              change<=rs_5;
+            else
+              change<=3'd0;
+          end
+        ten:
+          begin
+            vend<=1'b0;
+            if(coin==rs_25)
+              change<=rs_10;
+            else
+              change<=3'd0;
+          end
+        fifteen:
+          begin
+            vend<=1'b0;
+            if(coin==rs_25)
+              change<=rs_15;
+            else
+              change<=3'd0;
+          end
+        twenty:
+          begin
+            vend<=1'b0;
+            if(coin==rs_10)
+              change<=rs_5;
+            else
+              if(coin==rs_25)
+                change<=rs_20;
+              else
+                change<=3'd0;
+          end
+        twenty_five:
+          begin
+            vend<=1'b1;
+            change<=3'd0;
+          end
+        default: state<=idle;
+      endcase
+    end
+endmodule
TestBench: ​
v
module vending_machine_tb();
+  wire vend;
+  wire [2:0] change,state;
+  reg [2:0] coin;
+  reg clk,rst;
+  
+  vending_machine uut(vend,change,state,coin,clk,rst);
+  
+  parameter [2:0]rs_5= 3'b001;
+  parameter [2:0]rs_10= 3'b010;
+  parameter [2:0]rs_15= 3'b011;
+  parameter [2:0]rs_20= 3'b100;
+  parameter [2:0]rs_25= 3'b101;
+  
+  parameter [2:0]idle= 3'b000;
+  parameter [2:0]five= 3'b001;
+  parameter [2:0]ten= 3'b010;
+  parameter [2:0]fifteen= 3'b011;
+  parameter [2:0]twenty= 3'b100;
+  parameter [2:0]twenty_five=3'b101;
+  
+  initial 
+    begin
+    $dumpvars;
+	  $dumpfile("file.vcd");
+      clk=1'b0; rst=1'b1;
+      #2 rst=0; coin=rs_5;
+      #2 rst=1; coin=2'b00;
+      #2 rst=0;coin=rs_10;
+      #2 rst=1; coin=2'b00;
+	  #2 rst=0; coin=rs_25;
+      #2 rst=1; coin=2'b00;
+      #2 rst=0; coin=rs_5;
+      #2 coin=rs_5;
+      #2 coin=rs_5;
+      #2 coin=rs_5;
+      #2 coin=rs_5;
+      #2 rst=1; coin=2'b00;
+      #2 rst=0; coin=rs_5;
+      #2 coin=rs_10;
+      #2 coin=rs_10;
+      #2 rst=1; coin=2'b00;
+      #2 rst=0; coin=rs_10;
+      #2 coin=rs_25;
+      #2 coin=rs_5;
+      #2 rst=1; coin=2'b00;
+      #2 rst=0; coin=rs_10;
+      #2 coin= rs_10;
+      #2 coin=rs_25;
+      #2 rst=1; coin=2'b00;
+      #2 $finish;
+    end
+  always
+	#1 clk=~clk;
+  initial 
+    begin
+      if (rst)
+			coin=2'b00;
+	end
+endmodule
And with this we have come to the end of the manual for Finite State Machines. Up next, you will learning the implementation of a Single Cycle MIPS Processor. Hopefully this manual helped in broadening your understanding of Finite State Machines from a very basic to a fairly advanced level. You’ll be required to implement these concepts again in the Practice Questions.
References ​
  1. Digital Design: With An Introduction to Verilog HDL (5th Edition), M. Morris Mano, Michael D. Cilleti.
  2. FSM-based Digital Design using Verilog HDL, Peter Minns and Ian Elliott.
  3. http://www.csun.edu/~ags55111/
  4. [https://ocw.mit.edu/courses/6-111-introductory-digital-systems-
     laboratory-spring-2006/](https://ocw.mit.edu/courses/6-111-introductory-digital-systems-
     laboratory-spring-2006/)
  5. https://www.chipverify.com/verilog/verilog-tutorial
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diff --git a/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.lean.js b/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.lean.js
new file mode 100644
index 0000000..04903f4
--- /dev/null
+++ b/docs/.vitepress/dist/assets/fsm.md.BpozOCs2.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DRnJpP2i.js";const t="/hwlabnitc.github.io/assets/fsm-image-0010.T24H2Nci.png",e="/hwlabnitc.github.io/assets/fsm-image-0016.BirHtMRq.png",h="/hwlabnitc.github.io/assets/fsm-image-0022.B4FawsqK.png",l="/hwlabnitc.github.io/assets/fsm-image-0029.CbRphb6c.png",p="/hwlabnitc.github.io/assets/fsm-image-0035.BXkF_Dg3.png",k="/hwlabnitc.github.io/assets/fsm-image-0042.j6esA-Y4.png",r="/hwlabnitc.github.io/assets/fsm-image-0099.riYCyYMD.png",E="/hwlabnitc.github.io/assets/fsm-image-0100.DaiXE2Ht.png",d="/hwlabnitc.github.io/assets/fsm-image-0112.7vZ8vL9Z.png",g="/hwlabnitc.github.io/assets/fsm-image-0119.RUOc0GsR.png",o="/hwlabnitc.github.io/assets/fsm-image-0128.BYLXnBRZ.png",y="/hwlabnitc.github.io/assets/fsm-image-0135.D-DY2zzy.png",c="/hwlabnitc.github.io/assets/fsm-image-0153.CcG1zPoc.png",A=JSON.parse('{"title":"Introduction To Finite State Machines","description":"","frontmatter":{},"headers":[],"relativePath":"fsm.md","filePath":"fsm.md"}'),F={name:"fsm.md"},C=n("",92),b=[C];function u(m,f,B,w,_,v){return a(),i("div",null,b)}const D=s(F,[["render",u]]);export{A as __pageData,D as default};
diff --git a/docs/.vitepress/dist/assets/index.md.BiX3HcXP.js b/docs/.vitepress/dist/assets/index.md.BiX3HcXP.js
new file mode 100644
index 0000000..fb9740f
--- /dev/null
+++ b/docs/.vitepress/dist/assets/index.md.BiX3HcXP.js
@@ -0,0 +1 @@
+import{_ as e,c as t,o,a4 as a}from"./chunks/framework.DRnJpP2i.js";const g=JSON.parse('{"title":"Welcome to the Hardware Lab Guide","description":"","frontmatter":{"layout":"home","hero":{"image":"/NITC_Logo.png","name":"Hardware Lab NITC","text":"","tagline":"The official Hardware Lab Guide","actions":[{"theme":"brand","text":"Verilog Docs","link":"/markdown-examples"},{"theme":"alt","text":"MIPS Docs","link":"/api-examples"},{"theme":"alt","text":"Single Cycle Docs","link":"/guide-examples"}]},"features":[{"title":"Extensive documentation","details":"Study the documentation to understand the working of the topics hardware lab","link":"/markdown-examples"},{"title":"Video tutorials","details":"Watch the video tutorials to understand sample codes and key concepts"},{"title":"Sample Codes","details":"Practice the sample codes to understand the working of the topics"}]},"headers":[],"relativePath":"index.md","filePath":"index.md"}'),i={name:"index.md"},n=a('
Welcome to the Hardware Lab Guide ​
This course covers the following topics-
  • Introduction to Verilog and Single Cycle - Verilog is a hardware description language (HDL) used for designing and simulating digital systems. In this course, you will learn about Verilog in detail, including its syntax, data types, modules, behavioral modeling, and structural modeling. You will also understand how to simulate and test your Verilog designs and further run basic MIPS instructions using your own Single Cycle program.
  • Introduction to MIPS ISA - MIPS (Microprocessor without Interlocked Pipeline Stages) is a reduced instruction set computer (RISC) architecture commonly used in embedded systems and educational environments. In this course, you will dive into the details of the MIPS architecture, including its instruction set, registers, memory organization, and execution flow. You will also learn how to write MIPS assembly code and understand the basic concepts of computer organization and architecture.
Course Layout ​
This tutorial is split into a 2 parts for each topic-
  1. Theory - This part focuses on the theoretical concepts and principles of the topic. You will find comprehensive documentation and video explanation that covers the fundamental ideas, techniques, and best practices related to Verilog and MIPS. These resources will provide you with a solid understanding of the topics and their applications.
  2. Implementation - This part emphasizes the practical aspect of the course. You will find documentation and video tutorials that guide you through the implementation of Verilog designs and MIPS assembly code. This hands-on approach will help you gain practical skills and experience in designing and working with digital systems using Verilog and MIPS.
By following this course layout, you will have a well-rounded understanding of Verilog and MIPS, both from a theoretical and practical perspective.
',7),s=[n];function r(l,d,c,u,h,p){return o(),t("div",null,s)}const w=e(i,[["render",r]]);export{g as __pageData,w as default};
diff --git a/docs/.vitepress/dist/assets/index.md.BiX3HcXP.lean.js b/docs/.vitepress/dist/assets/index.md.BiX3HcXP.lean.js
new file mode 100644
index 0000000..47ab765
--- /dev/null
+++ b/docs/.vitepress/dist/assets/index.md.BiX3HcXP.lean.js
@@ -0,0 +1 @@
+import{_ as e,c as t,o,a4 as a}from"./chunks/framework.DRnJpP2i.js";const g=JSON.parse('{"title":"Welcome to the Hardware Lab Guide","description":"","frontmatter":{"layout":"home","hero":{"image":"/NITC_Logo.png","name":"Hardware Lab NITC","text":"","tagline":"The official Hardware Lab Guide","actions":[{"theme":"brand","text":"Verilog Docs","link":"/markdown-examples"},{"theme":"alt","text":"MIPS Docs","link":"/api-examples"},{"theme":"alt","text":"Single Cycle Docs","link":"/guide-examples"}]},"features":[{"title":"Extensive documentation","details":"Study the documentation to understand the working of the topics hardware lab","link":"/markdown-examples"},{"title":"Video tutorials","details":"Watch the video tutorials to understand sample codes and key concepts"},{"title":"Sample Codes","details":"Practice the sample codes to understand the working of the topics"}]},"headers":[],"relativePath":"index.md","filePath":"index.md"}'),i={name:"index.md"},n=a("",7),s=[n];function r(l,d,c,u,h,p){return o(),t("div",null,s)}const w=e(i,[["render",r]]);export{g as __pageData,w as default};
diff --git a/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.js b/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.js
deleted file mode 100644
index 208e1e2..0000000
--- a/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as t,o,a4 as a}from"./chunks/framework.CgMb17D3.js";const g=JSON.parse('{"title":"Welcome to the Hardware Lab Guide","description":"","frontmatter":{"layout":"home","hero":{"image":"/img/favicon.ico","name":"Hardware Lab NITC","text":"","tagline":"The official Hardware Lab Guide","actions":[{"theme":"brand","text":"Verilog Docs","link":"/markdown-examples"},{"theme":"alt","text":"MIPS Docs","link":"/api-examples"},{"theme":"alt","text":"Single Cycle Docs","link":"/guide-examples"}]},"features":[{"title":"Extensive documentation","details":"Study the documentation to understand the working of the topics hardware lab","link":"/markdown-examples"},{"title":"Video tutorials","details":"Watch the video tutorials to understand sample codes and key concepts"},{"title":"Sample Codes","details":"Practice the sample codes to understand the working of the topics"}]},"headers":[],"relativePath":"index.md","filePath":"index.md"}'),i={name:"index.md"},n=a('
Welcome to the Hardware Lab Guide ​
This course covers the following topics-
  • Introduction to Verilog and Single Cycle - Verilog is a hardware description language (HDL) used for designing and simulating digital systems. In this course, you will learn about Verilog in detail, including its syntax, data types, modules, behavioral modeling, and structural modeling. You will also understand how to simulate and test your Verilog designs and further run basic MIPS instructions using your own Single Cycle program.
  • Introduction to MIPS ISA - MIPS (Microprocessor without Interlocked Pipeline Stages) is a reduced instruction set computer (RISC) architecture commonly used in embedded systems and educational environments. In this course, you will dive into the details of the MIPS architecture, including its instruction set, registers, memory organization, and execution flow. You will also learn how to write MIPS assembly code and understand the basic concepts of computer organization and architecture.
Course Layout ​
This tutorial is split into a 2 parts for each topic-
  1. Theory - This part focuses on the theoretical concepts and principles of the topic. You will find comprehensive documentation and video explanation that covers the fundamental ideas, techniques, and best practices related to Verilog and MIPS. These resources will provide you with a solid understanding of the topics and their applications.
  2. Implementation - This part emphasizes the practical aspect of the course. You will find documentation and video tutorials that guide you through the implementation of Verilog designs and MIPS assembly code. This hands-on approach will help you gain practical skills and experience in designing and working with digital systems using Verilog and MIPS.
By following this course layout, you will have a well-rounded understanding of Verilog and MIPS, both from a theoretical and practical perspective.
',7),s=[n];function r(l,d,c,u,h,p){return o(),t("div",null,s)}const w=e(i,[["render",r]]);export{g as __pageData,w as default};
diff --git a/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.lean.js b/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.lean.js
deleted file mode 100644
index f6bdbe5..0000000
--- a/docs/.vitepress/dist/assets/index.md.Ccl4vJqT.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as t,o,a4 as a}from"./chunks/framework.CgMb17D3.js";const g=JSON.parse('{"title":"Welcome to the Hardware Lab Guide","description":"","frontmatter":{"layout":"home","hero":{"image":"/img/favicon.ico","name":"Hardware Lab NITC","text":"","tagline":"The official Hardware Lab Guide","actions":[{"theme":"brand","text":"Verilog Docs","link":"/markdown-examples"},{"theme":"alt","text":"MIPS Docs","link":"/api-examples"},{"theme":"alt","text":"Single Cycle Docs","link":"/guide-examples"}]},"features":[{"title":"Extensive documentation","details":"Study the documentation to understand the working of the topics hardware lab","link":"/markdown-examples"},{"title":"Video tutorials","details":"Watch the video tutorials to understand sample codes and key concepts"},{"title":"Sample Codes","details":"Practice the sample codes to understand the working of the topics"}]},"headers":[],"relativePath":"index.md","filePath":"index.md"}'),i={name:"index.md"},n=a("",7),s=[n];function r(l,d,c,u,h,p){return o(),t("div",null,s)}const w=e(i,[["render",r]]);export{g as __pageData,w as default};
diff --git a/docs/.vitepress/dist/assets/mips.md.D391O4eq.js b/docs/.vitepress/dist/assets/mips.md.D391O4eq.js
new file mode 100644
index 0000000..a0d800f
--- /dev/null
+++ b/docs/.vitepress/dist/assets/mips.md.D391O4eq.js
@@ -0,0 +1,924 @@
+import{_ as e,a as t,b as i,c as p,d as l,e as r,f as o,g as d,h,i as c,j as g,k as u,l as k,m,n as b,o as f}from"./chunks/mips2-image-0009.DFxqnWYO.js";import{_ as y,c as E,a as s,a4 as n,j as a,o as $}from"./chunks/framework.DRnJpP2i.js";const L=JSON.parse('{"title":"MIPS","description":"","frontmatter":{},"headers":[],"relativePath":"mips.md","filePath":"mips.md"}'),v={name:"mips.md"},w=n(`
MIPS ​
Setting up the MARS Code Editor ​
Introduction to MARS Simulator ​
MARS simulator will be the software on which we will be running our MIPS code.
Setting up JAVA SDK ​
(Please note this tutorial is to download SDK Ver 11)
Downloading Java SDK on MacOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your macOS version (e.g., macOS x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the macOS version and click on the provided download link.
  8. The JDK installer package will be downloaded to your computer.
  9. Locate the downloaded package in your Downloads folder or the folder you specified for downloads.
  10. Double-click on the JDK installer package to launch the installation wizard.
  11. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your macOS computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Windows version (e.g., Windows x64).
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Windows version and click on the provided download link.
  8. The JDK installer executable file (e.g., jdk-11.0.x_windows-x64_bin.exe) will be downloaded to your computer.
  9. Locate the downloaded executable file, and double-click on it to launch the installation wizard.
  10. Follow the instructions in the installation wizard to complete the installation of the Java SDK on your Windows computer.
Downloading Java SDK on Windows: ​
  1. Open a web browser on your Linux computer.
  2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ technologies/javase-jdk11-downloads.html.
  3. On the Downloads page, locate the JDK (Java Development Kit) section.
  4. Click on the "Download" button for the version of Java you want to install. Make sure to select the version suitable for your Linux distribution.
  5. You may be prompted to log in or create an Oracle account. Follow the instructions on the screen to proceed.
  6. Once logged in, review and accept the license agreement.
  7. On the download page, locate the Linux version and click on the provided download link.
  8. The JDK archive file (e.g., jdk-11.0.x_linux-x64_bin.tar.gz) will be downloaded to your computer.
  9. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  10. Navigate to the directory where you downloaded the JDK archive file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads 
  11. Extract the contents of the JDK archive using the following command: tar -xvzf jdk-11.0.x_linux-x64_bin
Setting Up MARS Simulator ​
Note: Is your MARS text unreadably small? Download and use a new release Java 9 or above which contains a fix to automatically scale and size AWT and Swing components for High Dots Per Inch (HiDPI) displays on Windows and Linux.
Downloading MIPS MARS Simulator on macOS: ​
  1. Open a web browser on your macOS computer.
  2. Go to the official website of MIPS MARS at [ http:// courses.missouristate.edu/kenvollmar/mars/]( http:// courses.missouristate.edu/kenvollmar/mars/).
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Double-click on the ZIP file to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Applications folder.
  8. Open Terminal on your macOS by going to Applications > Utilities > Terminal.
  9. In the Terminal window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Applications folder, you can use the following command:  cd/Applications
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your macOS computer.
Downloading MIPS MARS Simulator on Windows: ​
  1. Open a web browser on your Windows computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/]([http://courses.missouristate.edu/ kenvollmar/mars/])
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer.
  5. Locate the downloaded ZIP file in your Downloads folder or the folder you specified for downloads.
  6. Right-click on the ZIP file and select "Extract All" to extract its contents. This will create a JAR file named "mars4_5.jar".
  7. Move the "mars4_5.jar" file to a suitable location on your computer, such as the Program Files folder.
  8. Open the Command Prompt on your Windows computer by pressing the Windows key + R, typing "cmd," and hitting Enter.
  9. In the Command Prompt window, navigate to the directory where you placed the "mars4_5.jar" file. For example, if you placed it in the Program Files folder, you can use the following command: cd "C:\\Program Files"
  10. Once you are in the correct directory, execute the following command to run the MIPS MARS simulator: java -jar mars4_5.jar
  11. The MIPS MARS simulator should now launch on your Windows computer.
Downloading MIPS MARS Simulator on Linux: ​
  1. Open a web browser on your Linux computer.
  2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ kenvollmar/mars/](http://courses.missouristate.edu/ kenvollmar/mars/)
  3. On the homepage, click on the "MARS 4.5" link under the "Download MARS" section.
  4. A ZIP file named "Mars4_5.jar.zip" will be downloaded to your computer.
  5. Open the terminal on your Linux system. You can typically find it in the Applications menu or by using the shortcut Ctrl+Alt+T.
  6. Navigate to the directory where you downloaded the ZIP file. For example, if it's in the Downloads folder, you can use the following command: cd ~/Downloads
  7. Unzip the ZIP file using the following command: unzip Mars4_5.jar.zip
  8. This will extract the "Mars4_5.jar" file from the ZIP archive.
  9. Move the "Mars4_5.jar" file to a suitable location on your computer. For instance, you can move it to the /opt directory using the following command: sudo mv Mars4_5.jar /opt
  10. To run the MIPS MARS simulator, open the terminal and navigate to the directory where you placed the JAR file. For example, if you moved it to the / opt directory, use the following command: cd /opt
  11. Execute the following command to launch the MIPS MARS simulator java -jar Mars4_5.jar
  12. The MIPS MARS simulator should now launch on your Linux computer.
MARS ASSEMBLY AND SYSTEM CALLS ​
Before assembling, the environment of this simulator can be simplisticly split to three segments: the editor at the upper left where all of the code is being written, the compiler/output right beneath the editor and the list of registers that represent the "CPU" for our program.
After assembling (by simply pressing F3) the environment changes, with two new segments getting the position of the editor: the text segment where
i) each line of assembly code gets cleared of "pseudoinstructions" (we'll talk about those in a sec) at the "basic" column and
ii) the machine code for each instruction at the "code" column, and the data segment where we can have a look at a representation of the memory of a processor with little-endian order.
After assembling, we can execute our code either all at once (F5) or step by step (F7), as well as rewinding the execution several steps backwards to the back (F8).
MARS accepts and exports files with the .asm filetype
Pseudo instructions ​
Before looking at the instruction set , let us look at a few pseudo instructions that’ll help you understand the IS better.
Here's a list of useful pseudo-instructions.
mov $t0, $t1: Copy contents of register t1 to register t0.
li $s0, immed: Load immediate into to register s0. The way this is translated depends on whether immed is 16 bits or 32 bits.
la $s0, addr: Load address into to register s0.
lw $t0, address: Load a word at address into register t0
Given below are some standard arithmetic and logical instructions standard to the MIPS Instruction Set Architecture.
**MARS provides a small set of operating system-like services through the system call (syscall) instruction **
**To request a service, a program loads the system call code into register $v0 and arguments into registers $a0~$a3 **
System calls that return values put their results in register $v0
Arithmetic Instructions ​
InstructionExampleMeaningComments
addadd $1,$2,$3$1=$2+$3
subtractsub $1,$2,$3$1=$2-$3
add immediateaddi $1,$2,100$1=$2+100"Immediate" means a constant number
add unsignedaddu $1,$2,$3$1=$2+$3Values are treated as unsigned integers,not two's complement integer
subtract unsignedsubu $1,$2,$3$1=$2-$3Values are treated as unsigned integers,not two's complement integers
add immediate unsignedaddiu $1,$2,100$1=$2+100Values are treated as unsigned integers,not two's complement integers
multiply (without overflow)mul $1,$2,$3$1=$2*$3Result is only 32 bits!
multiplymult $1,$2,$3$hi, $low=$2*$3Upper 32 bits stored in special register hi. Lower 32 bits stored in special register lo
dividediv $1,$2,$3$hi,$low=$2/$3Remainder stored in special register hi. Quotient stored in special register lo
Logical ​
InstructionExampleMeaningComments
andand $1,$2,$3$1=$2&$3Bitwise AND
oror $1,$2,$3$1=$2$3
and immediateandi $1,$2,100$1=$2&100Bitwise AND with immediate value
or immediateori $1,$2,100$1=$2100
shift left logicalsll $1,$2,10$1=$2<<10Shift left by constant number of bits
shift right logicalsrl $1,$2,10$1=$2>>10Shift right by constant number of bits
Data Transfer ​
InstructionExampleMeaningComments
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
store wordsw $1,100($2)Memory[$2+100]=$1Copy from register to memory
load upper immediatelui $1,100$1=100x2^16Load constant into upper 16 bits. Lower 16 bits are set to zero
load addressla $1,label$1=Address of the labelPseudo-instruction (provided by assembler). Loads computed address of label (not it's contents) into register
load immediateli $1,100$1=100Pseudo instruction (provided by assembler). Loads immediate value into the register.
move from himfhi $2$2=hiCopy from special register hi to general register
move from lomflo $2$2=loCopy from special register lo to general register
load wordlw $1,100($2)$1=Memory[$2+100]Copy from memory to register
movemove $1,$2$1=$2Pseudo instruction (provided by assembler). Copy from register to register
Conditional Branch ​
InstructionExampleMeaningComments
branch on equalbeq $1,$2,100if($1==$2) go to PC+4+100Test if registers are equal
branch on not equalbne $1,$2,100if($1!=$2) go to PC+4+100Test if registers are not equal
branch on greater thanbgt $1,$2,100if($1>$2) go to PC+4+100Pseudo-instruction
branch on greater than or equalbge $1,$2,100if($1>=$2) go to PC+4+100Pseudo-instruction
branch on less thanblt $1,$2,100if($1<$2) go to PC+4+100Pseudo-instruction
branch on less than or equalble $1,$2,100if($1<=$2) go to PC+4+100Pseudo-instruction
Comparison ​
InstructionExampleMeaningComments
set on less thanslt $s1,$s2,$s3if($2<$3) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.
set on less than immediateslti $s1,$s2,100if($2<100) $1 = 1;else $1 = 0Test if less than. If true set $1 to 1. Otherwise set $1 to 0.
Unconditional Jump ​
InstructionExampleMeaningComments
jumpj 1000go to address 1000Jump to target address
jump registerjr $1go to address stored in $1For switch procedure return
jump and linkjal 1000$ra=PC+4 go to address 1000Use when making procedure call. This saves the return address in $ra
System Calls ​
ServiceOperationCode(in $v0)ArgumentsResults
print_intPrint integer number (32 bit)1$a0 = integer to be printedNone
print_floatPrint floating-point number (32 bit)2$f12 = float to be printedNone
print_doublePrint floating-point number (64 bit)3$f12 = integer to be printedNone
print_stringPrint null-terminated character string4$a0 = address of string in memoryNone
read_intRead integer number from user5NoneInteger returned in $v0
read_floatRead floating-point number from user6 NoneFloat returned in $f0
read_doubleRead double floating-point number from user7NoneDouble returned in $f0
read_stringWorks the same as Standard Clibrary fgets()8$a0 = memory address of string input buffer $a1 = length of string buffer (n)None
sbrkReturns the address to a block of memory containing n additional bytes (Useful for dynamic memory allocation)9$a0=amountaddress in $v0
exitStop program from running10NoneNone
print_charPrint character11$a0 = character to be printedNone
read_charRead character from user12NoneChar returned in $v0
exit2Stops program from running and returns an integer17$a0 = result(integer number)None
The complete list of syscalls can be accessed at
https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html
Assembler Directives ​
DirectiveResult
.word w1, ..., wnStore n 32-bit values in successive memory words
.half h1, ..., hnStore n 16-bit values in successive memory words
.byte b1, ..., bnStore n 8-bit values in successive memory words
.ascii strStore the ASCII string str in memory. Strings are in double-quotes, i.e. "Computer Science"
.asciiz strStore the ASCII string str in memory and null terminate it. Strings are in double-quotes, i.e. "Computer Science"
.space nLeave an empty n-byte region of memory for later use
.align nAlign the next datum on a 2^n byte boundary. For example, .align 2 aligns the next value ona word boundary
Registers ​
Register NumberRegister NameDescription
0$zeroThe value 0
2-3$v0-$v1Values from expression evaluation and function results
4-7$a0-$a3(arguments) First four parameters for subroutine
8-15, 24-25$t0-$t9Temporary variables
16-23$s0-$s7Saved values representing final computed results
31$raReturn address
MARS(MIPS Assembler/Simulator) Tutorial ​
1. Input the Tutorial program
1.1) Open the MARS program and click from the file menu choose “File...New”. A black document will open which you can enter your assembly code into. Click “File...Save As” and save the file as “Tutorial1.asm ”.
1.2) Enter the code as shown below into the editor and save the file.
v
# Program File: Tutorial1.asm 
+# Written by:   MoSaad 
+# Date Created: 10/05/2023 
+# Description:  Tutorial program to introduce MARS simulator  including: breakpoints, single-
+stepping, and register and memory windows. 
+#----------------------------------------------------------- 
+#----------------------- 
+# Declare some constants 
+#----------------------- 
+.data 
+string1: .asciiz "Welcome to Hardware Lab at NIT Calicut\\n" 
+string2: .asciiz "Hello World \\n" 
+string3: .asciiz "\\nLoop #" 
+#------------------ 
+# Main program body 
+#------------------ 
+.text 
+main: 
+li $v0,4 
+la $a0,string1 
+syscall 
+la $a0,string2 
+syscall 
+li $t0, 1 
+loop: 
+li $v0, 4 
+la $a0,string3 
+syscall 
+li $v0,1 
+move $a0,$t0 
+syscall 
+addi $t0,$t0,1 
+bne  $t0,4,loop 
+#----- 
+# Halt  
+#----- 
+li $v0, 10 
+syscall
1.4) From the menu, choose “Run...Assemble”. The “Mars Messages” window at the bottom of the screen will indicate if any errors occurred. No errors should occur.
2. Simulate the tutorial program
2.1) From the menu, choose “Run...Go” to execute the program. The program will execute displaying two lines of text and three iterations of a loop to the Run /IO window.
2.2) The buttons at the top of the window can be used as shortcuts for the run menu. Use the “Reset” button to reset the program, and then try tracing through the program by clicking the step button.
2.3) You can adjust the speed the program runs by moving the slider to the right of the buttons. If you have an infinite loop in your program, it may be necessary to adjust (slow down) the speed of the simulator to prevent the MARS program from crashing.
',70),C=a("img",{src:e},null,-1),F=a("img",{src:t},null,-1),x=a("img",{src:i},null,-1),q=a("img",{src:p},null,-1),A=a("img",{src:l},null,-1),S=a("img",{src:r},null,-1),D=n('
3. Using the Debugging Tools
3.1) When a program does not work as expected you will need to use the debugging tools provided with the simulator.
3.2) One of the primary tools used to debug a program is setting a breakpoint. You can break before execution of an instruction by clicking on the checkbox associated with each instruction on the far left of the execute window. Set a breakpoint at the instruction: addi $t0,$t0,1
3.3) Run the program until the breakpoint by clicking “Run”. At this point in the program only the first loop iteration has been printed. (You will need to click back to the Run/IO window to see the output.)
3.4) Now use the “Trace Into” button to step through the loop that prints out the next line of text one character at a time. Step through the instructions until “Loop #2” is printed to the output window. Stop and find the value of the registers “t0” and “pc” at that point? Has the line of code that the program counter points to executed yet?
3.5) The simulator also allows you to view the memory contents. The memory window appears in the middle of the screen and is titled “Data Segment”. Remove the earlier breakpoint and add a breakpoint to line 33, “syscall”. Click the run button so that the program executes up until the new breakpoint. We are now in the code right before “Loop #” is about to be printed for the third iteration. Notice that the $a0 register is now a pointer to the address where the “Loop #” text is stored. What is the memory location the register is pointing to?
3.6) Now look in the data segment area, and find the address $a0 points to. This is the memory section where the characters of the text “Loop #” is stored. Using an ASCII table find the address where the ‘p’ in “Loop” is located?
3.7) Exercise: Can you find where the word “Welcome” is stored in the memory?
Integer Handling ​
Unlike NASM where numbers are stored as characters, MIPS can store single or multiple digit integers directly. This chapter describes how to read and print integers. Basic operations in integer handling (add, sub, mul, div) will also be covered.
1. Declaring an integer
Integers can be declared as constants in the ‘.data’ section as shown below:
Code to declare constants ‘x’ and ‘y’ with values 30 and 40 respectively:
v
.data 
+x: .word 30 
+y: .word 40
2. Loading an integer value into a register
Another way of using integers in MIPS is to read their values into temporary registers using ‘I’ type instructions. The two commonly used methods of reading integer values are:
  1. Loading a value into a temporary register.
  2. Adding the value of the zero register and any value into a temporary register.
Code to enter integer values 5 and 10 using add and load instructions respectively into temporary registers:
v
.text 
+addi  $t0, $0, 5 
+li $t1, 10
3. Reading integers as input from the user
Integers can be read from the user using syscall (system call) instructions. The system call code for reading an integer is ‘5’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The input is then stored in $v0.
Code to read an integer input from the user:
v
.text 
+li $v0, 5 
+syscall
4. Printing integers
Integers stored in registers can also be printed using syscall instructions. The system call code for printing an integer is ‘1’. This syscall code value must be loaded into the register $v0 in order to perform its designated function. The integer to be printed must be stored in the $a0 register.
Code to print the integer ‘5’ after storing it in a register:
v
.text 
+li $a0, 5 
+li $v0, 1 
+syscall
We have now learnt how to store single and multi digit integers and how to print their values. We shall now combine all of these into a single program for a more robust understanding of the covered concepts.
Code to declare a constant x with value 10, load values 20 and 30 into two registers and read an integer value from the user and print all these values:
v
.data 
+x: .word 10 
+.text 
+addi $t0, $0, 20   #load value 20 
+li $t1, 30    #load value 30 
+li $v0, 5     #read integer input
+syscall 
+move  $t2, $v0   #move integer input 
+lw $a0, x     #print x 
+li $v0, 1 
+syscall 
+move $a0, $t0    
+li $v0, 1     #print value of $t0  
+syscall    
+move $a0, $t1   #print value of $t1 
+li $v0, 1 
+syscall 
+move $a0, $t2   #print integer input 
+li $v0, 1 
+syscall 
+li $v0, 10    #exit program 
+syscall
Output:Assume the value ‘5’ is entered by the user as input.
v
5
+1020305
+-- program is finished running --
5. Adding integers
Integers can be added in two ways, either by adding fixed or immediate values to an integer value stored in a register, or by adding two integers that are both stored in registers. Both methods to add integers are demonstrated below:
Code to add integer values stored in registers:
v
.text 
+addi  $t0, $t1, 5   #t0=t1+5  
+add $t2, $t2, $t1   #t2=t2+t1 
+addi  $t1, $zero, 5   #t1=0+5 
+add   $t2, $zero, $t1    #t2=0+t1
6. Subtracting integers
Unlike addition, values can only be subtracted if they are stored in a register.
Code to subtract integer values stored in registers:
.text 
+sub $t2, $t2, $t1   #t2=t2-t1    
+sub   $t2, $zero, $t1    #t2=0-t1
7. Multiplying integers
MIPS allows you to multiply the values present in two registers and stores the 32 most significant bits in the HI special register and the 32 least significant bits in the LO special register.
The value obtained in the HI and LO registers can be accessed using the mfhi and mflo instructions respectively.
Code to multiply two integers values and access the result after multiplication:
.text 
+mult  $t0, $t1     #signed mult 
+mflo  $s0     #s0=t0*t1 
+multu $t2, $t3    #unsigned mult  
+mflo  $s1     #s1=t2*t3
8. Dividing integers
Division in MIPS is similar to multiplication except for a key difference, the HI special register stores the remainder while the LO special register will hold the quotient of the division.
Code to divide to integers and access the remainder and quotient after division:
.text 
+div $t1, $t2    #signed div 
+mfhi  $s0     #s0=t1%t2 
+mflo  $s1     #s1=t1/t2 
+divu  $t3, $t4    #unsigned div 
+mfhi  $s2     #s2=t3%t4 
+mflo  $s3      #s3=t3/t4
Points To Note ​
1. Entering number of size larger than 32 bits The largest integer that can be entered in 32 bit space is 2,147,483,647. Entering a number larger than that results in the following error:
\`\`\` Runtime exception at 0x0040002c: invalid integer input (syscall 5)\`\`\`
+
2. Changing the value of $zero register It is not possible to change the value of the $zero register, any instructions that attempt to alter the value have no effect.
3. Multiplying numbers of size 32 bits In MIPS, all integer values must be 32 bits. So if there is a valid answer, it must be contained in the lower 32 bits of the answer. Thus to implement multiplication in MIPS, the two numbers must be multiplied using the mult operator, and the valid result moved from the lo register.
4. Division by zero If the divisor is zero, then the MIPS divide instructions do not compute any result in the HI and LO registers. Division by zero is ignored and no exception is produced.
5. Meaning of the .word directive The .word directive allocates 4 bytes of space in the data region. The .word directive can then be given an integer value, and it will initialize the allocated space to that integer value. Be careful as it is incorrect to think of a the .word directive as a declaration for an integer, as this directive simply allocates and initializes 4 bytes of memory, it is not a data type. What is stored in this memory can be any type of data.
String Operations ​
Strings in MIPS can be declared as constant in the .data part of the program. They are often stored this way so that they can be used as user prompts or to format output of a program. Strings can also be entered by the user during the runtime of the program. Both methods of using strings in MIPS will be demonstrated below.
1. Entering string constants
Pre-determined strings enclosed by double quotes can be declared in the .data section.
Code to store the string “enter an element:” in memory under the name “message”:
.data 
+message: .asciiz “enter an element:”
2. Enter strings as input from the user
To enter strings as input, the syscall code to be used is 8. Apart from that, the address of the memory space into which the string must be entered, is loaded into the $a0 register. The maximum size of the string must also be loaded into the $a1 register before performing the syscall.
Code to read a string as input from the user:
.data 
+input: .space 100 
+inputsize: .word 100 
+.text 
+li $v0, 8 
+la $a0, input 
+lw $a1, inputsize 
+syscall
3. Printing strings stored in memory
To print the required string, the syscall to be used is 4. The address of the string has to be loaded into the $a0 register.
Code to print a string named ‘message’ stored in memory:
.text 
+li $v0, 4 
+la $a0, output 
+syscall
We have now learnt how to declare strings constants as well as how to store strings entered by the user. We shall now write a program combining both the concepts for a more robust understanding of basic string operations.
Code to read a string, with prompts instructing the user:
.text 
+main: 
+    # Prompt for the string to enter 
+    li $v0, 4 
+    la $a0, prompt 
+    syscall 
+ 
+    # Read the string.  
+    li $v0, 8 
+    la $a0, input 
+    lw $a1, inputSize  
+    syscall 
+     
+    # Output the text 
+    li $v0, 4 
+    la $a0, output 
+    syscall
+
+    # Output the number 
+    li $v0, 4 
+    la $a0, input 
+    syscall 
+ 
+    # Exit the program 
+    li $v0, 10 
+    syscall 
+ 
+.data 
+input:        .space 81 
+inputSize:    .word 80 
+prompt:       .asciiz "Please enter a string: " 
+output:       .asciiz "\\nYou typed the string: "
Points To Note ​
  • The .space directive allocates n bytes of memory in the data region of the program, where n=81 in this program. Since the size of a character is 1 byte, this is equivalent to saving 80 characters for data. 81 was used here because in MIPS a sequence of ASCII characters is terminated by a null value (byte containing 0). This is known as a null terminator.
  • If the string the user enters is larger than the maximum size of the string, it is truncated to the maximum size. This is to prevent the program from accessing memory not allocated to the string.
Floating Point Numbers ​
Floating point numbers are stored according to the IEEE 754 Standard. There are 2 types of floating point numbers, single precision and double precision.
Floating point number representation ​
According to IEE 754 Standard, floating point numbers follow the given representation.
Sign Exponent Fraction
  • The sign bit is 0 or 1, for positive or negative respectively.
  • The exponent stores the exponent of the number in scientific notation of its binary representation, plus a bias.
  • The fraction stores the fractional part of the binary representation of the number.
DataSingle PrecisionDouble Precision
Size32 bits64 bits
Exponent size8 bits11 bits
Fraction size23 bits52 bits
Bias1271023
Note
  • Since there are some numbers with non-ending decimal part in there binary representation ( For Example- ( 1 /3) 10 = (0.01 0011 0011 0011 ....) 2 ) and we have only limited bits to store the fraction part, there will be some slight inaccuracy while storing certain floating point numbers. Therefore, it is recommended to always use double, as it has a higher precision due to its increased no. of bits.
MIPS floating point architecture ​
In MIPS, all floating point calculations are computed in a separate processor, called co- processor 1.
The coprocessor contains 32 floating point registers, each of width 32 bits. The registers are numbered from $f 0 to $f3 1.
Each register is can store a single precision floating point number, while double precision is stored in 2 registers in an even-odd pair. For instructions concerning double precision numbers, the even numbered register is used in the instruction. Using an odd numbered register will throw an error.
In addition to the registers, there are 8 condition flags, which are used in floating point compare and branch instructions.
Floating point registers in MIPS ​
RegistersUsage
$f0 - $f3Used for results of floating point procedures
$f4 - $f11Temporary floating point registers, whose values are NOT preserved across procedure calls
$f12 - $f15Floating point parameters, whose values are NOT preserved across procedure calls
$f16 - $f19More temporary floating point registers, whose values are NOT preserved across procedure calls
$f20 - $f31Saved floating point registers, whose values are preserved across procedure calls
Among the 32 registers, only $f 4 - $f 11 , $f 16 - $f 19 and $f 20 - $f 31 can be used by the programmer for storing values, as the others are reserved for special purposes.
Note
  • Unlike the general purpose register $ 0 , $f 0 is not hardwired to be zero, and is used for storing results of procedures.
Declaring a Floating point number ​
.data
+  num1: .float 3.
+  num2: .double 4.5 3
+
+  .align 2 # Since float has 2^2 bytes
+  float_arr: .space 100 it has to be aligned to 2
+
+  .align 3 # Since double has 2^3 bytes it has to be aligned to 3
+  double_arr: .space 100
Reading and Printing Floating point numbers ​
Reading and printing a floating point number is similar to that of an integer, using syscall, only difference being in the $v0 value and parameter registers.
Single precision ​
The $v0 value for reading a single precision floating point number is 6 while that of printing is 2.
main: 
+  li $v0, 6 
+  syscall    # The number is stored in $f0 
+        
+  li $v0, 2 
+  mov.s $f12, $f0   # The number to be printed is moved to $f12 
+  syscall
Double precision ​
The $v0 value for reading a double precision floating point number is 7 while that of printing is 3.
main: 
+  li $v0, 7 
+  syscall    # The number is stored in $f0/$f1 
+        
+  li $v0, 3 
+  mov.d $f12, $f0   # The number to be printed is 
+  syscall     moved to $f12/$f13
Data Movement Instructions ​
InstructionSyntaxRemarks
Load single/doublel.s fdest, address l.d fdest, addressThe single/double floating-point stored in address is loaded onto register fdest
Store single/doubles.s fsrc, address s.d fsrc, addressThe single/double floating-point stored in register fsrc is stored to address
Move single/doublemov.s fdest, fsrc mov.d fdest, fsrcThe single/double floating-point stored in register fsrc is moved to register fdest
Move from coprocessor 1mfc1 dest, fsrcThe 32 - bit data from floating register fsrc is copied to general purpose register dest
Move to coprocessor 1mtc1 src, fdestThe 32 - bit data from general purpose register src is copied to floating point register fdest
Note
  • There is no load immediate for floating point. So if a constant is needed, it has to be stored in the data segment and loaded to the required register.
  • For the move to/from coprocessor 1 instructions, the first operand is a general purpose register and the second one is the floating point register.
Arithmetic Instructions ​
InstructionSyntaxRemarks
Additionadd.s fdest, fsrc1, fsrc2 
 add.d fdest, fsrc1, fsrc		The single/double floating-point numbers stored in fsrc1 and fsrc2 
 are added and stored in register fdest
Subtractionsub.s fdest, fsrc1, fsrc2 
 sub.d fdest, fsrc1, fsrc2		The single/double floating-point number stored in fsrc 
 subtracted from fsrc1 and stored in register fdest
Multiplicationmul.s fdest, fsrc1, fsrc2 
 mul.d fdest, fsrc1, fsrc2		The single/double floating-point numbers stored in fsrc1 and fsrc2 
 are multiplied and stored in register fdest
Divisiondiv.s fdest, fsrc1, fsrc2 
 div.d fdest, fsrc1, fsrc		The single/double floating-point number stored in fsrc1 is divided by fsrc2 
 and the quotient is stored in register fdest
Negationneg.s fdest, fsrc 
 neg.d fdest, fsrc		The single/double floating-point number stored in fsrc 
 is negated (Sign changed) and stored in register fdest
Absolute valueabs.s fdest, fsrc 
 abs.d fdest, fsrc		Absolute value (Magnitude) of the single/double floating-point number stored in fsrc 
 is stored in register fdest
Square rootsqrt.s fdest, fsrc 
 sqrt.d fdest, fsrc		Square root of the single/double floating-point number stored in fsrc 
 is stored in register fdest
Sample Question 1 ​
Given a temperature in Fahrenheit, convert it into Celsius (Input and output has to be floating point values).
Temperature in degrees Celsius = (Temperature in degrees Fahrenheit - 32 ) * 5 / 9.
data 
+  # Constants used for calculation 
+  const1: .double 32.0 
+  const2: .double 5.0 
+  const3: .double 9.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the temperature in Fahrenheit: " 
+  msg2: .asciiz "The temperature in Celsius is: " 
+ 
+
+.text 
+.globl main 
+main: 
+ 
+  li $v0, 4                    # Printing msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7                    # Reading user input 
+  syscall 
+  
+  mov.d $f12, $f0              # $f12 = User Input 
+  l.d $f14, const1             # $f12 = $f12 - 32 
+  sub.d $f12, $f12, $f14 
+  
+  l.d $f14, const2             # $f12 = $f12 * 5 
+  mul.d $f12, $f12, $f14 
+  
+  l.d $f14, const3             # $f12 = $f12 / 9 
+  div.d $f12, $f12, $f14 
+  
+  li $v0, 4                    # Printing msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 3                    # Printing final answer 
+  syscall 
+  
+  li $v0, 10                   # Exit 
+  syscall
Comparison/Branch Instructions ​
InstructionSyntaxRemarks
Compare equalc.eq.s cc, fsrc1, fsrc2 
 c.eq.s fsrc1, fsrc2 
c.eq.d cc, fsrc1, fsrc2 
 c.eq.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the numbers in fsrc1 
 and fsrc2 are equal, 0 otherwise.
Compare less thanc.lt.s cc, fsrc1, fsrc2 
 c.lt.s fsrc1, fsrc2 
 c.lt.d cc, fsrc1, fsrc2 
 c.lt.d fsrc1, fsrc2		Sets the condition flag cc as 1 if the number in fsrc1 
 is less than that in fsrc2, 0 otherwise.
Compare less than or equal toc.le.s cc, fsrc1, fsrc2 
 c.le.s fsrc1, fsrc2 
 c.le.d cc, fsrc1, fsrc2 
 c.le.d fsrc1, fsrc		Sets the condition flag cc as 1 if the number in fsrc1 
 is less thanor equal to that in fsrc2, 0 otherwise.
Branch if truebc1t cc, label 
 bc1t label		Jumps to label if the condition flag cc is set as 1
Branch if falsebc1f cc, label 
 bc1f label		Jumps to label if the condition flag cc is set as 0
Note
  • The condition flag can be omitted in the above instructions, in which case condition flag 0 is taken as default.
  • As there is no comparison instruction for “Not equal to”, it has to be implemented by reversing the required branch condition Ex. We need to branch to label if $f4 and $f6 are not equal. This can be written as
      c.eq.d $f4, $f6
+  bc1.f label
  • For greater than and greater than and equal to, it is simpler to reverse the input registers. Ex. We need to branch to label if $f4 if greater than $f6. This can be written as
      c.le.d $f6 , $f4
+  bc1.t label
Sample Question 2 ​
Given an array of floating numbers of size n, print the maximum and minimum element
data 
+  # Array 
+  .align 3 
+  arr: .space 1000 
+  
+  # Characters 
+  newline: .asciiz "\\n" 
+ 
+  # User Prompts 
+  msg1: .asciiz "Enter n: " 
+  msg2: .asciiz "Enter no. " 
+  msg3: .asciiz ": " 
+  msg4: .asciiz "The maximum no. is: " 
+  msg5: .asciiz "The minimum no. is: " 
+ 
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4    # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 5    # Read n 
+  syscall 
+  move $t0, $v0 
+  
+  li $t1, 0    # $t1 will be the loop variable  
+               # going from 0,1,2.. 
+  li $t2, 0    # $t2 will be the element indices 
+               # going from 0,8,16.. 
+  loop1:                      # Loop to read n elements 
+    beq $t0, $t1, end_loop1   # Termination condition 
+   
+    li $v0, 4                 # Print msg2 
+    la $a0, msg2 
+    syscall 
+   
+    li $v0, 1                 # Print position of                    
+    move $a0, $t1             # number to be inputted 
+    addi $a0, $a0, 1 
+    syscall 
+   
+    li $v0, 4                 # Print msg3 
+    la $a0, msg3 
+    syscall 
+   
+    li $v0, 7                 # Read input and  
+    syscall                   # store in arr 
+    s.d $f0, arr($t2) 
+   
+    addi $t1, $t1, 1   # Increamenting #t1  
+    addi $t2, $t2, 8   # and $t2 
+    j loop1 
+  
+  end_loop1: 
+  
+  li $t1, 0    # Resetting $t1 and $t2 
+  li $t2, 0 
+  l.d $f4, arr($zero)  # $f4 stores the max value 
+  l.d $f6, arr($zero)  # $f6 stores the min value
+
+  loop2:                        # Loop to compute max and min 
+    beq $t0, $t1, end_loop2     # Termination Condition 
+   
+    l.d $f8, arr($t2)           # Load a number from arr 
+   
+    c.lt.d $f4, $f8             # Compare if the number is  
+                                # greater than current max 
+    bc1f not_max  
+      mov.d $f4, $f8            # If yes then update new max 
+    not_max: 
+   
+    c.lt.d $f8, $f6             # Compare if the number is  
+                                # less than current min 
+    bc1f not_min 
+      mov.d $f6, $f8            # If yes then update new min 
+    not_min: 
+   
+    addi $t1, $t1, 1            # Incrementing $t1 and $t2 
+    addi $t2, $t2, 8 
+    j loop2 
+  
+  end_loop2: 
+  
+  li $v0, 4                      # Print msg4 
+  la $a0, msg4 
+  syscall 
+  
+  li $v0, 3                      # Print max number 
+  mov.d $f12, $f4 
+  syscall 
+
+  i $v0, 4    # Print newline 
+  la $a0, newline 
+  syscall 
+  
+  li $v0, 4    # Print msg5 
+  la $a0, msg5 
+  syscall 
+  
+  li $v0, 3    # Print min number 
+  mov.d $f12, $f6 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall
Data Conversion Instructions ​
Conversion within floating point ​
InstructionSyntaxRemarks
Convert single to doublecvt.d.s fdest, fsrcThe single floating-point stored in fsrc is converted to double and stored in fdest
Convert double to singlecvt.s.d fdest, fsrcThe double floating-point stored in fsrc is converted to single and stored in fdest
Conversion to integers ​
InstructionSyntaxRemarks
Convert single to integercvt.w.s fdest, fsrcThe single floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) 
 and stored in 2 ’s compliment form in fdest
Convert double to integercvt.w.d fdest, fsrcThe double floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) and 
 stored in 2 ’s compliment form in fdest
 Note 
  • The output of the above two instructions is in 2 ’s compliment form, which should not be used with any other instructions other than mfc1. Other instructions always assume the data in registers are according to IEEE standards, which can cause errors.
Conversion from integers ​
InstructionSyntaxRemarks
Convert integer to singlecvt.s.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and 
 is converted to single precision floating point and is stored in fdest
Convert integer to doublecvt.d.w fdest, fsrcThe data stored in fsrc is considered as an integer in 2 ’s compliment form and 
 is converted to double precision floating point and is stored in fdest
Special Instructions ​
InstructionSyntaxRemarks
Ceilingceil.w.s fdest, fsrc 
 ceil.w.d fdest, fsrc		The smallest integer not greater than the floating point number in fsrc 
 is stored in fdest in 2 ’s compliment form
Floorfloor.w.s fdest, fsrc 
 floor.w.d fdest, fsrc		The greatest integer not smaller than the floating point number in fsrc 
 is stored in fdest in 2 ’s compliment form
Round to nearest integerround.w.s fdest, fsrc 
 round.w.d fdest, fsrc		The floating-point stored in fsrc is rounded off to 
 nearest integer and stored in fdest in 2 ’s compliment form
Sample Question 3 ​
Given a floating point number and an integer n, round off the floating point number to n digits.
 Hint- 
Multiplty then given number with 10^n, and round off using round.w.d instruction. Divide the result by 10^n to obtain the final result.
data 
+  # Constants used for calculation 
+  const1: .double 0.0 
+  const2: .double 1.0 
+  const3: .double 10.0 
+  
+  # User prompts 
+  msg1: .asciiz "Enter the number : " 
+  msg2: .asciiz "Enter number of digits to round off to: " 
+  msg3: .asciiz "The rounded off number is: " 
+  
+.text 
+.globl main 
+main: 
+  
+  li $v0, 4     # Print msg1 
+  la $a0, msg1 
+  syscall 
+  
+  li $v0, 7     # Read number to round off 
+  syscall 
+  
+  mov.d $f12, $f0    # $f12 = user input 
+  
+  li $v0, 4     # Print msg2 
+  la $a0, msg2 
+  syscall 
+  
+  li $v0, 7     # Read n 
+  syscall 
+
+  mov.d $f16, $f0    # $f16 = n 
+  l.d $f4, const1    # $f4 used as a loop varibale 
+                     # initialised to 0 
+  l.d $f6, const2    # $f6 used to store 10^n 
+  l.d $f8, const3    # $f8 used to store 10 for  
+                     # calculating power 
+  l.d $f10, const2   # $f10 used to store 1 for  
+                     # incrementing loop variable 
+  loop1:    # Loop to compute 10^n 
+    c.eq.d $f4, $f16  # Ternminaltion Condition 
+    bc1t end_loop1 
+  
+    mul.d $f6, $f6, $f8 # $f6 = $f6 * 10 
+    add.d $f4, $f4, $f10  # $f4 = $f4 + 1 
+  
+    j loop1 
+  end_loop1: 
+  
+  mul.d $f12, $f12, $f6  # $f12 = $f12 * (10^n) 
+  round.w.d $f12, $f12   # $f12 is rounded to nearest 
+                         # integer 
+  cvt.d.w $f12, $f12     # Output after rounding,  
+                         # which is a word, is  
+                         # converted back to double 
+  div.d $f12, $f12, $f6  # $f12 = $f12 / (10^n) 
+  
+  li $v0, 4    # Print msg3 
+  la $a0, msg3 
+  syscall  
+ 
+  li $v0, 3    # Print final answer 
+  syscall 
+  
+  li $v0, 10   # Exit 
+  syscall
Integer Arrays ​
An Integer Array is continuous storage block in memory in which each element is an integer. Each element of an array is accessed using the base address of the array and the index of the element we must access.
Declaration and Initialization ​
Integer arrays can be initialized using .word or an empty array can be declared using the .space keyword inside the .data section of the program
data: 
+arr: .word 3,4,-5,6    #initialized an array arr=[3,4,-5,6] 
+arr2: .space 40  # empty array with 40 bytes reserved for arr2
Array Traversal ​
Array traversal refers to accessing each element of the array using its index.
Each integer element of an array occupies a word (4 bytes). Therefore,4 bytes needed to be added to the current address to obtain the address of the following element.
Address of arr [k] = base address of arr + 4 * k
Eg: To access arr[3] and store it to $t
a $s0,arr   # base add address of array is stored in $s0 
+addi $s0,$s0,12    #  $s0 = address of arr[3] = arr + 4 * 3 
+lw $t2,0($s0)    # $t2=arr[3]
or
a $s0,arr   # base add address of array is stored in $s0 
+lw $t2,12($s0)  # $t2=value of (arr + 12)
Array Input ​
The elements of an integer array can be received from the user using the syscall for integer input and a for loop.
An empty array must be declared in the .data by allocating the necessary space as shown before.
Each integer element of an array occupies 4 bytes. Therefore, 4 bytes needed to be added to the current address after each insertion.
The following code segment can be used to create an array of size n by receiving inputs from the user:
Assume $s1 contains n, $s0 contains base address of an empty array and $t0 is the loop counter
for: 
+  beq $t0,$s1,exit      # loop termination condition 
+  sll $t1,$t0,2         # $t1=i*4 
+  add $t1,$t1,$s0   # $t1 = arr + i * 4         
+       
+  li $v0,5           # input integer and store in $t2 
+  syscall 
+  move $t2,$v0 
+  sw $t2,0($t1)      # $t2 = arr[i] 
+  addi $t0,$t0,1     # increment loop counter i 
+  j for
Printing an Integer Array ​
Integer Array can be printed by traversing each element by using array traversal rules (as discussed above) and integer printing (code 1 is loaded to $v0).
Consider the following code snippet to print the array created in the previous example in which every element is provided by the user:
la $s0,arr             # store base address of array in $s0 
+li $t0,0 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       # array traversal to access arr[i] 
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)       # $t2=arr[i] 
+  li $v0,1            # 1 is the syscall number to print integers 
+  move $a0,$t2         # print $t2   
+  syscall 
+    
+  li $a0, 32     # 32 is the ASCII code for space  
+  li $v0, 11          # syscall number for printing character 
+  syscall 
+  addi $t0,$t0,1 # increment loop counter 
+  j print 
+end:                         
+li $v0,10   #end program        
+syscall
Negative Numbers as Elements ​
All integer operations in MIPS support both positive and negative numbers. No changes are required to the program for the input and output of positive integers.
enter array element: -5 
+enter array element: -6 
+enter array element: 8 
+enter array element: -2 
+The elements of the array are: -5.0 -6.0 8.0 -2.0  
+-- program is finished running --
Floating Point Numbers as Elements ​
An array of floating-point numbers can be created by replacing all the integer operations with floating-point operations. The following changes need to be made to convert an integer array into an array of floating-point numbers:
  1. Replace the integer code loaded to $v0 by floating-point code
  2. Replace the load, store and move operation by l.s , s.s and mov.s where floating point data type is used
# program to input array 
+for: 
+  beq $t0,$s1,exit
+  sll $t1,$t0,2
+  add $t1,$t1,$s0  
+  li $v0,6          # code for floating point input 
+  syscall
+  s.s $f0,0($t1)    # arr[i]=$f0 
+  addi $t0,$t0,1 
+  j for  
+exit: 
+
+# print array 
+print: 
+  beq $t0,$s1,end  
+  sll $t1,$t0,2       
+  add $t1,$t1,$s0 
+  l.s $f0,0($t1)       # $f0=arr[i] 
+  li $v0,2           # code for printing floating point 
+  mov.s $f12,$f0   
+  syscall 
+  li $a0, 32           
+  li $v0, 11           
+  syscall 
+  addi $t0,$t0,1  
+  j print 
+end
One Dimensional Arrays ​
To calculate the sum of n numbers in an n sized array ​
li $t0,0 
+la $s0,arr 
+li $t3,0        #t3 stores the sum 
+sum:          #for loop 
+  beq $t0,$s1,end     # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)      # $t2=arr[i] 
+  add $t3,$t3,$t2    # $t3=$t3+$t2 
+  addi $t0,$t0,1     # increment loop counter 
+  j sum 
+end:                 
+li $v0,1              # print sum 
+move $a0,$t3                 
+syscall
To find the largest element in an n sized array ​
la $s0,arr 
+li $t0,0 
+li $t3,-1000 # $t3=max 
+  # initialized to -1000   
+max: 
+  beq $t0,$s1,end # $s1 contains n 
+  sll $t1,$t0,2              
+  add $t1,$t1,$s0 
+  lw $t2,0($t1)  # $t2=arr[i] 
+  ble $t2,$t3,inc_i  # if arr[i]<=max, jump to inc_count 
+  move $t3,$t2   # if arr[i]>max, max=arr[i] 
+  inc_count: 
+    addi $t0,$t0,1  # increment loop counter 
+    j max 
+end:  
+li $v0,1                  # print max 
+move $a0,$t3                 
+syscall
String Operations (Advanced) ​
Null Character and Newline ​
When strings are created by using user input (code 8 passed to $vo), it forms a sequence of ASCII characters that are terminated by a newline character, followed by a NULL character. The newline character is triggered by the pressing of enter key during user input.
The ASCII code for newline is 10. Hence beq, $t1,10,label can be used as a comparing instruction
MIPS treats NULL character as a zero. Hence beqz, $t1, label can be used as a comparing instruction
String Traversal ​
Strings are made up of characters, in which each character occupies a byte. Hence, unlike an Integer Array, each character must be traversed byte by byte.
Eg:
To find the length of a string (newline character need not be included)
# assume string is input to str1 
+li $s1,0 #loop counter (i) 
+  
+len: 
+  lb $t1,str1($s1)  # $t1=str[i] 
+  beq $t1,10,start  # termination condition 
+  addi $s1,$s1,1    # i=i+1 
+  j len 
+start: 
+  li $v0,1          # print len=i  
+  move $a0,$s1 
+  syscall
If the newline character needs to be included in the length, beq should be replaced with beqz
String Concatenation ​
Concatenation of two strings can be done using 2 loops. The presence of newline and null character at the end of each string should be considered.
Consider two strings, str1 and str2. The following is the pseudocode and the code snippet for concatenating str2 to str1:
Pseudo Code:
c
i=0
+
+j=0
+
+while str1[i]!='\\n'
+
+i++
+
+while str2[j]!='\\0'
+
+str1[i]=str2[j]
+
+i++
+
+j++
MIPS:
mips
i $s1,0           # i=0 
+li $s2,0           # j=0 
+loop1: 
+   lb $t1,str1($s1)  
+  beq $t1,10,loop2 
+  addi $s1,$s1,1           # i++ 
+  j loop1 
+loop2: 
+  lb $t1,str2($s2) 
+  beqz $t1,end 
+  sb $t1,str1($s1)    # str1[i]=str[j] 
+  addi $s1,$s1,1      # i++ 
+  addi $s2,$s2,1      # j++ 
+  j loop2 
+end:
Palindrome Checking ​
A palindrome sequence that reads the same backwards as forwards. Palindrome checking uses two pointer method.
Assume a string str, whole length is n. Length of the string is calculated by previous method and stored in $s1. The following code snippet shows the while loop necessary for checking whether the string is palindrome
addi $s1,$s1,-1 # j=n-1  
+li $s0,0        # i=0 
+for: 
+  lb $t1,str($s0)   
+  lb $t2,str($s1)   
+  bge $s0,$s1,true    # if i>=j,exit loop. return True 
+  bne $t1,$t2,false   # if str[i]!=str[j], return False 
+  addi $s0,$s0,1      #  i++ 
+  addi $s1,$s1,-1     #  j-- 
+  j for
Two Dimensional Arrays ​
2-DArrays/Matrices/Tables aren’t stored in memory the way it is normally visualized; rather it is stored as a single array in either row major form or column major form. Let’s see how a matrix is represented in memory in both the forms with a starting address of 1230. (Remember:In an array each element is 4 bytes long).
a) Row Major form : Here elements are stored row wise. First we store the first row, then the second and soon.
b) Column Major form: Here elements are stored column wise. First we store the first column, then the second and soon.
Row Major form ( starting address 1000 )
Column Major form ( starting address 1000 )
Sample code ​
->Insertion of elements and printing the 2D-array
**We are using row major form to input the elements as a string
**NOTE: all characters need to be space separated, the end of the sequence also need to have a space
Pseudo code-> ​
Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D array
+Print the matrix:
+- Loop through rows:
+- Loop through columns:
+- Print each element of the matrix
+- Print a space between elements
+- Print a newline after each row
+Exit the program
MIPS Code-> ​
.data
+newline: .asciiz "\\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+mat1: .space 100
+input: .space 100
+
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0         # $t0 = number of rows
+
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+
+  li $v0, 5
+  syscall
+  move $t1, $v0         # $t1 = number of columns
+
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+
+  li $t5, 0
+
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+# when a space is detected add the number calculated to the array and continue
+
+  beq $t4, $zero , end_input
+
+#In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+
+#This loop exist to calculate numbers that have more than one digit , since our input is a string.
+
+# We need to iterate and add the characters until we detect a space
+
+  sub $t6 , $t4, 48 # converts character to integer
+
+# for calculating the number
+  
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  
+  j input_loop
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+print_loop:
+  beq $t6 , $t0 , end_programme
+  li $t7 , 0 # Initialize column index
+
+print_column_loop:
+  lw $t9 , 0($t8) # Load number from array
+  li $v0, 1 # syscall for print_int
+  move $a0, $t9 # Load number to print
+  syscall
+
+  li $v0, 4 # syscall for print_str 
+  la $a0, space # Load address of space
+  syscall
+
+  addi $t7, $t7, 1 # Increment column index
+  addi $t8 , $t8 , 4 # Increment base address
+  blt $t7, $t1 , print_column_loop # Print all elements in the row
+
+# Print newline after each row
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+
+# Reset column index for next row
+  li $t7 , 0
+
+# Increment row index
+  addi $t6 , $t6 , 1
+
+  j print_loop
+  
+end_programme :
+  li $v0, 10 # syscall for exit
+  syscall
Output ​
  Enter number of rows:3
+  Enter number of columns:3
+  Enter matrix(row major form) : 1 2 3 4 5 6 7 8 9
+
+  1 2 3 
+  4 5 6 
+  7 8 9
->To find maximum and minimum element in a 2-D array ​
**We are using row major form to input the elements as a string
**same process of taking the input as the above
**NOTE: all characters need to be space separated, the end of the sequence also need to have a space
Pseudo code-> ​
Prompt user for number of rows and columns
+Initialize 2D array
+Prompt user to enter matrix values as a string
+Loop through input string:
+- Extract numbers delimited by spaces
+- Convert each substring to integer and store in the 2D
+array
+Find minimum and maximum elements in the matrix:
+- Initialize minimum element to maximum possible value
+and maximum element to 0
+- Loop through each element of the matrix:
+- Update minimum and maximum elements if necessary
+Print the maximum element message:
+- Print "The maximum element is: "
+- Print the maximum element
+Print the minimum element message:
+- Print "The minimum element is: "
+- Print the minimum element
+Exit the program
MIPS Code-> ​
.data
+newline: .asciiz "\\n"
+space: .asciiz " "
+msg_rows: .asciiz "Enter number of rows : "
+msg_columns: .asciiz "Enter number of columns : "
+msg_input: .asciiz "Enter matrix ( row major form ) : "
+maximum : .asciiz"The maximum element is : "
+minimum : .asciiz"The minimum element is :
+mat1: .space 100
+input: .space 100
+.text
+main:
+  li $v0, 4
+  la $a0, msg_rows
+  syscall
+  
+  li $v0, 5
+  syscall
+  move $t0, $v0 # $t0 = number of rows
+  
+  li $v0, 4
+  la $a0, msg_columns
+  syscall
+  
+  li $v0, 5
+  syscall 
+  move $t1, $v0 # $t1 = number of columns
+  
+  li $v0, 4
+  la $a0, msg_input
+  syscall
+  
+  li $v0, 8 # syscall for read_str
+  la $a0, input # Load address of input buer
+  li $a1, 100 # Maximum length
+  syscall
+
+  la $t2, input
+  la $t3, mat1
+  
+  li $t5, 0
+  
+  # t2 - address of input string
+  # t3 - address of matrix
+  # t4 - used to iterate through string
+  # t5 - used to calculate number
+
+input_loop:
+  lb $t4, 0($t2)
+  beq $t4, 32, store
+
+  # when a space is detected add the number calculated to the array and continue
+  
+  beq $t4, $zero , end_input
+  
+  #In ASCII encoding, the decimal value 32 corresponds to the space character (' ')
+  
+  #This loop exist to calculate numbers that have more than one digit , since our input is a string
+  # we need to iterate and add the characters until we detect a space
+  
+  sub $t6 , $t4, 48 # converts character to integer
+
+  # for calculating the number
+  mul $t5, $t5, 10
+  add $t5, $t5, $t6
+  addi $t2, $t2, 1
+  j input_loop
+
+store:
+  sw $t5, 0($t3) #store the number obtained in the 2D-array
+  addi $t3, $t3, 4 #increment the address to next memory block
+  li $t5, 0
+  add $t2 , $t2 , 1 #increment the index of string
+  j input_loop #loop back to the input to continue iteration of string
+
+end_input :
+  li $t6 , 0 # Initialize row index
+  la $t8, mat1 # Load address of array for printing
+  li $v0, 4
+  la $a0, newline
+  syscall
+
+find_min_max:
+  li $t3 , 0 # Initialize max element to 0
+  li $t2 , 0xffffffff
+  li $t6 , 0 # Initialize row index to 0
+  la $a0 , mat1
+
+row_loop:
+  beq $t6, $t0 , end # If all rows have been checked, exit
+  
+  li $t7, 0 # Initialize column index to 0 
+
+column_loop:
+  beq $t7, $t1 , end_column_loop # If all columns have been checked, move to next row
+  
+  lw $t8, 0($a0) # Load current element from array
+
+# Compare current element with max element and the min element
+  bgt $t8, $t3, update_max # if element greater than max element , update max
+  
+  min :
+  blt $t8 , $t2 , update_min # if element smaller than min element, update min
+  
+  increment :
+  addi $a0, $a0, 4 # Move to next column
+  addi $t7, $t7, 1 # Increment column index
+  j column_loop
+
+update_max:
+  move $t3 , $t8 # Update max element
+  j min # control goes back to checking for the conditional statement of min element
+
+update_min:
+  move $t2 , $t8 # Update min element
+  j increment # control goes back to incrementing the looping values
+
+End_column_loop:
+  addi $t6, $t6, 1 # Increment row index
+  j row_loop
+
+end :
+  li $v0 , 4
+  la $a0 , maximum  
+  syscall
+  
+  li $v0 , 1
+  move $a0 , $t3 # printing the maximum element
+  syscall
+  
+  li $v0 , 4
+  la $a0 , newline
+  syscall
+  
+  li $v0 , 4
+  la $a0 , minimum # printing the minimum element
+  syscall
+
+  li $v0 , 1
+  move $a0 , $t2
+  syscall
+  
+  li $v0 , 10
+  syscall
Output ​
  Enter number of rows :3
+  Enter number of columns :3
+  Enter matrix ( row major form ) : 1 2 34 5 6 7 300 9 22
+
+  The maximum element is : 300
+  The minimum element is : 1
More Questions ​
->Searching in Matrix: Write a MIPS assembly program to search for a given element in a matrix and return its position if found.
->Matrix Addition: Write a MIPS program to add two matrices of the same size
->Transpose of a Matrix: Write a MIPS assembly program to find the transpose of a given matrix.
★ MIPS code for if statements ● Iftheconditionisanequalityusebeq,bne ● Iftheconditionisacomparisoncombinebeq/bnewithset-on-less-than
Why not blt or bge? While blt and bge (pseudo-instructions) are available in MIPS, beq and bne are favoured inconditional statements for their efficiency making them the common choice.
Example 1) Given,f:$s0, g:$s1, h:$s2, i:$s3, j:$s4
  if(i==j)
+    f = g + h;
+  else
+    f = g - h;
Solution 1 :- Corresponding MIPS code
  bne $s3, $s4, else
+  add $s0, $s1, $s2
+  j endif
+else: sub $s0, $s1, $s2
+endif: ...........
Example 2) Given,f:$s0 ,g:$s1 ,h:$s2 ,i:$s3 ,j:$s4
  if(i<j)
+    f=g+h;
+  else
+    f=g-h;
Solution 2 :- Corresponding MIPS code
  slt $to, $s3, $s4
+  beq $to, $zero, else
+  add $s0, $s1, $s2
+  j endif
+else:
+  sub $s0, $s1, $s2
+endif: .......
★ MIPS code for Loop statements
Although there are said to be 3 different types of loops in C namely, do/while, while and for loop, they are all functionally identical. In other words, you can take any for-loop and easily turn it into a while-loop.
asm
  int i;
+  for(i= 0 ;i< 10 ;i++){
+    loopbody;
+  }
or
asm
  inti=0;
+  while(i< 10 ){
+    loopbody;
+    i++;
+  }
Example 1) Given, i:$s3, k:$s
asm
  while(i < j)
+    i+=1;
Solution 1 :- Corresponding MIPS code
asm
loop:
+  slt $t0, $s3, $s4
+  beq $t0, $zero, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit: ...
Example 2) Given i:$t0, k is some integer
asm
  int i;
+  for(i = 0; i < k; i++){
+    // loop body
+  }
Solution 2 :- Corresponding MIPS code
asm
  add $t0, $zero, $zero # i is initialized to 0, $t0 = 0
+Loop: // loop body
+  addi $t0, $t0, 1 # i ++
+  slti $t1, $t0, 4 # $t1 = 1 if i < 4
+  bne $t1, $zero, Loop # go to Loop if i < 4
Example 3) Given, i:$s3, base address of arr:$s6, k:$s
asm
  while(arr[i] == k)
+    i+=3;
Solution 3 :- Corresponding MIPS code
asm
loop:
+  sll $t0, $s3, 3
+  add $t1, $t0, $s6
+  lw $t2, 0($t1)
+  bne $t2, $s5, exit
+  addi $s3, $s3, 1
+  j loop
+
+exit:...
★ Procedures in MIPS
Understanding the memory layout and the way procedures are called is crucial for writing efficient and correct MIPS assembly code.
➢ Memory Layout
➢ Stack allocation (refer Recursion in MIPS(non-leaf procedure) for detailed explanation)
(a) before, (b) during, and (c) after a procedure call.
There are two types of procedure calling-
1) Leaf Procedures: These procedures do not call other procedures.
When a leaf procedure is called:
● There turn address is saved on the stack. ● A stack frame/procedure frame/activation record is setup to store local variables. ● Arguments may be passed in registers or on the stack. ● The procedure executes its code.
Upon completion,it restores the stack pointer and returns to the saved return address.
2) Non-leaf Procedures(NestedProcedures): These procedures call other procedures, eg.- Recursive Functions/Procedures.
In addition to the steps for leaf procedures, non-leaf procedures must manage:
● Saving and restoring additional registers beyond there turn address. ● Managing multiple levels of procedure calls and returns. ● Ensuring that data in registers is preserved a cross nested calls. ● Properly handling there turn value from called procedures.
★ Function (Procedure) calling in MIPS
In MIPS assembly language, passing parameters to functions involves using registers. Unlike high-level languages where parameters are often passed on the stack,MIPS typically uses specific registers for passing arguments.
● $a0 to $a3 :These are argument registers and are used to pass the first four arguments to a function. If a function has more than four parameters,additional parameters are typically passed on the stack.
● $v0 and $v1: These are value registers and are used to return values from functions. Functions can return up to two values using these registers.
(Note:-i) Register 1, called $at, is reserved for the assembler.
 ii) Registers 26–27, called $k0–$k1 are reserved for the operating system.)
➢ Steps in calling a procedure (function)
In MIPS assembly language, procedure calling follows a similar structure to function calls in high-level languages like C.
The following steps typically occur in both leaf and non-leaf functions but there are some nuances in how they're implemented, especially regarding the handling of the stack:
● Arguments Passing :.Arguments to the function can be passed via registers or the stack, depending on the calling convention. In register-based passing, arguments are loaded in to designated argument registers like $a0-$a3. If there are more arguments than available registers, excess arguments are typically passed on the stack.
● Jump and Link (jal) :jal makes the control jump to the given address while storing there turn address at PC+4 in the $ra register This effectively sets up the return mechanism for the function call.
● Function Prologue (Non-leaf functions): Non-leaf functions need to setup a stack frame. This involves: Saving the return address($ra) on to the stack, saving any callee- saved registers on to the stack(these are typically $s0-$s7),setting up the frame pointer($fp) to establish a reference point for accessing local variables and saved registers.
● Function Execution :The function performs its task, accessing arguments, local variables, and performing computations.
● Function Epilogue (Non-leaf functions): Before returning, non-leaf functions need to cleanup the stack frame and restore the state of callee-saved registers.This involves restoring callee-saved registers from the stack, restoring the return address($ra) from the stack resetting the stack pointer($sp) to deallocate the stack frame, jumping back to the return address using the jr $ra instruction.
● Return: Upon completing its task, the function returns control to the caller. If it's a leaf function, it typically involves jumping back to the return address stored in $ra using the jr $ra instruction. For non-leaf functions, the return sequence includes restoring the stack frame and registers before jumping back to the caller.
(Note:-For simplicity we will only use $sp and extend the stack at procedure entry/exit)
Example 1) Calling a procedure which prints a string
asm
//code
+printFunction();
+a=a+2;
+//code
Solution 1 :- Corresponding MIPS code
asm
data
+hello_string: .asciiz "Hello, world!\\n" # String definition
+
+.text
+main:
+....previous code
+jal printFunction #jump to printFunction
+addi $s2, 2
+....further code
+li $v0, 10 # Set syscall code 10 for exit
+syscall # Perform syscall to exit the program
+
+printFunction:
+li $v0, 4 # Set syscall code 4 to print a string
+la $a0, hello_string # Load the address of the string
+syscall # Perform syscall to print
+jr $ra # Return control to PC + 4
● When jal is used, the control moves to the address specified in the instruction and the address of the next instruction is stored in $ra.
● When the procedure ends jr $ra is used to return control back to the next address from where it jumped.
● These procedures are usually placed after the “main” procedure to avoid instruction overlap.
Example 1) Calling a function with parameters
asm
//code
+result=addNumbers(5,7);
+//code
Solution 1 :- Corresponding MIPS code
asm
text
+main:
+  li $a0, 5 # Load first parameter (5) into $a0
+  li $a1, 7 # Load second parameter (7) into $a1
+  jal addNumbers # Jump to addNumbers function
+  move $s0, $v0 # Store the result returned by addNumbers in $s0
+  # Further code
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+addNumbers:
+  add $v0, $a0, $a1 # Add the values of $a0 and $a1 and store the result in $v0
+  jr $ra # Return control to the next instruction after jal
● In the main function, parameters are passed to the addNumbers function by loading values into registers $a0 and $a1.
● The jal instruction is used to jump to the addNumbers function.
● Inside the addNumbers function, the parameters are accessed from the $a0 and $a1 registers.
● The result of the addition is stored in register $v0, which is commonly used to return function results in MIPS.
● Finally, jr $ra is used to return control back to the instruction after the jal in the main function.
★ Recursion in MIPS (non-leaf procedure)
In MIPS assembly language, implementing recursion involves understanding function calls and stack manipulation.
The Stack in MIPS Assembly
● The stack is a crucial data structure used in MIPS assembly language for managing function calls, local variables, and return addresses. ● It operates based on the Last-In-First-Out (LIFO) principle, meaning the last item pushed onto the stack is the first item to be popped off.
Stack Operations:
Stack Pointer ($sp): ● The stack pointer register, $sp, points to the top of the stack. It keeps track of the current position in memory where new items are pushed onto or popped off the stack.
Push Operation: ● To push data onto the stack, the stack pointer is decremented to reserve space for the new item, and then the data is stored at the memory location pointed to by the stack pointer.
Pop Operation: ● To pop data off the stack,the data is retrieved from the memory location pointed to by the stack pointer, and then the stack pointer is incremented to remove the item from the stack.
Stack Usage in Function Calls:Function Prologue: ● When a function is called, the current contents of relevant registers (such as there turn address and callee-saved registers) are typically saved on the stack to ensure they are preserved. ● This process is often referred to as the function prologue.
Function Epilogue: ● Upon completion of the function, the saved values on the stack are restored to their original registers. ● This process is known as the function epilogue.
Example) Function Call and Stack Usage
● When main calls my Function using jal, the return address (the address of the instruction following the function call) is automatically saved in register $ra. ● Inside my Function, the function prologue allocates space on the stack to save the return address. ● The function body executes the desired operations. ● Finally, in the function epilogue, the return address is restored, and the stack space allocated in the prologue is deallocated before returning control to the caller.
To understand recursion in MIPS, a good understanding of the stack pointer and how it operates on memory is imperative. Recursion involves careful management of the function call stack, ensuring that return addresses and local variables are properly saved and restored. This example illustrates the process of calculating the factorial of a number using recursion in MIPS assembly language.
Example) Calculating the factorial of a number using recursion
asm
//code
+result = factorial(5);
+//code
Solution 1 :- Corresponding MIPS code
asm
text
+main:
+  li $a0, 5 # Load the value 5 (number whose factorial is to be calculated) into $a0
+  jal factorial # Jump to the factorial function
+  move $s0, $v0 # Store the result returned by factorial in $s0
+  
+  # Further code using the result stored in $s0
+  # ...
+
+  li $v0, 10 # Set syscall code 10 for exit
+  syscall # Perform syscall to exit the program
+
+factorial:
+  # Function prologue
+  addi $sp, $sp, -4 # Allocate space on the stack for local variables
+  sw $ra, 0($sp) # Save the return address on the stack
+  
+  # Check for base case: if n <= 1, return 1
+  li $t0, 1 # Load the value 1 into $t0
+  ble $a0, $t0, base_case # Branch to base_case if $a0 (n) <= $t0 (1)
+
+  # Recursive case: n * factorial(n - 1)
+  addi $a0, $a0, -1 # Decrement $a0 (n) by 1
+  jal factorial # Recursive call to factorial function
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  mul $v0, $a0, $v0 # Multiply n by the result of factorial(n - 1)
+  jr $ra # Return control to the caller
+
+base_case:
+  # Base case: n <= 1, return 1
+  li $v0, 1 # Load the value 1 into $v0
+  lw $ra, 0($sp) # Restore the return address from the stack
+  addi $sp, $sp, 4 # Deallocate space on the stack for local variables
+  jr $ra # Return control to the caller
● In the main function, the value 5 is loaded into register $a0 to calculate its factorial.
 ● The factorial function is then called using the jal instruction.
 ● Inside the factorial function, the base case checks if the input value n is less than or equal to 1.If so,it returns 1.
 ● Otherwise,the function decrements n by 1 and recursively calls itself with the decremented value.
 ● The result of the recursive call is then multiplied by n to compute the factorial. ● Finally,the result is returned to the caller using register $v0.
References ​
J.L.Hennessy and D.A.Patterson Computer Organization and Design:The Hardware/Software Interface, Fifth Edition
 “Digital Logic and Computer Design” by M.Morris Mano “Digital Fundamentals” by Thomas L.Flyod http://www.cs.missouristate.edu/MARS/https://www.d.umn.edu/~gshute/mips/directives-registers.pdfhttps://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.htmlhttps://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.htmlhttps://riptutorial.com/mips/example/29993/mars-mips-simulatorhttps://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf
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Registers ​
A register is a collection of flip-flops that are edge triggered. Registers capture and store data based on a trigger- either a rising or falling edge. Registers are crucial for CPUs as they serve as temporary data storage elements. To code for a register using behavioural modelling in Verilog, it is expected of us to mimic the behaviour of a register using a variable such that it is assigned a value and stores it until the next edge triggering. We shall discuss how to implement a register using D flip-flops as well.
The reg datatype in Verilog is used to declare variables which model data storage elements, they store the value assigned to them and can represent either combinational or sequential logic.
 To design a simple 4-bit register in Verilog in which only 1 operation – read or write is allowed at a time, we need to declare:
1. A reg variable with the required number of bits (4 in this case) to act as our register.
2. A read/write signal as input (one or multiple depending on whether the question permits more than one operation to be performed at a time).
3. A reset signal which enables us to reset the value in the register to 0- it can be active high or low.
4. Input ports: write_data for the data to be written, read_address and write_address (both are not necessary here since we write to only 1 register but we'll see them in register files).
5. Output port: read_data, write to it when the read/write signal is high and read its value when the read/write signal is low.
v
module register(input clk, rst, rw, 
+                input [3:0] write_data, 
+                output [3:0] read_data); 
+    
+    reg [3:0] block; 
+    always@(posedge clk) begin 
+        if(!rst)   block <= 0; 
+        else begin 
+            if(rw==1) block <= write_data; 
+            else read_data <= block; 
+        end 
+    end 
+endmodule
Since we have written our read logic in the else block, even if the rw signal is any value other than 0 or 1 at the beginning we just read the register displaying its contents, which is ‘x’ initially. This is to avoid unintentionally writing a value, giving read operation a higher priority over write. You can initialize the block reg to 0 too (it can depend on the question).
If we have a register with multiple read and write ports, the question will mention certain specifications for e.g. reads can occur parallelly but not writes. To demonstrate how to go about coding for such a question, let us see an example of a 4-bit register with 1 read ports and 2 write ports. A read and write operation cannot occur simultaneously but we can have 2 such writes and every time we write to the register, we alternately use either of the write ports. Initially, when we perform a write operation, we write into the register with write_data_1, the next time with write_data_2, etc.
v
module reg_wr(input clk, 
+              input rst, 
+              input rw, 
+              input[15:0] data1, data2, 
+              output reg [15:0] read); 
+    // perform writ1 & writ2 alternatively 
+    reg [15:0] block; 
+    reg track=0; 
+    always@(posedge clk) begin 
+        if(rst==0) begin // reset is active low 
+            read <= 0; 
+        end 
+        else if(rw==0) begin // write 
+            if(track==0) begin 
+                block <= data1; 
+                track <= 1; 
+            end 
+            else begin 
+                block <= data2; 
+                track <= 0; 
+            end 
+        end 
+        else begin // read 
+            read <= block; 
+        end 
+    end 
+endmodule
To design a register using flip-flops, let’s consider the first example wherein we had a 4-bit register with one read and write port. We instantiate four D flip-flops and assign the incoming input as input to the flip-flops if the rw signal is high, else we assign the contents of the flip-flop to the output variable. Note that in case of the write operation, the output variable reflects the previously read/stored value.
v
module dflfl(output reg op, input ip, input clk); 
+    always @(posedge clk) begin 
+        op <= ip; 
+    end 
+endmodule 
+   
+module four_bit_reg(output reg [3:0] out, input [3:0] ip, input clk, input rw); 
+    reg [3:0]intermed;  
+    reg [3:0]temp; 
+    
+    dflfl g1(temp[3], rw ? ip[3]:temp[3], clk); 
+    dflfl g2(temp[2], rw ? ip[2]:temp[2], clk); 
+    dflfl g3(temp[1], rw ? ip[1]:temp[1], clk); 
+    dflfl g4(temp[0], rw ? ip[0]:temp[0], clk); 
+   
+    always @(*) begin 
+        if(rw==1'b1) intermed <= temp; // storing previous value in intermed 
+    end 
+    
+    always @(posedge clk) begin 
+        if(rw==1'b1) out <= intermed; // if a write occurs then previously read value is displayed 
+        else out <= temp; // else in case of a read 
+    end 
+endmodule
When we instantiate the D flip-flops, we check whether the rw signal is high i.e. whether a write is occurring to pass the input to it. Since we cannot mix case and if else statements with our combinational block i.e. we cannot instantiate the dffs conditionally (Verilog does not support this), the dffs will therefore be instantiated at every rising edge transition and so for a read operation, we pass it dummy data which would be the previously written (currently stored) value.
Register Files ​
Register Files contain an array of registers. Hence there is a need for read and write address inputs to ascertain which register to read from or write data into.
 Ports are input and output signals. When a question mentions that the register has to have multiple read ports or multiple write ports- this means that there are several read_address, write_address and write_data ports- we can perform more than 1 operation at the same time on different registers within the register file. There are several cases to consider in such questions- if a question permits multiple writes at the same time, you need to think of the possibility of more than one operation attempting to write to the same register, or if a read and write can occur together, you need to think of the possibility of an operation attempting to read from and another attempting to write to the same register. So assigning priorities is important. More than one read operation occurring simultaneously won’t create a problem.
 Let’s look at the code for a register file with 8 registers capable of storing 8-bit data each. It has 2 read ports and 1 write port. Two reads are permitted simultaneously, however only read or write is allowed at a time.
v
module reg_file(input clk, rst, 
+                input [1:0]r1r2w, 
+                input[2:0] port1, 
+                input[2:0] port2, 
+                input [2:0] port3, 
+                input [7:0] data, 
+                output reg [7:0] read1, read2); 
+  
+    reg [WIDTH-1:0] block[WIDTH-1:0]; 
+    // 2 read ports, 1 write port 
+    always@(posedge clk) begin 
+    // r1r2w- 0: write case  
+    // r1r2w- 1: read1 case  
+    // r1r2w- 2: read2 case  
+    // r1r2w- 3: read1 & read2 case  
+        if(rst==0) begin 
+            read1 <= 0; 
+            read2 <= 0; 
+        end 
+        else if(r1r2w == 0) begin // write 
+            block[port1] <= data; 
+        end 
+        else if(r1r2w == 1) begin  
+            read1 <= block[port2]; 
+        end 
+        else if(r1r2w == 2) begin 
+            read2 <= block[port3];  
+        end 
+        else begin 
+            read1 <= block[port2]; 
+            read2 <= block[port3]; 
+        end 
+    end 
+endmodule
We declare a r1r2w signal because we are permitted to perform two reads but a read and write cannot occur simultaneously. Besides the ports, we declare an array of eight eight-bit registers in Verilog in this format: reg [x:0] block [y:0] where you declare the number of bits of each register before the variable name ‘block’ and the number of array elements i.e. registers after block.
Here's a pictorial representation of the register file:

 If we are permitted to perform multiple write operations, then we must assign priorities to the write ports. We can do this by structuring our if else blocks in a favourable manner.
Let’s assume that we have eight eight-bit registers contained in a register file that has 1 read port and 2 write ports. Similar to the last example, we cannot have a read and write operation at once but we can perform both write operations simultaneously. In case two writes try to access the same register, give priority to write_data_1.
v
module reg_file(input clk, rst, 
+                input [1:0] rw1w2, 
+                input [2:0] write_add_1, 
+                input [2:0] write_add_2, 
+                input [2:0] read_add, 
+                input [7:0] write_data_1, 
+                input [7:0] write_data_2, 
+                output reg [7:0] read_data); 
+    
+    parameter WIDTH=8; 
+    reg [WIDTH-1:0] block[WIDTH-1:0]; 
+ 
+    always@(posedge clk) begin 
+    // rw1w2- 0: read case  
+    // rw1w2- 1: write1 case  
+    // rw1w2- 2: write2 case  
+    // rw1w2- 3: write1 & write2 case  
+        if(rst==0) begin 
+            read_data <= 0; 
+        end 
+        else if(rw1w2 == 0) begin // read 
+            read_data <= block[read_add]; 
+        end 
+        else if(rw1w2 == 1) begin // write1 
+            block[write_add_1] <= write_data_1; 
+        end 
+        else if(rw1w2 == 2) begin // write2 
+            block[write_add_2] <= write_data_2; 
+        end 
+        else begin 
+            if (write_add_1 == write_add_2) 
+                block[write_add_1] <= write_data_1; 
+            else begin 
+                block[write_add_1] <= write_data_1; 
+                block[write_add_2] <= write_data_2; 
+            end  
+        end 
+    end 
+endmodule
Q: Can you take the previous example and modify it such that the register file now has 2 read ports and 2 write ports and any pair of operations can occur simultaneously? Let the read operation be of higher priority when a read and write occur simultaneously, and if two operations attempt to write to the same register, let the one with the lower serial number e.g. write_data_1 over write_data_2 be of higher priority.
Shift Registers ​
Shift registers are a cascade of flip-flops used to store values which are passed on to the consecutive register at every edge triggering. They are used for temporary data storage, data transfer and data manipulation. Here is an example of a SISO (Serial In, Serial Out) type shift register:
 Assuming that the ffs are initialized to store a value of 0. Data can be serially shifted to the left or right, in this example we shift to the right. 
CLK TransitionDQ1Q2Q_out
↑1100
↑1110
↑0011
↑0001
↑1100
↑0010
This example shown above is that of a SISO shift register wherein there is only 1 (serial) input and 1 output each such that the data is stored and shifted bit by bit sequentially either leftwards or rightwards.
Other types of shift registers include:
1. SIPO: Serial In, Parallel Out (One input, outputs Qi where i=1,2,..,n for each of the n flipflops)
CLK TransitionDQ1Q2Q_out
↑1100
↑1110
↑0011
↑0001
↑1100
↑0010
2.PISO: Parallel In, Serial Out (Multiple inputs fed separately to each ff, one output Q_out)
',29),g=s('
3. PIPO: Parallel In, Parallel Out (Separate inputs for each ff, separate outputs at each ff)
CLK TransitionD1D2D3Q1Q2Q3
↑101101
↑100100
↑001001
↑000000
↑111111
↑010010
Let’s look at the design of a 4-bit shift register (SISO) in Verilog:
v
module shift_reg(input clk, en, in, output reg out); 
+    reg [3:0] sreg; 
+    integer i; 
+    
+    always@(posedge clk) begin 
+        if(en) begin 
+            for(i=0; i<3; i++) begin 
+                sreg[i+1] <= sreg[i]; 
+                sreg[0] <= in; 
+            end  
+            out <= sreg[15]; 
+        end 
+    end 
+endmodule
When the EN signal is active, the shift register operates according to SISO logic; however, when the EN signal is inactive, no shifting or alteration occurs.
 If we were to implement a 4-bit shift register (SISO) with D flip-flops (hierarchical modelling), it would look like this:
v
module dflfl(output reg op, input ip, input clk); 
+    always @(posedge clk) begin 
+        op <= ip; 
+    end 
+endmodule 
+   
+module siso(output reg [3:0] out, 
+            input ip, 
+            input clk,en); 
+   reg [3:0] temp; 
+   
+   dflfl g1(out[3], en ? ip:out[3], clk); 
+   dflfl g2(out[2], en ? out[3]:out[2], clk); 
+   dflfl g3(out[1], en ? out[2]:out[1], clk); 
+   dflfl g4(out[0], en ? out[1]:out[0], clk); 
+   
+ endmodule
This is an example of a shift right SISO shift register wherein the input gets serially shifted to the right at every positive edge triggering. The combinational block involves instantiation of four D flip-flops and applying the serial shifting logic by passing the input to the MSB flip-flop. The inputs to the other flip-flops are the outputs of the flip-flops preceding them. If the enable signal is low, we freeze the current values and we don’t make any changes.
Q: Attempt to design a bidirectional shift register in Verilog.
 We need to have two modes- shift left and shift right, and so we have an additional input control signal.
 Try it out and see if you can implement it in code.
Q. Attempt to design a 4-bit SIPO shift register in Verilog. What changes would you have to make to the SISO code and what additional input and output signals would you have to include?
Some useful short notes ​
1. A note on parameterization: The code that we write for n-bit registers is limited for registers which are strictly n-bits. In order to write code and design registers that are more reusable, that can accommodate an arbitrary number of bits for each instantiation, we can utilize instantiation parameters. We can pass the required value of the parameter at the time of instantiation and we can also specify a default value.
v
module register #(parameter WIDTH=4) (
+    input clk, rst, rw,
+    input [WIDTH-1:0] write_data, 
+    output [WIDTH-1:0] read_data); 
+    reg [WIDTH-1:0] block; 
+ 
+    always@(posedge clk) begin 
+        if(!rst)   block <= 0; 
+        else begin 
+            if(rw==1) block <= write_data; 
+            else read_data <= block; 
+        end 
+    end 
+endmodule
The syntax for parametrizing a module is:
module module_name #(parameter PARAMETER_NAME =default_value) (declare input and output signals)
References ​
  1. https://my.eng.utah.edu/~cs6710/handouts/verilog-xl-behavioral.pdf
  2. https://www.realdigital.org/doc/43c79714a7f3d0bbb8098d60c63fde48
  3. PISO Shift Register: https://www.geeksforgeeks.org/piso-shift-register/
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new file mode 100644
index 0000000..bc05d2b
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diff --git a/docs/.vitepress/dist/assets/verilog_main.md.yPPbu8m8.js b/docs/.vitepress/dist/assets/verilog_main.md.B_DAyBtb.js
similarity index 99%
rename from docs/.vitepress/dist/assets/verilog_main.md.yPPbu8m8.js
rename to docs/.vitepress/dist/assets/verilog_main.md.B_DAyBtb.js
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--- a/docs/.vitepress/dist/assets/verilog_main.md.yPPbu8m8.js
+++ b/docs/.vitepress/dist/assets/verilog_main.md.B_DAyBtb.js
@@ -1,4 +1,4 @@
-import{_ as e,c as t,o,a4 as r}from"./chunks/framework.CgMb17D3.js";const g=JSON.parse('{"title":"Welcome to the Verilog Guide","description":"","frontmatter":{"layout":null,"hero":{"name":"Hardware Lab NITC","text":"","tagline":"The official Hardware Lab Guide","actions":[{"theme":"brand","text":"Verilog Docs","link":"/markdown-examples"},{"theme":"alt","text":"MIPS Docs","link":"/api-examples"},{"theme":"alt","text":"Single Cycle Docs","link":"/guide-examples"}]},"features":[{"title":"Extensive documentation","details":"Study the documentation to understand the working of the topics hardware lab","link":"/markdown-examples"},{"title":"Video tutorials","details":"Watch the video tutorials to understand sample codes and key concepts"},{"title":"Sample Codes","details":"Practice the sample codes to understand the working of the topics"}]},"headers":[],"relativePath":"verilog_main.md","filePath":"verilog_main.md"}'),a={name:"verilog_main.md"},i=r(`
Welcome to the Verilog Guide ​
This course covers the following topics-
  • Introduction To Verilog - Learn the Basics of Verilog HDL.
  • Finite State Machines - Design a Verilog-based Finite State Machine (FSM) that enhances your circuits with efficient sequential control and decision-making capabilities.
  • MIPS Single Cycle Processor - Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.
Introduction to Verilog ​
Theory :
Documentation: Link to Main Documentation
 Video Explanation of Theory:
  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS) 
  2. Theory Vid Part 2 (PARITY-TILL END) 
Implementation :
 How to Run Verilog Files in Quartus: How to Run ? :simple-youtube:
 Sample Codes: Link to Sample Codes :simple-github:
 Video Explanation of Select Codes:
  1. Verilog Syntax :simple-youtube: 
  2. Adder Subtractor :simple-youtube:
  3. DEMUX :simple-youtube:
  4. Counter :simple-youtube:
  5. Decoder :simple-youtube:
     Assignment 1: Download Here
Finite State Machines ​
Theory :
 Documentation: Link to Main Documentation :simple-googledrive:
 Video Explanation of Concept:
  1.  Main Concept :simple-youtube:
  2.  Syntax (Optional) :simple-youtube:
This course covers the following topics-
  • Introduction To Verilog - Learn the Basics of Verilog HDL.
  • Finite State Machines - Design a Verilog-based Finite State Machine (FSM) that enhances your circuits with efficient sequential control and decision-making capabilities.
  • MIPS Single Cycle Processor - Build an exciting MIPS single cycle processor which will allow you to run MIPS hardware commands.
Introduction to Verilog ​
Theory :
Documentation: Link to Main Documentation
 Video Explanation of Theory:
  1. Theory Vid Part 1 (INTRO TO VERILOG-LOGIC GATES-ADDERS-SUBTRACTORS) 
  2. Theory Vid Part 2 (PARITY-TILL END) 
Implementation :
 How to Run Verilog Files in Quartus: How to Run ? :simple-youtube:
 Sample Codes: Link to Sample Codes :simple-github:
 Video Explanation of Select Codes:
  1. Verilog Syntax :simple-youtube: 
  2. Adder Subtractor :simple-youtube:
  3. DEMUX :simple-youtube:
  4. Counter :simple-youtube:
  5. Decoder :simple-youtube:
     Assignment 1: Download Here
Finite State Machines ​
Theory :
 Documentation: Link to Main Documentation :simple-googledrive:
 Video Explanation of Concept:
  1.  Main Concept :simple-youtube:
  2.  Syntax (Optional) :simple-youtube:
Single Cycle MIPS Processor ​
Theory :
 Documentation: Link to Main Documentation :simple-googledrive:
 Video Explanation of Concept:
  1.  Control Unit Theory :simple-youtube:
  2.  Datapath Theory :simple-youtube:
Implementation :
 Video Explanation of Code (From Documentation) :
  1.  Code Modules 1 to 5 explained :simple-youtube:
  2.  Code Modules 6 to 10 explained :simple-youtube:
  3.  All Testbenches explained :simple-youtube:
     Code Bank:
     Link to Sample Codes :simple-github:
     Assignment 3:  Download Here 
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diff --git a/docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.js b/docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.js
similarity index 98%
rename from docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.js
rename to docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.js
index 076d947..085f69d 100644
--- a/docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.js
+++ b/docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.js
@@ -1 +1 @@
-import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.CgMb17D3.js";const p=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"mips_main.md","filePath":"mips_main.md"}'),i={name:"mips_main.md"},n=t('
This course covers the following topics-
​
  • Introduction to MIPS - Setting up and understanding MIPS ISA.
  • Basic Integer and String Handling - Learn the Basics of MIPS integers.
  • Integer Array Handling - Learn how to make integer arrays and operate them.
  • 2-D Array Handling - Extend your array knowledge with 2-D arrays.
  • Strings (Advanced) - String Handling explained in detail.
  • Floating Points - Learn how to handle floating point numbers.
Introduction to MIPS ​
Main Documentation :material-google-drive: : Click Here
 Theory explanation:  Video Link :simple-youtube: 
 Setting up MARS:
  1.  Video Link :simple-youtube: 
  2.  Sample Code :simple-github: 
Basic Integer and String Handling ​
Main Documentation :material-google-drive: : Click Here
 Theory Explanation: Video Link :simple-youtube: 
 Sample Code Bank:
  1.  Reversing 2 digit number 
  2.  Calculating Average Marks 
  3.  Finding Spy Number 
Floating Point Handling ​
Main Documentation :material-google-drive: : Click Here
 Farenheit to Celcius:
 Sample Code :simple-github: 
 Maximum and Minimum in Float Array:
 Sample Code :simple-github: 
 Round off to n digits:
 Sample Code :simple-github: 
Integer Array Handling ​
Main Documentation (Also contains String advanced):material-google-drive: : Click Here
Introduction to Integer Arrays:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Sum of Elements of an Array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Greatest Element in Array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Merge 2 Sorted Arrays:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Highest and Lowest occurrence of an element in an array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Binary Search:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Quicksort:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
2-D Integer Array Handling ​
Main Documentation :material-google-drive: : Click Here
Theory Explanation: Video Link :simple-youtube:
 Sample Code Bank:
  1.  Taking Input 
  2.  Printing a Matrix 
  3.  Sum of Two Matrices 
String Handling (advanced) ​
Input/Output of Strings:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Traversal of Strings (Advanced string operations):
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Length of String:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Palindrome Check:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Concatenation of strings:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
',48),o=[n];function l(s,d,g,h,b,m){return a(),r("div",null,o)}const u=e(i,[["render",l]]);export{p as __pageData,u as default};
+import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.DRnJpP2i.js";const p=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"mips_main.md","filePath":"mips_main.md"}'),i={name:"mips_main.md"},n=t('
Welcome to the MIPS Guide ​
This course covers the following topics-
​
  • Introduction to MIPS - Setting up and understanding MIPS ISA.
  • Basic Integer and String Handling - Learn the Basics of MIPS integers.
  • Integer Array Handling - Learn how to make integer arrays and operate them.
  • 2-D Array Handling - Extend your array knowledge with 2-D arrays.
  • Strings (Advanced) - String Handling explained in detail.
  • Floating Points - Learn how to handle floating point numbers.
Introduction to MIPS ​
Main Documentation :material-google-drive: : Click Here
 Theory explanation:  Video Link :simple-youtube: 
 Setting up MARS:
  1.  Video Link :simple-youtube: 
  2.  Sample Code :simple-github: 
Basic Integer and String Handling ​
Main Documentation :material-google-drive: : Click Here
 Theory Explanation: Video Link :simple-youtube: 
 Sample Code Bank:
  1.  Reversing 2 digit number 
  2.  Calculating Average Marks 
  3.  Finding Spy Number 
Floating Point Handling ​
Main Documentation :material-google-drive: : Click Here
 Farenheit to Celcius:
 Sample Code :simple-github: 
 Maximum and Minimum in Float Array:
 Sample Code :simple-github: 
 Round off to n digits:
 Sample Code :simple-github: 
Integer Array Handling ​
Main Documentation (Also contains String advanced):material-google-drive: : Click Here
Introduction to Integer Arrays:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Sum of Elements of an Array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Greatest Element in Array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Merge 2 Sorted Arrays:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Highest and Lowest occurrence of an element in an array:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Binary Search:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Quicksort:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
2-D Integer Array Handling ​
Main Documentation :material-google-drive: : Click Here
Theory Explanation: Video Link :simple-youtube:
 Sample Code Bank:
  1.  Taking Input 
  2.  Printing a Matrix 
  3.  Sum of Two Matrices 
String Handling (advanced) ​
Input/Output of Strings:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Traversal of Strings (Advanced string operations):
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Length of String:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Palindrome Check:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
Concatenation of strings:
  1.  Video :simple-youtube: 
  2.  Sample Code :simple-github: 
',48),o=[n];function l(s,d,g,h,b,m){return a(),r("div",null,o)}const u=e(i,[["render",l]]);export{p as __pageData,u as default};
diff --git a/docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.lean.js b/docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.lean.js
similarity index 67%
rename from docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.lean.js
rename to docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.lean.js
index fedee67..8be2f24 100644
--- a/docs/.vitepress/dist/assets/mips_main.md.B6bGXt9J.lean.js
+++ b/docs/.vitepress/dist/assets/mips_main.md.B6aCW--E.lean.js
@@ -1 +1 @@
-import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.CgMb17D3.js";const p=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"mips_main.md","filePath":"mips_main.md"}'),i={name:"mips_main.md"},n=t("",48),o=[n];function l(s,d,g,h,b,m){return a(),r("div",null,o)}const u=e(i,[["render",l]]);export{p as __pageData,u as default};
+import{_ as e,c as r,o as a,a4 as t}from"./chunks/framework.DRnJpP2i.js";const p=JSON.parse('{"title":"Welcome to the MIPS Guide","description":"","frontmatter":{},"headers":[],"relativePath":"mips_main.md","filePath":"mips_main.md"}'),i={name:"mips_main.md"},n=t("",48),o=[n];function l(s,d,g,h,b,m){return a(),r("div",null,o)}const u=e(i,[["render",l]]);export{p as __pageData,u as default};
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diff --git a/docs/.vitepress/dist/assets/registers-image-0058.B18gUSRJ.jpg b/docs/.vitepress/dist/assets/registers-image-0058.B18gUSRJ.jpg
new file mode 100644
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Y-nI5g|C(troLCBZ8Re@fQgIntroduction To Registers ​
Welcome to the MIPS Guide ​
Introduction To Finite State Machines ​

Copyright © 2024 National Institute of Technology Calicut

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znkFF@Y1i?8tXOA3Zzx?Mmp6KQs%Ayz!lx_{9mzaN|KhU8K;|*lz}+l4BcGt^T2(`= zSSA#$C?_MXUB%N~lF6i&3iVX)qM~jAj{%m}x^faqo(({E5H7?>kU8^!GI(E>${PaV zTQa{o6{_K3J^AvRtMG&)iUEEB%;m9Ugt%e;x{G+{h%PDXDX^Lyttowvg|uJ!ohaN! zm3N=etF1f&`o57${>D)XPk?1ABmGbo$$yNV^ZFuj?T_n!Gh6-mK02iIAj(dVp^uVV Sh2}qyOF>3ey8OLq@V@}oBT?D_ literal 0 HcmV?d00001 diff --git a/docs/MIPS/index.md b/docs/MIPS/index.md index d6a7696..faa4ebc 100644 --- a/docs/MIPS/index.md +++ b/docs/MIPS/index.md @@ -1,46 +1,73 @@ -# Welcome to the MIPS Guide +--- +# https://vitepress.dev/reference/default-theme-home-page +layout: home + +hero: + name: Welcome to the MIPS Guide + text: "" + tagline: This part covers the following topics + +features: + - title: Introduction to MIPS + details: Setting up and understanding MIPS ISA. + link: '#introduction-to-mips' + - title: Basic Integer and String Handling + details: Learn the Basics of MIPS integers. + link: '#introduction-to-mips' + - title: Integer Array Handling + details: Learn how to make integer arrays and operate them. + link: '#introduction-to-mips' + - title: 2-D Array Handling + details: Extend your array knowledge with 2-D arrays. + link: '#introduction-to-mips' + - title: Strings (Advanced) + details: String Handling explained in detail. + link: '#introduction-to-mips' + - title: Floating Points + details: Learn how to handle floating point numbers. + link: '#introduction-to-mips' + + +--- - + ## **Introduction to MIPS** -Main Documentation :material-google-drive: : [Click Here](https://drive.google.com/file/d/1ioiGx-AY5g9wbuYAzQ1hQwh_USFIAlrg/view?usp=sharing) +Main Documentation : [Click Here](./mips.md) Theory explanation: [ Video Link ](https://youtu.be/T40qoR7V6oU) -Setting up MARS: - 1. [Video Link]( https://youtu.be/FM-0bSelrjw ) - - 2. [Sample Code](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/First%20program/Tutorial1.asm ) +### Setting up MARS: +- [Video Link]( https://youtu.be/FM-0bSelrjw ) +- [Sample Code](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/First%20program/Tutorial1.asm ) ## **Basic Integer and String Handling** -Main Documentation :material-google-drive: : [Click Here](https://drive.google.com/file/d/105FBBHBQZX-1MJW7P27LlPcv1Jij5xnz/view?usp=sharing) -Theory Explanation: [Video Link ](https://youtu.be/R5UB4CnZo7Y) -Sample Code Bank: +Main Documentation : [Click Here](https://drive.google.com/file/d/105FBBHBQZX-1MJW7P27LlPcv1Jij5xnz/view?usp=sharing) +Theory Explanation: [Video Link ](https://youtu.be/R5UB4CnZo7Y) + +### Sample Code Bank: 1. [Reversing 2 digit number]( https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/Integers%20and%20Strings_q1.asm) - 2. [Calculating Average Marks](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/Integers%20and%20Strings_q2.asm ) - 3. [Finding Spy Number](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/Integers%20and%20Strings_q3.asm ) ## **Floating Point Handling** -Main Documentation :material-google-drive: : [Click Here](https://drive.google.com/file/d/1BybUxaKDMDrL3FIs_8W87zXCUnqun1HT/view?usp=sharing) +Main Documentation : [Click Here](https://drive.google.com/file/d/1BybUxaKDMDrL3FIs_8W87zXCUnqun1HT/view?usp=sharing) Farenheit to Celcius: [ Sample Code ](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Floating%20point/Q1.asm ) @@ -53,7 +80,7 @@ Maximum and Minimum in Float Array: ## **Integer Array Handling** -Main Documentation (Also contains String advanced):material-google-drive: : [Click Here](https://drive.google.com/file/d/1zscvtdHjjzVDhKyP9l7cfaFXMhMfeBQj/view?usp=sharing) +Main Documentation (Also contains String advanced : [Click Here](https://drive.google.com/file/d/1zscvtdHjjzVDhKyP9l7cfaFXMhMfeBQj/view?usp=sharing) Introduction to Integer Arrays: @@ -81,7 +108,7 @@ Merge 2 Sorted Arrays: Highest and Lowest occurrence of an element in an array: - 1. [ Video]( https://youtu.be/1tUfRNTi1t4) ▶️ + 1. [Video]( https://youtu.be/1tUfRNTi1t4) ▶️ 2. [ Sample Code](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Integer%20Arrays%20Advanced/Integer_Array_Advanced_Practice_Q2_Highest_Lowest_Frequency.asm ) @@ -100,7 +127,7 @@ Quicksort: ### **2-D Integer Array Handling** -Main Documentation :material-google-drive: : [Click Here](https://drive.google.com/file/d/1PSKVY8JSxPmQUKMK4aZ0Q41GEBkVXjG8/view?usp=sharing) +Main Documentation : [Click Here](https://drive.google.com/file/d/1PSKVY8JSxPmQUKMK4aZ0Q41GEBkVXjG8/view?usp=sharing) Theory Explanation: [Video Link](https://youtu.be/SHl3shv24jc) Sample Code Bank: @@ -114,24 +141,25 @@ Sample Code Bank: Input/Output of Strings: - 1. [ Video ]( https://youtu.be/R5UB4CnZo7Y) ▶️ - 2. [ Sample Code ]( https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/Integers%20and%20Strings_q2.asm) + 1. [Video]( https://youtu.be/R5UB4CnZo7Y) ▶️ + 2. [Sample Code]( https://github.com/hwlab-csed/MIPS-Codes/blob/main/Intro%20to%20MIPS/Integers%20and%20Strings_q2.asm) Traversal of Strings (Advanced string operations): - 1. [ Video ](https://youtu.be/HiqgMrXHeyQ ) ▶️ - 2. [ Sample Code ](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings%20Advanced_Sample%20Codes_1.asm ) + +- [Video](https://youtu.be/HiqgMrXHeyQ ) ▶️ +- [Sample Code](https://github.com/hwlab-csed/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings%20Advanced_Sample%20Codes_1.asm ) Length of String: - 1. [ Video ](https://youtu.be/GWlaAK4VdWo ) ▶️ - 2. [ Sample Code ](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q1.asm ) + +- [Video](https://youtu.be/GWlaAK4VdWo ) ▶️ +- [Sample Code](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q1.asm ) Palindrome Check: - 1. [ Video ]( https://youtu.be/7mD-2DHDjEc) ▶️ - 2. [ Sample Code ](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q2.asm ) -Concatenation of strings: - 1. [ Video ]( https://youtu.be/SDeHKgsCJE8) ▶️ - 2. [ Sample Code ](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q3.asm ) +- [Video]( https://youtu.be/7mD-2DHDjEc) ▶️ +- [Sample Code](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q2.asm ) +Concatenation of strings: ---- \ No newline at end of file +- [Video]( https://youtu.be/SDeHKgsCJE8) ▶️ +- [Sample Code](https://github.com/hwlabnitc/MIPS-Codes/blob/main/Strings%20Advanced/MIPS_Strings_Advanced_Practice_Q3.asm ) \ No newline at end of file diff --git a/docs/MIPS/mips.md b/docs/MIPS/mips.md new file mode 100644 index 0000000..d6ab589 --- /dev/null +++ b/docs/MIPS/mips.md @@ -0,0 +1,2216 @@ +# **MIPS** + +## **Setting up the MARS Code Editor** + +### **Introduction to MARS Simulator** + +MARS simulator will be the software on which we will be running our MIPS code. + +#### **Setting up JAVA SDK** +*__(Please note this tutorial is to download SDK Ver 11)__* + +##### **Downloading Java SDK on MacOS:** +1. Open a web browser on your macOS computer. +2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ +technologies/javase-jdk11-downloads.html. +3. On the Downloads page, locate the JDK (Java Development Kit) section. +4. Click on the "Download" button for the version of Java you want to install. +Make sure to select the version suitable for your macOS version (e.g., +macOS x64). +5. You may be prompted to log in or create an Oracle account. Follow the +instructions on the screen to proceed. +6. Once logged in, review and accept the license agreement. +7. On the download page, locate the macOS version and click on the provided +download link. +8. The JDK installer package will be downloaded to your computer. +9. Locate the downloaded package in your Downloads folder or the folder you +specified for downloads. +10. Double-click on the JDK installer package to launch the installation wizard. +11. Follow the instructions in the installation wizard to complete the installation +of the Java SDK on your macOS computer. + +##### **Downloading Java SDK on Windows:** +1. Open a web browser on your Windows computer. +2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ +technologies/javase-jdk11-downloads.html. +3. On the Downloads page, locate the JDK (Java Development Kit) section. +4. Click on the "Download" button for the version of Java you want to install. +Make sure to select the version suitable for your Windows version (e.g., +Windows x64). +5. You may be prompted to log in or create an Oracle account. Follow the +instructions on the screen to proceed. +6. Once logged in, review and accept the license agreement. +7. On the download page, locate the Windows version and click on the +provided download link. +8. The JDK installer executable file (e.g., jdk-11.0.x_windows-x64_bin.exe) +will be downloaded to your computer. +9. Locate the downloaded executable file, and double-click on it to launch the +installation wizard. +10. Follow the instructions in the installation wizard to complete the installation +of the Java SDK on your Windows computer. + +##### **Downloading Java SDK on Windows:** +1. Open a web browser on your Linux computer. +2. Go to the Oracle Java SE Downloads page at https://www.oracle.com/java/ +technologies/javase-jdk11-downloads.html. +3. On the Downloads page, locate the JDK (Java Development Kit) section. +4. Click on the "Download" button for the version of Java you want to install. +Make sure to select the version suitable for your Linux distribution. +5. You may be prompted to log in or create an Oracle account. Follow the +instructions on the screen to proceed. +6. Once logged in, review and accept the license agreement. +7. On the download page, locate the Linux version and click on the provided +download link. +8. The JDK archive file (e.g., jdk-11.0.x_linux-x64_bin.tar.gz) will be +downloaded to your computer. +9. Open the terminal on your Linux system. You can typically find it in the +Applications menu or by using the shortcut Ctrl+Alt+T. +10. Navigate to the directory where you downloaded the JDK archive file. For +example, if it's in the Downloads folder, you can use the following +command: ```cd ~/Downloads ``` +11. Extract the contents of the JDK archive using the following command: +```tar -xvzf jdk-11.0.x_linux-x64_bin``` + +#### **Setting Up MARS Simulator** + *__Note: Is your MARS text unreadably small? Download and use a +new release Java 9 or above which contains a fix to automatically +scale and size AWT and Swing components for High Dots Per Inch +(HiDPI) displays on Windows and Linux.__* + +##### **Downloading MIPS MARS Simulator on macOS:** +1. Open a web browser on your macOS computer. +2. Go to the official website of MIPS MARS at [ http:// +courses.missouristate.edu/kenvollmar/mars/]( http:// +courses.missouristate.edu/kenvollmar/mars/). +3. On the homepage, click on the "MARS 4.5" link under the +"Download MARS" section. +4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your +computer. +5. Locate the downloaded ZIP file in your Downloads folder or the folder +you specified for downloads. +6. Double-click on the ZIP file to extract its contents. This will create a JAR +file named "mars4_5.jar". +7. Move the "mars4_5.jar" file to a suitable location on your computer, such +as the Applications folder. +8. Open Terminal on your macOS by going to Applications > Utilities > +Terminal. +9. In the Terminal window, navigate to the directory where you placed the +"mars4_5.jar" file. For example, if you placed it in the Applications folder, +you can use the following command: ``` cd/Applications``` +10. Once you are in the correct directory, execute the following command to +run the MIPS MARS simulator: ```java -jar mars4_5.jar``` +11. The MIPS MARS simulator should now launch on your macOS computer. + +##### **Downloading MIPS MARS Simulator on Windows:** +1. Open a web browser on your Windows computer. +2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ +kenvollmar/mars/]([http://courses.missouristate.edu/ +kenvollmar/mars/]) +3. On the homepage, click on the "MARS 4.5" link under the "Download +MARS" section. +4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer. +5. Locate the downloaded ZIP file in your Downloads folder or the folder you +specified for downloads. +6. Right-click on the ZIP file and select "Extract All" to extract its contents. This +will create a JAR file named "mars4_5.jar". +7. Move the "mars4_5.jar" file to a suitable location on your computer, such as +the Program Files folder. +8. Open the Command Prompt on your Windows computer by pressing the +Windows key + R, typing "cmd," and hitting Enter. +9. In the Command Prompt window, navigate to the directory where you placed +the "mars4_5.jar" file. For example, if you placed it in the Program Files +folder, you can use the following command: ```cd "C:\Program Files"``` +10. Once you are in the correct directory, execute the following command to run +the MIPS MARS simulator: ```java -jar mars4_5.jar``` +11. The MIPS MARS simulator should now launch on your Windows computer. + +##### **Downloading MIPS MARS Simulator on Linux:** +1. Open a web browser on your Linux computer. +2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ +kenvollmar/mars/](http://courses.missouristate.edu/ +kenvollmar/mars/) +3. On the homepage, click on the "MARS 4.5" link under the "Download +MARS" section. +4. A ZIP file named "Mars4_5.jar.zip" will be downloaded to your computer. +5. Open the terminal on your Linux system. You can typically find it in the +Applications menu or by using the shortcut Ctrl+Alt+T. +6. Navigate to the directory where you downloaded the ZIP file. For example, if +it's in the Downloads folder, you can use the following command: ```cd ~/Downloads``` +7. Unzip the ZIP file using the following command: ```unzip Mars4_5.jar.zip``` +8. This will extract the "Mars4_5.jar" file from the ZIP archive. +9. Move the "Mars4_5.jar" file to a suitable location on your computer. For +instance, you can move it to the /opt directory using the following command: +```sudo mv Mars4_5.jar /opt``` +10. To run the MIPS MARS simulator, open the terminal and navigate to the +directory where you placed the JAR file. For example, if you moved it to the / +opt directory, use the following command: +```cd /opt``` +11. Execute the following command to launch the MIPS MARS simulator +```java -jar Mars4_5.jar``` +12. The MIPS MARS simulator should now launch on your Linux computer. + +### **MARS ASSEMBLY AND SYSTEM CALLS** +Before assembling, the environment of this simulator can be simplisticly split to three +segments: the editor at the upper left where all of the code is being written, the +compiler/output right beneath the editor and the list of registers that represent the +"CPU" for our program. + +After assembling (by simply pressing F3) the environment changes, with two new +segments getting the position of the editor: the text segment where + +i) each line of assembly code gets cleared of "pseudoinstructions" (we'll talk about +those in a sec) at the "basic" column and + +ii) the machine code for each instruction at the "code" column, +and the data segment where we can have a look at a representation of the memory of +a processor with little-endian order. + +After assembling, we can execute our code either all at once (F5) or step by step (F7), +as well as rewinding the execution several steps backwards to the back (F8). + +_**MARS accepts and exports files with the .asm filetype**_ + +##### **Pseudo instructions** + +Before looking at the instruction set , let us look at a few pseudo instructions that’ll +help you understand the IS better. + +_**Here's a list of useful pseudo-instructions.**_ + +`mov $t0, $t1`: Copy contents of register t1 to register t0. + +`li $s0, immed`: Load immediate into to register s0. +The way this is translated depends on whether immed is 16 bits or 32 bits. + +`la $s0, addr`: Load address into to register s0. + +`lw $t0, address`: Load a word at address into register t0 + +_**Given below are some standard arithmetic and logical instructions standard to +the MIPS Instruction Set Architecture.**_ + +_**MARS provides a small set of operating system-like services through the system +call (syscall) instruction **_ + +_**To request a service, a program loads the system call code into register $v0 and +arguments into registers $a0~$a3 **_ + +_**System calls that return values put their results in register $v0**_ + +##### **Arithmetic Instructions** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| add | add $1,$2,$3 | $1=$2+$3 | | +| subtract | sub $1,$2,$3 | $1=$2-$3 | | +| add immediate | addi $1,$2,100 | $1=$2+100 | "Immediate" means a constant number | +| add unsigned | addu $1,$2,$3 | $1=$2+$3 | Values are treated as unsigned integers,not two's complement integer| +| subtract unsigned | subu $1,$2,$3 | $1=$2-$3 | Values are treated as unsigned integers,not two's complement integers| +| add immediate unsigned | addiu $1,$2,100 | $1=$2+100 | Values are treated as unsigned integers,not two's complement integers| +| multiply (without overflow) | mul $1,$2,$3 | $1=$2*$3 | Result is only 32 bits! | +| multiply | mult $1,$2,$3 | $hi, $low=$2*$3 | Upper 32 bits stored in special register ``hi``. Lower 32 bits stored in special register ``lo``| +| divide | div $1,$2,$3 | $hi,$low=$2/$3 |Remainder stored in special register ``hi``. Quotient stored in special register ``lo`` | + +#### **Logical** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| and | and $1,$2,$3 | $1=$2&$3 | Bitwise AND| +| or | or $1,$2,$3 | $1=$2|$3 | Bitwise OR| +| and immediate | andi $1,$2,100 | $1=$2&100 | Bitwise AND with immediate value | +| or immediate | ori $1,$2,100 | $1=$2|100 | Bitwise OR with immediate value| +| shift left logical | sll $1,$2,10 | $1=$2<<10 | Shift left by constant number of bits| +| shift right logical | srl $1,$2,10 | $1=$2>>10 | Shift right by constant number of bits| + +#### **Data Transfer** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| load word | lw $1,100($2) | $1=Memory[$2+100] | Copy from memory to register| +| store word | sw $1,100($2) | Memory[$2+100]=$1 | Copy from register to memory| +| load upper immediate | lui $1,100 | $1=100x2^16 | Load constant into upper 16 bits. Lower 16 bits are set to zero| +| load address | la $1,label | $1=Address of the label | Pseudo-instruction (provided by assembler). Loads computed address of label (not it's contents) into register| +| load immediate | li $1,100 | $1=100 | Pseudo instruction (provided by assembler). Loads immediate value into the register.| +| move from hi | mfhi $2 | $2=hi | Copy from special register ``hi`` to general register| +| move from lo | mflo $2 | $2=lo | Copy from special register ``lo`` to general register| +| load word | lw $1,100($2) | $1=Memory[$2+100] | Copy from memory to register| +| move | move $1,$2 | $1=$2 | Pseudo instruction (provided by assembler). Copy from register to register| + +#### **Conditional Branch** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| branch on equal | beq $1,$2,100 | if($1==$2) go to PC+4+100 | Test if registers are equal| +| branch on not equal | bne $1,$2,100 | if($1!=$2) go to PC+4+100 | Test if registers are not equal| +| branch on greater than | bgt $1,$2,100 | if($1>$2) go to PC+4+100 | Pseudo-instruction | +| branch on greater than or equal | bge $1,$2,100 | if($1>=$2) go to PC+4+100 | Pseudo-instruction| +| branch on less than | blt $1,$2,100 | if($1<$2) go to PC+4+100 | Pseudo-instruction| +| branch on less than or equal | ble $1,$2,100 | if($1<=$2) go to PC+4+100 | Pseudo-instruction| + +#### **Comparison** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| set on less than | slt $s1,$s2,$s3 | if($2<$3) $1 = 1;else $1 = 0 | Test if less than. If true set $1 to 1. Otherwise set $1 to 0. +| set on less than immediate | slti $s1,$s2,100 | if($2<100) $1 = 1;else $1 = 0 | Test if less than. If true set $1 to 1. Otherwise set $1 to 0. + +#### **Unconditional Jump** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| jump | j 1000 | go to address 1000 | Jump to target address| +| jump register | jr $1 | go to address stored in $1 | For switch procedure return| +| jump and link | jal 1000 | $ra=PC+4 go to address 1000 | Use when making procedure call. This saves the return address in $ra| + +#### **System Calls** +| Service | Operation | Code(in $v0) | Arguments | Results | +|---|---|---|---|---| +| print_int | Print integer number (32 bit) | 1 | $a0 = integer to be printed | None | +| print_float | Print floating-point number (32 bit) | 2 | $f12 = float to be printed | None | +| print_double | Print floating-point number (64 bit) | 3 | $f12 = integer to be printed | None | +| print_string | Print null-terminated character string | 4 | $a0 = address of string in memory | None | +| read_int | Read integer number from user | 5 | None | Integer returned in $v0 | +| read_float | Read floating-point number from user | 6 None | Float returned in $f0| +| read_double | Read double floating-point number from user | 7 |None | Double returned in $f0| +| read_string | Works the same as Standard Clibrary fgets() | 8 | $a0 = memory address of string input buffer $a1 = length of string buffer (n) | None | +| sbrk | Returns the address to a block of memory containing n additional bytes (Useful for dynamic memory allocation) | 9 | $a0=amount | address in $v0 | +| exit | Stop program from running | 10 | None | None | +| print_char | Print character | 11 | $a0 = character to be printed | None | +| read_char | Read character from user | 12 | None | Char returned in $v0 | +| exit2 | Stops program from running and returns an integer | 17 | $a0 = result(integer number) | None | + +The complete list of syscalls can be accessed at +[https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html](https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html ) + +#### **Assembler Directives** +| Directive | Result | +|---|---| +| .word w1, ..., wn| Store n 32-bit values in successive memory words | +| .half h1, ..., hn| Store n 16-bit values in successive memory words | +| .byte b1, ..., bn| Store n 8-bit values in successive memory words | +| .ascii str| Store the ASCII string str in memory. Strings are in double-quotes, i.e. "Computer Science" | +| .asciiz str| Store the ASCII string str in memory and null terminate it. Strings are in double-quotes, i.e. "Computer Science" | +| .space n| Leave an empty n-byte region of memory for later use | +| .align n| Align the next datum on a 2^n byte boundary. For example, .align 2 aligns the next value ona word boundary | + +#### **Registers** +|Register Number | Register Name| Description| +|---|---|---| +| 0 | $zero | The value 0 | +| 2-3 | $v0-$v1 | Values from expression evaluation and function results | +| 4-7 | $a0-$a3 | (arguments) First four parameters for subroutine | +| 8-15, 24-25 | $t0-$t9 | Temporary variables | +| 16-23 | $s0-$s7 | Saved values representing final computed results | +| 31 | $ra | Return address | + +#### **MARS(MIPS Assembler/Simulator) Tutorial** +**1. Input the Tutorial program** + +1.1) Open the MARS program and click from the file menu choose “File...New”. A +black document will open which you can enter your assembly code into. Click +“File...Save As” and save the file as “Tutorial1.asm ”. + +1.2) Enter the code as shown below into the editor and save the file. + +```v +# Program File: Tutorial1.asm +# Written by: MoSaad +# Date Created: 10/05/2023 +# Description: Tutorial program to introduce MARS simulator including: breakpoints, single- +stepping, and register and memory windows. +#----------------------------------------------------------- +#----------------------- +# Declare some constants +#----------------------- +.data +string1: .asciiz "Welcome to Hardware Lab at NIT Calicut\n" +string2: .asciiz "Hello World \n" +string3: .asciiz "\nLoop #" +#------------------ +# Main program body +#------------------ +.text +main: +li $v0,4 +la $a0,string1 +syscall +la $a0,string2 +syscall +li $t0, 1 +loop: +li $v0, 4 +la $a0,string3 +syscall +li $v0,1 +move $a0,$t0 +syscall +addi $t0,$t0,1 +bne $t0,4,loop +#----- +# Halt +#----- +li $v0, 10 +syscall +``` + + + +1.4) From the menu, choose “Run...Assemble”. The “Mars Messages” window at the +bottom of the screen will indicate if any errors occurred. No errors should occur. + + + +**2. Simulate the tutorial program** + +2.1) From the menu, choose “Run...Go” to execute the program. The program will +execute displaying two lines of text and three iterations of a loop to the Run /IO +window. + +2.2) The buttons at the top of the window can be used as shortcuts for the run menu. +Use the “Reset” button to reset the program, and then try tracing through the +program by clicking the step button. + +2.3) You can adjust the speed the program runs by moving the slider to the right of the +buttons. If you have an infinite loop in your program, it may be necessary to adjust +(slow down) the speed of the simulator to prevent the MARS program from +crashing. + + +Run the program. If a breakpoint has been set the program will stop at the next breakpoint. + + +Trace (Step) Into. Executes a single instruction. If +the instruction is a procedure call (jal) the simulator will stop at the first instruction of the procedure. + + +Backstep. Undo the last step taken in the code. + + +Pause the currently running program. Press the run button to continue execution. + + +Stop the currently running program. You will need to reset the simulator to execute the program again after stopping it. + + +Reset. Resets the simulator, reinitializing the registers, program counter, and memory. + + +Adjusts the speed that the simulator runs at. + +**3. Using the Debugging Tools** + +3.1) When a program does not work as expected you will need to use the debugging +tools provided with the simulator. + +3.2) One of the primary tools used to debug a program is setting a breakpoint. You can +break before execution of an instruction by clicking on the checkbox associated +with each instruction on the far left of the execute window. Set a breakpoint at +the instruction: addi $t0,$t0,1 + +3.3) Run the program until the breakpoint by clicking “Run”. At this point in the +program only the first loop iteration has been printed. (You will need to click +back to the Run/IO window to see the output.) + +3.4) Now use the “Trace Into” button to step through the loop that prints out the next line +of text one character at a time. Step through the instructions until “Loop #2” is +printed to the output window. Stop and find the value of the registers “t0” and +“pc” at that point? Has the line of code that the program counter points to executed +yet? + +3.5) The simulator also allows you to view the memory contents. The memory window +appears in the middle of the screen and is titled “Data Segment”. Remove the +earlier breakpoint and add a breakpoint to line 33, “syscall”. Click the run button +so that the program executes up until the new breakpoint. We are now in the code +right before “Loop #” is about to be printed for the third iteration. Notice that the $a0 register is now a pointer to the address where the “Loop #” text is stored. What +is the memory location the register is pointing to? + +3.6) Now look in the data segment area, and find the address $a0 points to. This is the +memory section where the characters of the text “Loop #” is stored. Using an +ASCII table find the address where the ‘p’ in “Loop” is located? + +3.7) Exercise: Can you find where the word “Welcome” is stored in the memory? + + + +## **Integer Handling** + +Unlike NASM where numbers are stored as characters, MIPS can store single or multiple digit +integers directly. This chapter describes how to read and print integers. Basic operations in integer +handling (add, sub, mul, div) will also be covered. + +**1. Declaring an integer** + +Integers can be declared as constants in the ‘.data’ section as shown below: + +*Code to declare constants ‘x’ and ‘y’ with values 30 and 40 respectively:* + +```v +.data +x: .word 30 +y: .word 40 +``` + +**2. Loading an integer value into a register** + +Another way of using integers in MIPS is to read their values into temporary registers +using ‘I’ type instructions. +The two commonly used methods of reading integer values are: + +1. Loading a value into a temporary register. +2. Adding the value of the zero register and any value into a temporary register. + +*Code to enter integer values 5 and 10 using add and load instructions respectively into temporary +registers:* +```v +.text +addi $t0, $0, 5 +li $t1, 10 +``` +**3. Reading integers as input from the user** + +Integers can be read from the user using _syscall_ (system call) instructions. +The system call code for reading an integer is ‘5’. This syscall code value must be +loaded into the register $v0 in order to perform its designated function. The input is +then stored in $v0. + +_Code to read an integer input from the user:_ +```v +.text +li $v0, 5 +syscall +``` +**4. Printing integers** + +Integers stored in registers can also be printed using syscall instructions. The system call +code for printing an integer is ‘1’. This syscall code value must be loaded into the +register $v0 in order to perform its designated function. The integer to be printed must +be stored in the $a0 register. + +_Code to print the integer ‘5’ after storing it in a register:_ +```v +.text +li $a0, 5 +li $v0, 1 +syscall +``` +We have now learnt how to store single and multi digit integers and how to print their +values. We shall now combine all of these into a single program for a more robust +understanding of the covered concepts. + +_Code to declare a constant x with value 10, load values 20 and 30 into two registers and read +an integer value from the user and print all these values:_ + +```v +.data +x: .word 10 +.text +addi $t0, $0, 20 #load value 20 +li $t1, 30 #load value 30 +li $v0, 5 #read integer input +syscall +move $t2, $v0 #move integer input +lw $a0, x #print x +li $v0, 1 +syscall +move $a0, $t0 +li $v0, 1 #print value of $t0 +syscall +move $a0, $t1 #print value of $t1 +li $v0, 1 +syscall +move $a0, $t2 #print integer input +li $v0, 1 +syscall +li $v0, 10 #exit program +syscall +``` + +_Output:_ +_Assume the value ‘5’ is entered by the user as input._ +```v +5 +1020305 +-- program is finished running -- +``` + +**5. Adding integers** + +Integers can be added in two ways, either by adding fixed or immediate values to an +integer value stored in a register, or by adding two integers that are both stored in registers. +Both methods to add integers are demonstrated below: + +_Code to add integer values stored in registers:_ +```v +.text +addi $t0, $t1, 5 #t0=t1+5 +add $t2, $t2, $t1 #t2=t2+t1 +addi $t1, $zero, 5 #t1=0+5 +add $t2, $zero, $t1 #t2=0+t1 +``` + +**6. Subtracting integers** + +Unlike addition, values can only be subtracted if they are stored in a register. + +_Code to subtract integer values stored in registers:_ +``` +.text +sub $t2, $t2, $t1 #t2=t2-t1 +sub $t2, $zero, $t1 #t2=0-t1 +``` +**7. Multiplying integers** + +MIPS allows you to multiply the values present in two registers and stores the 32 most +significant bits in the HI special register and the 32 least significant bits in the LO special +register. + +The value obtained in the HI and LO registers can be accessed using the mfhi and mflo +instructions respectively. + +_Code to multiply two integers values and access the result after multiplication:_ +``` +.text +mult $t0, $t1 #signed mult +mflo $s0 #s0=t0*t1 +multu $t2, $t3 #unsigned mult +mflo $s1 #s1=t2*t3 +``` + +**8. Dividing integers** + +Division in MIPS is similar to multiplication except for a key difference, the HI special +register stores the remainder while the LO special register will hold the quotient of the +division. + +_Code to divide to integers and access the remainder and quotient after division:_ + +``` +.text +div $t1, $t2 #signed div +mfhi $s0 #s0=t1%t2 +mflo $s1 #s1=t1/t2 +divu $t3, $t4 #unsigned div +mfhi $s2 #s2=t3%t4 +mflo $s3 #s3=t3/t4 +``` + +### **Points To Note** + +**1.** Entering number of size larger than 32 bits + The largest integer that can be entered in 32 bit space is 2,147,483,647. Entering a + number larger than that results in the following error: + + ``` Runtime exception at 0x0040002c: invalid integer input (syscall 5)``` + +**2.** Changing the value of $zero register + It is not possible to change the value of the $zero register, any instructions that attempt + to alter the value have no effect. + +**3.** Multiplying numbers of size 32 bits + In MIPS, all integer values must be 32 bits. So if there is a valid answer, it must be + contained in the lower 32 bits of the answer. Thus to implement multiplication in MIPS, + the two numbers must be multiplied using the mult operator, and the valid result moved + from the lo register. + +**4.** Division by zero + If the divisor is zero, then the MIPS divide instructions do not compute any result in the + HI and LO registers. Division by zero is ignored and no exception is produced. + +**5.** Meaning of the _.word_ directive +The _.word_ directive allocates 4 bytes of space in the data region. The .word directive can +then be given an integer value, and it will initialize the allocated space to that integer +value. Be careful as it is incorrect to think of a the .word directive as a declaration for an +integer, as this directive simply allocates and initializes 4 bytes of memory, it is not a +data type. What is stored in this memory can be any type of data. + +## **String Operations** + +Strings in MIPS can be declared as constant in the _.data_ part of the program. They are often stored +this way so that they can be used as user prompts or to format output of a program. Strings can also +be entered by the user during the runtime of the program. Both methods of using strings in MIPS +will be demonstrated below. + +**1. Entering string constants** + +Pre-determined strings enclosed by double quotes can be declared in the _.data_ section. + +_Code to store the string “enter an element:” in memory under the name “message”:_ + +``` +.data +message: .asciiz “enter an element:” +``` +**2. Enter strings as input from the user** + +To enter strings as input, the syscall code to be used is 8. Apart from that, the address of the +memory space into which the string must be entered, is loaded into the $a0 register. The +maximum size of the string must also be loaded into the $a1 register before performing the +syscall. + +_Code to read a string as input from the user:_ + +``` +.data +input: .space 100 +inputsize: .word 100 +.text +li $v0, 8 +la $a0, input +lw $a1, inputsize +syscall +``` +**3. Printing strings stored in memory** + +To print the required string, the syscall to be used is 4. The address of the string has to be +loaded into the $a0 register. + +_Code to print a string named ‘message’ stored in memory:_ +``` +.text +li $v0, 4 +la $a0, output +syscall +``` +We have now learnt how to declare strings constants as well as how to store strings entered +by the user. We shall now write a program combining both the concepts for a more robust +understanding of basic string operations. + +_Code to read a string, with prompts instructing the user:_ + +``` +.text +main: + # Prompt for the string to enter + li $v0, 4 + la $a0, prompt + syscall + + # Read the string. + li $v0, 8 + la $a0, input + lw $a1, inputSize + syscall + + # Output the text + li $v0, 4 + la $a0, output + syscall + + # Output the number + li $v0, 4 + la $a0, input + syscall + + # Exit the program + li $v0, 10 + syscall + +.data +input: .space 81 +inputSize: .word 80 +prompt: .asciiz "Please enter a string: " +output: .asciiz "\nYou typed the string: " +``` + +### **Points To Note** + +- The _.space_ directive allocates n bytes of memory in the data region of the program, where + n=81 in this program. Since the size of a character is 1 byte, this is equivalent to saving 80 + characters for data. 81 was used here because in MIPS a sequence of ASCII characters is + terminated by a null value (byte containing 0). This is known as a null terminator. + +- If the string the user enters is larger than the maximum size of the string, it is truncated to + the maximum size. This is to prevent the program from accessing memory not allocated to + the string. + +## **Floating Point Numbers** + +Floating point numbers are stored according to the IEEE 754 Standard. There are 2 types +of floating point numbers, single precision and double precision. + +### **Floating point number representation** + +According to IEE 754 Standard, floating point numbers follow the given representation. + +```Sign Exponent Fraction``` + +- The sign bit is 0 or 1, for positive or negative respectively. + +- The exponent stores the exponent of the number in scientific notation of its binary +representation, plus a bias. + +- The fraction stores the fractional part of the binary representation of the number. + + +| Data | Single Precision | Double Precision | +|----|----|----| +|Size | 32 bits | 64 bits | +|Exponent size | 8 bits | 11 bits | +|Fraction size | 23 bits| 52 bits | +|Bias |127| 1023| + +Note + +- Since there are some numbers with non-ending decimal part in there binary representation + ( For Example- ( 1 /3) 10 = (0.01 0011 0011 0011 ....) 2 ) and we have only limited bits to store + the fraction part, there will be some slight inaccuracy while storing certain floating point + numbers. Therefore, it is recommended to always use double, as it has a higher precision due + to its increased no. of bits. + +### **MIPS floating point architecture** + +In MIPS, all floating point calculations are computed in a separate processor, called co- +processor 1. + +The coprocessor contains 32 floating point registers, each of width 32 bits. The registers +are numbered from $f 0 to $f3 1. + +Each register is can store a single precision floating point number, while double precision is +stored in 2 registers in an even-odd pair. For instructions concerning double precision numbers, the +even numbered register is used in the instruction. Using an odd numbered register will throw an +error. + +In addition to the registers, there are 8 condition flags, which are used in floating point +compare and branch instructions. + + +#### **Floating point registers in MIPS** + +|Registers | Usage | +|---|---| +|$f0 - $f3 | Used for results of floating point procedures | +| $f4 - $f11 | Temporary floating point registers, whose values are NOT preserved across procedure calls| +|$f12 - $f15 | Floating point parameters, whose values are NOT preserved across procedure calls | +| $f16 - $f19 | More temporary floating point registers, whose values are NOT preserved across procedure calls | +|$f20 - $f31 | Saved floating point registers, whose values are preserved across procedure calls | + +Among the 32 registers, only $f 4 - $f 11 , $f 16 - $f 19 and $f 20 - $f 31 can +be used by the programmer for storing values, as the others are reserved for special purposes. + +Note + +- Unlike the general purpose register $ 0 , $f 0 is not hardwired to be zero, and is used for storing results of procedures. + +### **Declaring a Floating point number** + +``` +.data + num1: .float 3. + num2: .double 4.5 3 + + .align 2 # Since float has 2^2 bytes + float_arr: .space 100 it has to be aligned to 2 + + .align 3 # Since double has 2^3 bytes it has to be aligned to 3 + double_arr: .space 100 +``` + +### **Reading and Printing Floating point numbers** + +Reading and printing a floating point number is similar to that of an integer, using syscall, +only difference being in the $v0 value and parameter registers. + +#### **Single precision** + +The $v0 value for reading a single precision floating point number is 6 while that of printing is 2. + +``` +main: + li $v0, 6 + syscall # The number is stored in $f0 + + li $v0, 2 + mov.s $f12, $f0 # The number to be printed is moved to $f12 + syscall +``` + +#### **Double precision** + +The $v0 value for reading a double precision floating point number is 7 while that of +printing is 3. + +``` +main: + li $v0, 7 + syscall # The number is stored in $f0/$f1 + + li $v0, 3 + mov.d $f12, $f0 # The number to be printed is + syscall moved to $f12/$f13 +``` + +### **Data Movement Instructions** + +|Instruction | Syntax | Remarks | +|---|---|---| +|Load single/double| l.s fdest, address l.d fdest, address | The single/double floating-point stored in address is loaded onto register fdest | +|Store single/double | s.s fsrc, address s.d fsrc, address | The single/double floating-point stored in register fsrc is stored to address | +| Move single/double | mov.s fdest, fsrc mov.d fdest, fsrc | The single/double floating-point stored in register fsrc is moved to register fdest | +|Move from coprocessor 1 |mfc1 dest, fsrc | The 32 - bit data from floating register fsrc is copied to general purpose register dest | +| Move to coprocessor 1 | mtc1 src, fdest | The 32 - bit data from general purpose register src is copied to floating point register fdest | + +Note + +- There is no load immediate for floating point. So if a constant is needed, it has to be stored in + the data segment and loaded to the required register. +- For the move to/from coprocessor 1 instructions, the first operand is a general purpose + register and the second one is the floating point register. + +### **Arithmetic Instructions** + +|Instruction | Syntax | Remarks| +|:----|------|-----| +|Addition | add.s fdest, fsrc1, fsrc2
add.d fdest, fsrc1, fsrc |The single/double floating-point numbers stored in fsrc1 and fsrc2
are added and stored in register fdest | +|Subtraction | sub.s fdest, fsrc1, fsrc2
sub.d fdest, fsrc1, fsrc2 |The single/double floating-point number stored in fsrc
subtracted from fsrc1 and stored in register fdest | +| Multiplication | mul.s fdest, fsrc1, fsrc2
mul.d fdest, fsrc1, fsrc2 |The single/double floating-point numbers stored in fsrc1 and fsrc2
are multiplied and stored in register fdest | +|Division | div.s fdest, fsrc1, fsrc2
div.d fdest, fsrc1, fsrc |The single/double floating-point number stored in fsrc1 is divided by fsrc2
and the quotient is stored in register fdest | +|Negation | neg.s fdest, fsrc
neg.d fdest, fsrc | The single/double floating-point number stored in fsrc
is negated (Sign changed) and stored in register fdest | +| Absolute value | abs.s fdest, fsrc
abs.d fdest, fsrc | Absolute value (Magnitude) of the single/double floating-point number stored in fsrc
is stored in register fdest | +| Square root | sqrt.s fdest, fsrc
sqrt.d fdest, fsrc | Square root of the single/double floating-point number stored in fsrc
is stored in register fdest + +### **Sample Question 1** + +Given a temperature in Fahrenheit, convert it into Celsius (Input and output has to be floating point values). + +Temperature in degrees Celsius = (Temperature in degrees Fahrenheit - 32 ) * 5 / 9. +``` +data + # Constants used for calculation + const1: .double 32.0 + const2: .double 5.0 + const3: .double 9.0 + + # User prompts + msg1: .asciiz "Enter the temperature in Fahrenheit: " + msg2: .asciiz "The temperature in Celsius is: " + + +.text +.globl main +main: + + li $v0, 4 # Printing msg1 + la $a0, msg1 + syscall + + li $v0, 7 # Reading user input + syscall + + mov.d $f12, $f0 # $f12 = User Input + l.d $f14, const1 # $f12 = $f12 - 32 + sub.d $f12, $f12, $f14 + + l.d $f14, const2 # $f12 = $f12 * 5 + mul.d $f12, $f12, $f14 + + l.d $f14, const3 # $f12 = $f12 / 9 + div.d $f12, $f12, $f14 + + li $v0, 4 # Printing msg2 + la $a0, msg2 + syscall + + li $v0, 3 # Printing final answer + syscall + + li $v0, 10 # Exit + syscall +``` + +## **Comparison/Branch Instructions** + +|Instruction | Syntax | Remarks| +|---|---|---| +| Compare equal | c.eq.s cc, fsrc1, fsrc2
c.eq.s fsrc1, fsrc2
c.eq.d cc, fsrc1, fsrc2
c.eq.d fsrc1, fsrc2 |Sets the condition flag cc as 1 if the numbers in fsrc1
and fsrc2 are equal, 0 otherwise.| +|Compare less than | c.lt.s cc, fsrc1, fsrc2
c.lt.s fsrc1, fsrc2
c.lt.d cc, fsrc1, fsrc2
c.lt.d fsrc1, fsrc2 | Sets the condition flag cc as 1 if the number in fsrc1
is less than that in fsrc2, 0 otherwise. | +| Compare less than or equal to | c.le.s cc, fsrc1, fsrc2
c.le.s fsrc1, fsrc2
c.le.d cc, fsrc1, fsrc2
c.le.d fsrc1, fsrc|Sets the condition flag cc as 1 if the number in fsrc1
is less thanor equal to that in fsrc2, 0 otherwise. | +|Branch if true | bc1t cc, label
bc1t label | Jumps to label if the condition flag cc is set as 1 | +|Branch if false | bc1f cc, label
bc1f label | Jumps to label if the condition flag cc is set as 0 | + +Note + +- The condition flag can be omitted in the above instructions, in which case condition flag 0 is + taken as default. +- As there is no comparison instruction for “Not equal to”, it has to be implemented by + reversing the required branch condition + Ex. We need to branch to label if $f4 and $f6 are not equal. This can be written as + ``` + c.eq.d $f4, $f6 + bc1.f label + ``` +- For greater than and greater than and equal to, it is simpler to reverse the input registers. + Ex. We need to branch to label if $f4 if greater than $f6. This can be written as + ``` + c.le.d $f6 , $f4 + bc1.t label + ``` + +### **Sample Question 2** +Given an array of floating numbers of size n, print the maximum and minimum element + + +``` +data + # Array + .align 3 + arr: .space 1000 + + # Characters + newline: .asciiz "\n" + + # User Prompts + msg1: .asciiz "Enter n: " + msg2: .asciiz "Enter no. " + msg3: .asciiz ": " + msg4: .asciiz "The maximum no. is: " + msg5: .asciiz "The minimum no. is: " + +.text +.globl main +main: + + li $v0, 4 # Print msg1 + la $a0, msg1 + syscall + + li $v0, 5 # Read n + syscall + move $t0, $v0 + + li $t1, 0 # $t1 will be the loop variable + # going from 0,1,2.. + li $t2, 0 # $t2 will be the element indices + # going from 0,8,16.. + loop1: # Loop to read n elements + beq $t0, $t1, end_loop1 # Termination condition + + li $v0, 4 # Print msg2 + la $a0, msg2 + syscall + + li $v0, 1 # Print position of + move $a0, $t1 # number to be inputted + addi $a0, $a0, 1 + syscall + + li $v0, 4 # Print msg3 + la $a0, msg3 + syscall + + li $v0, 7 # Read input and + syscall # store in arr + s.d $f0, arr($t2) + + addi $t1, $t1, 1 # Increamenting #t1 + addi $t2, $t2, 8 # and $t2 + j loop1 + + end_loop1: + + li $t1, 0 # Resetting $t1 and $t2 + li $t2, 0 + l.d $f4, arr($zero) # $f4 stores the max value + l.d $f6, arr($zero) # $f6 stores the min value + + loop2: # Loop to compute max and min + beq $t0, $t1, end_loop2 # Termination Condition + + l.d $f8, arr($t2) # Load a number from arr + + c.lt.d $f4, $f8 # Compare if the number is + # greater than current max + bc1f not_max + mov.d $f4, $f8 # If yes then update new max + not_max: + + c.lt.d $f8, $f6 # Compare if the number is + # less than current min + bc1f not_min + mov.d $f6, $f8 # If yes then update new min + not_min: + + addi $t1, $t1, 1 # Incrementing $t1 and $t2 + addi $t2, $t2, 8 + j loop2 + + end_loop2: + + li $v0, 4 # Print msg4 + la $a0, msg4 + syscall + + li $v0, 3 # Print max number + mov.d $f12, $f4 + syscall + + i $v0, 4 # Print newline + la $a0, newline + syscall + + li $v0, 4 # Print msg5 + la $a0, msg5 + syscall + + li $v0, 3 # Print min number + mov.d $f12, $f6 + syscall + + li $v0, 10 # Exit + syscall +``` + +### **Data Conversion Instructions** + +#### **Conversion within floating point** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert single to double | cvt.d.s fdest, fsrc |The single floating-point stored in fsrc is converted to double and stored in fdest | +|Convert double to single | cvt.s.d fdest, fsrc| The double floating-point stored in fsrc is converted to single and stored in fdest | + +### **Conversion to integers** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert single to integer | cvt.w.s fdest, fsrc |The single floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point)
and stored in 2 ’s compliment form in fdest | +|Convert double to integer | cvt.w.d fdest, fsrc | The double floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) and
stored in 2 ’s compliment form in fdest | + + Note + +- The output of the above two instructions is in 2 ’s compliment form, which should not be + used with any other instructions other than mfc1. Other instructions always assume the data + in registers are according to IEEE standards, which can cause errors. + +#### **Conversion from integers** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert integer to single | cvt.s.w fdest, fsrc |The data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to single precision floating point and is stored in fdest | +| Convert integer to double | cvt.d.w fdest, fsrc | The data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to double precision floating point and is stored in fdest | + +### **Special Instructions** + +| Instruction | Syntax | Remarks | +|---|---|---| +| Ceiling | ceil.w.s fdest, fsrc
ceil.w.d fdest, fsrc | The smallest integer not greater than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form | +|Floor | floor.w.s fdest, fsrc
floor.w.d fdest, fsrc | The greatest integer not smaller than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form | +|Round to nearest integer |round.w.s fdest, fsrc
round.w.d fdest, fsrc | The floating-point stored in fsrc is rounded off to
nearest integer and stored in fdest in 2 ’s compliment form | + +### **Sample Question 3** + +Given a floating point number and an integer n, round off the floating point number to n +digits. + + Hint- + +Multiplty then given number with 10^n, and round off using round.w.d instruction. +Divide the result by 10^n to obtain the final result. + +``` +data + # Constants used for calculation + const1: .double 0.0 + const2: .double 1.0 + const3: .double 10.0 + + # User prompts + msg1: .asciiz "Enter the number : " + msg2: .asciiz "Enter number of digits to round off to: " + msg3: .asciiz "The rounded off number is: " + +.text +.globl main +main: + + li $v0, 4 # Print msg1 + la $a0, msg1 + syscall + + li $v0, 7 # Read number to round off + syscall + + mov.d $f12, $f0 # $f12 = user input + + li $v0, 4 # Print msg2 + la $a0, msg2 + syscall + + li $v0, 7 # Read n + syscall + + mov.d $f16, $f0 # $f16 = n + l.d $f4, const1 # $f4 used as a loop varibale + # initialised to 0 + l.d $f6, const2 # $f6 used to store 10^n + l.d $f8, const3 # $f8 used to store 10 for + # calculating power + l.d $f10, const2 # $f10 used to store 1 for + # incrementing loop variable + loop1: # Loop to compute 10^n + c.eq.d $f4, $f16 # Ternminaltion Condition + bc1t end_loop1 + + mul.d $f6, $f6, $f8 # $f6 = $f6 * 10 + add.d $f4, $f4, $f10 # $f4 = $f4 + 1 + + j loop1 + end_loop1: + + mul.d $f12, $f12, $f6 # $f12 = $f12 * (10^n) + round.w.d $f12, $f12 # $f12 is rounded to nearest + # integer + cvt.d.w $f12, $f12 # Output after rounding, + # which is a word, is + # converted back to double + div.d $f12, $f12, $f6 # $f12 = $f12 / (10^n) + + li $v0, 4 # Print msg3 + la $a0, msg3 + syscall + + li $v0, 3 # Print final answer + syscall + + li $v0, 10 # Exit + syscall +``` + +## Integer Arrays + +An Integer Array is continuous storage block in memory in which each element is an integer. Each +element of an array is accessed using the base address of the array and the index of the element we +must access. + +### **Declaration and Initialization** + +Integer arrays can be initialized using .word or an empty array can be declared using +the .space keyword inside the .data section of the program + +``` +data: +arr: .word 3,4,-5,6 #initialized an array arr=[3,4,-5,6] +arr2: .space 40 # empty array with 40 bytes reserved for arr2 +``` + +### **Array Traversal** + +Array traversal refers to accessing each element of the array using its index. + +Each integer element of an array occupies a word (4 bytes). Therefore,4 bytes needed to be added to the current address to obtain the address of the following element. + +_Address of arr [k] = base address of arr + 4 * k_ + +Eg: To access arr[3] and store it to $t + +``` +a $s0,arr # base add address of array is stored in $s0 +addi $s0,$s0,12 # $s0 = address of arr[3] = arr + 4 * 3 +lw $t2,0($s0) # $t2=arr[3] +``` +or +``` +a $s0,arr # base add address of array is stored in $s0 +lw $t2,12($s0) # $t2=value of (arr + 12) +``` + +### **Array Input** + +The elements of an integer array can be received from the user using the syscall for +integer input and a for loop. + +_An empty array must be declared in the .data by allocating the necessary space as shown before._ + +_Each integer element of an array occupies 4 bytes. Therefore, 4 bytes needed to be added to the current address after each insertion._ + +The following code segment can be used to create an array of size n by receiving inputs from the user: + +Assume $s1 contains n, $s0 contains base address of an empty array and $t0 is the loop counter + +``` +for: + beq $t0,$s1,exit # loop termination condition + sll $t1,$t0,2 # $t1=i*4 + add $t1,$t1,$s0 # $t1 = arr + i * 4 + + li $v0,5 # input integer and store in $t2 + syscall + move $t2,$v0 + sw $t2,0($t1) # $t2 = arr[i] + addi $t0,$t0,1 # increment loop counter i + j for +``` + +### **Printing an Integer Array** + +Integer Array can be printed by traversing each element by using array traversal rules (as discussed above) and integer printing (code 1 is loaded to $v0). + +Consider the following code snippet to print the array created in the previous example in which every element is provided by the user: + +``` +la $s0,arr # store base address of array in $s0 +li $t0,0 +print: + beq $t0,$s1,end + sll $t1,$t0,2 # array traversal to access arr[i] + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + li $v0,1 # 1 is the syscall number to print integers + move $a0,$t2 # print $t2 + syscall + + li $a0, 32 # 32 is the ASCII code for space + li $v0, 11 # syscall number for printing character + syscall + addi $t0,$t0,1 # increment loop counter + j print +end: +li $v0,10 #end program +syscall +``` + +### **Negative Numbers as Elements** + +All integer operations in MIPS support both positive and negative numbers. No changes are required to the program for the input and output of positive integers. + +``` +enter array element: -5 +enter array element: -6 +enter array element: 8 +enter array element: -2 +The elements of the array are: -5.0 -6.0 8.0 -2.0 +-- program is finished running -- +``` + +### **Floating Point Numbers as Elements** + +An array of floating-point numbers can be created by replacing all the integer +operations with floating-point operations. The following changes need to be made to +convert an integer array into an array of floating-point numbers: + +1) Replace the integer code loaded to $v0 by floating-point code +2) Replace the load, store and move operation by l.s , s.s and mov.s where floating point data type is used + +``` +# program to input array +for: + beq $t0,$s1,exit + sll $t1,$t0,2 + add $t1,$t1,$s0 + li $v0,6 # code for floating point input + syscall + s.s $f0,0($t1) # arr[i]=$f0 + addi $t0,$t0,1 + j for +exit: + +# print array +print: + beq $t0,$s1,end + sll $t1,$t0,2 + add $t1,$t1,$s0 + l.s $f0,0($t1) # $f0=arr[i] + li $v0,2 # code for printing floating point + mov.s $f12,$f0 + syscall + li $a0, 32 + li $v0, 11 + syscall + addi $t0,$t0,1 + j print +end +``` + +### **One Dimensional Arrays** + +#### **To calculate the sum of n numbers in an n sized array** + +``` +li $t0,0 +la $s0,arr +li $t3,0 #t3 stores the sum +sum: #for loop + beq $t0,$s1,end # $s1 contains n + sll $t1,$t0,2 + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + add $t3,$t3,$t2 # $t3=$t3+$t2 + addi $t0,$t0,1 # increment loop counter + j sum +end: +li $v0,1 # print sum +move $a0,$t3 +syscall +``` + +#### **To find the largest element in an n sized array** + +``` +la $s0,arr +li $t0,0 +li $t3,-1000 # $t3=max + # initialized to -1000 +max: + beq $t0,$s1,end # $s1 contains n + sll $t1,$t0,2 + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + ble $t2,$t3,inc_i # if arr[i]<=max, jump to inc_count + move $t3,$t2 # if arr[i]>max, max=arr[i] + inc_count: + addi $t0,$t0,1 # increment loop counter + j max +end: +li $v0,1 # print max +move $a0,$t3 +syscall +``` + +## **String Operations (Advanced)** + +### **Null Character and Newline** + +When strings are created by using user input (code 8 passed to $vo), it forms a sequence of ASCII +characters that are terminated by a newline character, followed by a NULL character. The newline +character is triggered by the pressing of enter key during user input. + +_The ASCII code for newline is 10. Hence_ beq, $t1,10,label _can be used as a comparing instruction_ + +_MIPS treats NULL character as a zero. Hence_ beqz, $t1, label _can be used as a comparing instruction_ + +### **String Traversal** + +Strings are made up of characters, in which each character occupies a byte. Hence, unlike an Integer +Array, each character must be traversed byte by byte. + +Eg: + +To find the length of a string (newline character need not be included) + +``` +# assume string is input to str1 +li $s1,0 #loop counter (i) + +len: + lb $t1,str1($s1) # $t1=str[i] + beq $t1,10,start # termination condition + addi $s1,$s1,1 # i=i+1 + j len +start: + li $v0,1 # print len=i + move $a0,$s1 + syscall +``` + +_If the newline character needs to be included in the length, beq should be replaced with beqz_ + +### **String Concatenation** + +Concatenation of two strings can be done using 2 loops. The presence of newline and null character +at the end of each string should be considered. + +Consider two strings, str1 and str2. The following is the pseudocode and the code snippet for +concatenating str2 to str1: +_Pseudo Code:_ + +```c +i=0 + +j=0 + +while str1[i]!='\n' + +i++ + +while str2[j]!='\0' + +str1[i]=str2[j] + +i++ + +j++ +``` +_MIPS:_ + +```mips +i $s1,0 # i=0 +li $s2,0 # j=0 +loop1: + lb $t1,str1($s1) + beq $t1,10,loop2 + addi $s1,$s1,1 # i++ + j loop1 +loop2: + lb $t1,str2($s2) + beqz $t1,end + sb $t1,str1($s1) # str1[i]=str[j] + addi $s1,$s1,1 # i++ + addi $s2,$s2,1 # j++ + j loop2 +end: +``` + +### **Palindrome Checking** + +A palindrome sequence that reads the same backwards as forwards. Palindrome checking uses two +pointer method. + +Assume a string str, whole length is n. Length of the string is calculated by previous method and +stored in $s1. The following code snippet shows the while loop necessary for checking whether the +string is palindrome + +``` +addi $s1,$s1,-1 # j=n-1 +li $s0,0 # i=0 +for: + lb $t1,str($s0) + lb $t2,str($s1) + bge $s0,$s1,true # if i>=j,exit loop. return True + bne $t1,$t2,false # if str[i]!=str[j], return False + addi $s0,$s0,1 # i++ + addi $s1,$s1,-1 # j-- + j for +``` + +## **Two Dimensional Arrays** + +2-DArrays/Matrices/Tables aren’t stored in memory the way it is normally visualized; rather it is stored as a single array in either row major form or column major form. Let’s see how a matrix is represented in memory in both the forms with a starting address of 1230. (Remember:In an array each element is 4 bytes long). + +a) Row Major form : Here elements are stored row wise. First we store the first row, then the second and soon. + + + +b) Column Major form: Here elements are stored column wise. First we store the first column, then the second and soon. + +Row Major form ( starting address 1000 ) + + + +Column Major form ( starting address 1000 ) + + + +### **Sample code** + +_->Insertion of elements and printing the 2D-array_ + +_**We are using row major form to input the elements as a string_ + +_**NOTE: all characters need to be space separated, the end of the sequence also need to have a space_ + +### **Pseudo code->** + +``` +Prompt user for number of rows and columns +Initialize 2D array +Prompt user to enter matrix values as a string +Loop through input string: +- Extract numbers delimited by spaces +- Convert each substring to integer and store in the 2D array +Print the matrix: +- Loop through rows: +- Loop through columns: +- Print each element of the matrix +- Print a space between elements +- Print a newline after each row +Exit the program +``` +### **MIPS Code->** + +``` +.data +newline: .asciiz "\n" +space: .asciiz " " +msg_rows: .asciiz "Enter number of rows : " +msg_columns: .asciiz "Enter number of columns : " +msg_input: .asciiz "Enter matrix ( row major form ) : " +mat1: .space 100 +input: .space 100 + +.text +main: + li $v0, 4 + la $a0, msg_rows + syscall + + li $v0, 5 + syscall + move $t0, $v0 # $t0 = number of rows + + li $v0, 4 + la $a0, msg_columns + syscall + + li $v0, 5 + syscall + move $t1, $v0 # $t1 = number of columns + + li $v0, 4 + la $a0, msg_input + syscall + + li $v0, 8 # syscall for read_str + la $a0, input # Load address of input buer + li $a1, 100 # Maximum length + syscall + + la $t2, input + la $t3, mat1 + + li $t5, 0 + + # t2 - address of input string + # t3 - address of matrix + # t4 - used to iterate through string + # t5 - used to calculate number + +input_loop: + lb $t4, 0($t2) + beq $t4, 32, store + +# when a space is detected add the number calculated to the array and continue + + beq $t4, $zero , end_input + +#In ASCII encoding, the decimal value 32 corresponds to the space character (' ') + +#This loop exist to calculate numbers that have more than one digit , since our input is a string. + +# We need to iterate and add the characters until we detect a space + + sub $t6 , $t4, 48 # converts character to integer + +# for calculating the number + + mul $t5, $t5, 10 + add $t5, $t5, $t6 + addi $t2, $t2, 1 + + j input_loop +store: + sw $t5, 0($t3) #store the number obtained in the 2D-array + + addi $t3, $t3, 4 #increment the address to next memory block + li $t5, 0 + + add $t2 , $t2 , 1 #increment the index of string + j input_loop #loop back to the input to continue iteration of string + +end_input : + li $t6 , 0 # Initialize row index + la $t8, mat1 # Load address of array for printing + + li $v0, 4 + la $a0, newline + syscall + +print_loop: + beq $t6 , $t0 , end_programme + li $t7 , 0 # Initialize column index + +print_column_loop: + lw $t9 , 0($t8) # Load number from array + li $v0, 1 # syscall for print_int + move $a0, $t9 # Load number to print + syscall + + li $v0, 4 # syscall for print_str + la $a0, space # Load address of space + syscall + + addi $t7, $t7, 1 # Increment column index + addi $t8 , $t8 , 4 # Increment base address + blt $t7, $t1 , print_column_loop # Print all elements in the row + +# Print newline after each row + + li $v0 , 4 + la $a0 , newline + syscall + +# Reset column index for next row + li $t7 , 0 + +# Increment row index + addi $t6 , $t6 , 1 + + j print_loop + +end_programme : + li $v0, 10 # syscall for exit + syscall +``` +### **Output** +``` + Enter number of rows:3 + Enter number of columns:3 + Enter matrix(row major form) : 1 2 3 4 5 6 7 8 9 + + 1 2 3 + 4 5 6 + 7 8 9 +``` + +### **->To find maximum and minimum element in a 2-D array** + +**We are using row major form to input the elements as a string + +**same process of taking the input as the above + +__**NOTE: all characters need to be space separated, the end of the sequence also need to have a space__ + +#### **Pseudo code->** + +``` +Prompt user for number of rows and columns +Initialize 2D array +Prompt user to enter matrix values as a string +Loop through input string: +- Extract numbers delimited by spaces +- Convert each substring to integer and store in the 2D +array +Find minimum and maximum elements in the matrix: +- Initialize minimum element to maximum possible value +and maximum element to 0 +- Loop through each element of the matrix: +- Update minimum and maximum elements if necessary +Print the maximum element message: +- Print "The maximum element is: " +- Print the maximum element +Print the minimum element message: +- Print "The minimum element is: " +- Print the minimum element +Exit the program +``` + +### **MIPS Code->** + +``` +.data +newline: .asciiz "\n" +space: .asciiz " " +msg_rows: .asciiz "Enter number of rows : " +msg_columns: .asciiz "Enter number of columns : " +msg_input: .asciiz "Enter matrix ( row major form ) : " +maximum : .asciiz"The maximum element is : " +minimum : .asciiz"The minimum element is : +mat1: .space 100 +input: .space 100 +.text +main: + li $v0, 4 + la $a0, msg_rows + syscall + + li $v0, 5 + syscall + move $t0, $v0 # $t0 = number of rows + + li $v0, 4 + la $a0, msg_columns + syscall + + li $v0, 5 + syscall + move $t1, $v0 # $t1 = number of columns + + li $v0, 4 + la $a0, msg_input + syscall + + li $v0, 8 # syscall for read_str + la $a0, input # Load address of input buer + li $a1, 100 # Maximum length + syscall + + la $t2, input + la $t3, mat1 + + li $t5, 0 + + # t2 - address of input string + # t3 - address of matrix + # t4 - used to iterate through string + # t5 - used to calculate number + +input_loop: + lb $t4, 0($t2) + beq $t4, 32, store + + # when a space is detected add the number calculated to the array and continue + + beq $t4, $zero , end_input + + #In ASCII encoding, the decimal value 32 corresponds to the space character (' ') + + #This loop exist to calculate numbers that have more than one digit , since our input is a string + # we need to iterate and add the characters until we detect a space + + sub $t6 , $t4, 48 # converts character to integer + + # for calculating the number + mul $t5, $t5, 10 + add $t5, $t5, $t6 + addi $t2, $t2, 1 + j input_loop + +store: + sw $t5, 0($t3) #store the number obtained in the 2D-array + addi $t3, $t3, 4 #increment the address to next memory block + li $t5, 0 + add $t2 , $t2 , 1 #increment the index of string + j input_loop #loop back to the input to continue iteration of string + +end_input : + li $t6 , 0 # Initialize row index + la $t8, mat1 # Load address of array for printing + li $v0, 4 + la $a0, newline + syscall + +find_min_max: + li $t3 , 0 # Initialize max element to 0 + li $t2 , 0xffffffff + li $t6 , 0 # Initialize row index to 0 + la $a0 , mat1 + +row_loop: + beq $t6, $t0 , end # If all rows have been checked, exit + + li $t7, 0 # Initialize column index to 0 + +column_loop: + beq $t7, $t1 , end_column_loop # If all columns have been checked, move to next row + + lw $t8, 0($a0) # Load current element from array + +# Compare current element with max element and the min element + bgt $t8, $t3, update_max # if element greater than max element , update max + + min : + blt $t8 , $t2 , update_min # if element smaller than min element, update min + + increment : + addi $a0, $a0, 4 # Move to next column + addi $t7, $t7, 1 # Increment column index + j column_loop + +update_max: + move $t3 , $t8 # Update max element + j min # control goes back to checking for the conditional statement of min element + +update_min: + move $t2 , $t8 # Update min element + j increment # control goes back to incrementing the looping values + +End_column_loop: + addi $t6, $t6, 1 # Increment row index + j row_loop + +end : + li $v0 , 4 + la $a0 , maximum + syscall + + li $v0 , 1 + move $a0 , $t3 # printing the maximum element + syscall + + li $v0 , 4 + la $a0 , newline + syscall + + li $v0 , 4 + la $a0 , minimum # printing the minimum element + syscall + + li $v0 , 1 + move $a0 , $t2 + syscall + + li $v0 , 10 + syscall +``` +### **Output** +``` + Enter number of rows :3 + Enter number of columns :3 + Enter matrix ( row major form ) : 1 2 34 5 6 7 300 9 22 + + The maximum element is : 300 + The minimum element is : 1 +``` + +### **More Questions** + + _->Searching in Matrix: Write a MIPS assembly program to search for a given element in a matrix and return its position if found._ + + _->Matrix Addition: Write a MIPS program to add two matrices of the same size_ + + _->Transpose of a Matrix: Write a MIPS assembly program to find the transpose of a given matrix._ + + +★ **MIPS code for if statements** + ● Iftheconditionisanequalityusebeq,bne + ● Iftheconditionisacomparisoncombinebeq/bnewithset-on-less-than + + +**Why not blt or bge?** + While blt and bge (pseudo-instructions) are available in MIPS, beq and bne are favoured inconditional statements for their efficiency making them the common choice. + +**Example 1)** Given,f:$s0, g:$s1, h:$s2, i:$s3, j:$s4 +``` + if(i==j) + f = g + h; + else + f = g - h; +``` + +**Solution 1 :-** Corresponding MIPS code +``` + bne $s3, $s4, else + add $s0, $s1, $s2 + j endif +else: sub $s0, $s1, $s2 +endif: ........... +``` +**Example 2)** Given,f:$s0 ,g:$s1 ,h:$s2 ,i:$s3 ,j:$s4 +``` + if(i + +➢ Stack allocation (refer Recursion in MIPS(non-leaf procedure) for detailed explanation) + + + +(a) before, (b) during, and (c) after a procedure call. + +There are two types of procedure calling- + +**1) Leaf Procedures:** These procedures do not call other procedures. + +When a leaf procedure is called: + +● There turn address is saved on the stack. +● A stack frame/procedure frame/activation record is setup to store local variables. +● Arguments may be passed in registers or on the stack. +● The procedure executes its code. + +Upon completion,it restores the stack pointer and returns to the saved return address. + +**2) Non-leaf Procedures(NestedProcedures):** These procedures call other procedures, eg.- **Recursive Functions/Procedures.** + +In addition to the steps for leaf procedures, non-leaf procedures must manage: + +● Saving and restoring additional registers beyond there turn address. +● Managing multiple levels of procedure calls and returns. +● Ensuring that data in registers is preserved a cross nested calls. +● Properly handling there turn value from called procedures. + +★ **Function (Procedure) calling in MIPS** + + +In MIPS assembly language, passing parameters to functions involves using +registers. Unlike high-level languages where parameters are often passed on the stack,MIPS typically uses specific registers for passing arguments. + +● $a0 to $a3 :These are argument registers and are used to pass the first four arguments to a function. If a function has more than four parameters,additional parameters are typically passed on the stack. + +● $v0 and $v1: These are value registers and are used to return values from functions. Functions can return up to two values using these registers. + + + +(Note:-i) Register 1, called $at, is reserved for the assembler. + ii) Registers 26–27, called $k0–$k1 are reserved for the operating system.) + +➢ **Steps in calling a procedure (function)** + +In MIPS assembly language, procedure calling follows a similar structure to function calls in high-level languages like C. + +The following steps typically occur in both leaf and non-leaf functions but there are some nuances in how they're implemented, especially regarding the handling of the stack: + +● **Arguments Passing** :.Arguments to the function can be passed via registers or the stack, depending on the calling convention. In register-based passing, arguments are loaded in to designated argument registers like $a0-$a3. If there are more arguments than available registers, excess arguments are typically passed on the stack. + +● **Jump and Link (jal)** :jal makes the control jump to the given address while storing there turn address at PC+4 in the $ra register This effectively sets up the return mechanism for the function call. + +● **Function Prologue (Non-leaf functions):** Non-leaf functions need to setup a stack frame. This involves: Saving the return address($ra) +on to the stack, saving any callee- saved registers on to the stack(these are typically $s0-$s7),setting up the frame pointer($fp) to establish a reference point for accessing local variables and saved registers. + +● **Function Execution** :The function performs its task, accessing arguments, local variables, and performing computations. + +**● Function Epilogue (Non-leaf functions):** Before returning, non-leaf functions need to cleanup the stack frame and restore the state of callee-saved registers.This involves restoring callee-saved registers from the stack, restoring the return address($ra) from the stack resetting the stack pointer($sp) to deallocate the stack frame, jumping back to the return address using the jr $ra instruction. + +● Return: Upon completing its task, the function returns control to the caller. If it's a leaf function, it typically involves jumping back to the return address stored in $ra using the jr $ra instruction. For non-leaf + functions, the return sequence includes restoring the stack frame and registers before jumping back to the caller. + +(Note:-For simplicity we will only use $sp and extend the stack at procedure entry/exit) + +**Example 1)** Calling a procedure which prints a string +```asm +//code +printFunction(); +a=a+2; +//code +``` + +**Solution 1 :-** Corresponding MIPS code +```asm +data +hello_string: .asciiz "Hello, world!\n" # String definition + +.text +main: +....previous code +jal printFunction #jump to printFunction +addi $s2, 2 +....further code +li $v0, 10 # Set syscall code 10 for exit +syscall # Perform syscall to exit the program + +printFunction: +li $v0, 4 # Set syscall code 4 to print a string +la $a0, hello_string # Load the address of the string +syscall # Perform syscall to print +jr $ra # Return control to PC + 4 +``` + +● When jal is used, the control moves to the address specified in the instruction and the address of the next instruction is stored in $ra. + +● When the procedure ends jr $ra is used to return control back to the +next address from where it jumped. + +● These procedures are usually placed after the “main” procedure to avoid instruction overlap. + +**Example 1)** Calling a function with parameters +```asm +//code +result=addNumbers(5,7); +//code +``` + + +**Solution 1 :-** Corresponding MIPS code +```asm +text +main: + li $a0, 5 # Load first parameter (5) into $a0 + li $a1, 7 # Load second parameter (7) into $a1 + jal addNumbers # Jump to addNumbers function + move $s0, $v0 # Store the result returned by addNumbers in $s0 + # Further code + li $v0, 10 # Set syscall code 10 for exit + syscall # Perform syscall to exit the program + +addNumbers: + add $v0, $a0, $a1 # Add the values of $a0 and $a1 and store the result in $v0 + jr $ra # Return control to the next instruction after jal +``` + +● In the main function, parameters are passed to the addNumbers function by loading values into registers $a0 and $a1. + +● The jal instruction is used to jump to the addNumbers function. + +● Inside the addNumbers function, the parameters are accessed from the $a0 and $a1 registers. + +● The result of the addition is stored in register $v0, which is commonly used to return function results in MIPS. + +● Finally, jr $ra is used to return control back to the instruction after the jal in the main function. + +★ **Recursion in MIPS (non-leaf procedure)** + +In MIPS assembly language, implementing recursion involves understanding function calls and stack manipulation. + +**The Stack in MIPS Assembly** + +● The stack is a crucial data structure used in MIPS assembly language for managing function calls, local variables, and return addresses. +● It operates based on the Last-In-First-Out (LIFO) principle, meaning the +last item pushed onto the stack is the first item to be popped off. + +**Stack Operations:** + +**Stack Pointer ($sp):** +● The stack pointer register, $sp, points to the top of the stack. It keeps track of the current position in memory where new items are pushed onto or popped off the stack. + +**Push Operation:** +● To push data onto the stack, the stack pointer is decremented to reserve space for the new item, and then the data is stored at the memory location pointed to by the stack pointer. + +**Pop Operation:** +● To pop data off the stack,the data is retrieved from the memory location +pointed to by the stack pointer, and then the stack pointer is incremented to remove the item from the stack. + +**Stack Usage in Function Calls:** +**Function Prologue:** +● When a function is called, the current contents of relevant registers (such as there turn address and callee-saved registers) are typically saved on the stack to ensure they are preserved. +● This process is often referred to as the function prologue. + +**Function Epilogue:** +● Upon completion of the function, the saved values on the stack are restored to their original registers. +● This process is known as the function epilogue. + + +**Example)** Function Call and Stack Usage + +● When main calls my Function using jal, the return address (the address of the instruction following the function call) is automatically saved in register $ra. +● Inside my Function, the function prologue allocates space on the stack +to save the return address. +● The function body executes the desired operations. +● Finally, in the function epilogue, the return address is restored, and the stack space allocated in the prologue is deallocated before returning control to the caller. + +To understand recursion in MIPS, a good understanding of the stack pointer and how it operates on memory is imperative. Recursion involves careful management of the function call stack, ensuring that return addresses and local variables are properly saved and restored. This example illustrates the process of calculating the factorial of a number using recursion in MIPS assembly language. + +**Example) Calculating the factorial of a number using recursion** + +```asm +//code +result = factorial(5); +//code +``` + +**Solution 1 :-** Corresponding MIPS code +```asm +text +main: + li $a0, 5 # Load the value 5 (number whose factorial is to be calculated) into $a0 + jal factorial # Jump to the factorial function + move $s0, $v0 # Store the result returned by factorial in $s0 + + # Further code using the result stored in $s0 + # ... + + li $v0, 10 # Set syscall code 10 for exit + syscall # Perform syscall to exit the program + +factorial: + # Function prologue + addi $sp, $sp, -4 # Allocate space on the stack for local variables + sw $ra, 0($sp) # Save the return address on the stack + + # Check for base case: if n <= 1, return 1 + li $t0, 1 # Load the value 1 into $t0 + ble $a0, $t0, base_case # Branch to base_case if $a0 (n) <= $t0 (1) + + # Recursive case: n * factorial(n - 1) + addi $a0, $a0, -1 # Decrement $a0 (n) by 1 + jal factorial # Recursive call to factorial function + lw $ra, 0($sp) # Restore the return address from the stack + addi $sp, $sp, 4 # Deallocate space on the stack for local variables + mul $v0, $a0, $v0 # Multiply n by the result of factorial(n - 1) + jr $ra # Return control to the caller + +base_case: + # Base case: n <= 1, return 1 + li $v0, 1 # Load the value 1 into $v0 + lw $ra, 0($sp) # Restore the return address from the stack + addi $sp, $sp, 4 # Deallocate space on the stack for local variables + jr $ra # Return control to the caller +``` + +● In the main function, the value 5 is loaded into register $a0 to calculate its factorial. +● The factorial function is then called using the jal instruction. +● Inside the factorial function, the base case checks if the input value n is less than or equal to 1.If so,it returns 1. +● Otherwise,the function decrements n by 1 and recursively calls itself +with the decremented value. +● The result of the recursive call is then multiplied by n to compute the factorial. +● Finally,the result is returned to the caller using register $v0. + + + + +### **References** +J.L.Hennessy and D.A.Patterson Computer Organization and Design:The Hardware/Software Interface, Fifth Edition +“Digital Logic and Computer Design” by M.Morris Mano +“Digital Fundamentals” by Thomas L.Flyod +[http://www.cs.missouristate.edu/MARS/](http://www.cs.missouristate.edu/MARS/) +[https://www.d.umn.edu/~gshute/mips/directives-registers.pdf](https://www.d.umn.edu/~gshute/mips/directives-registers.pdf) +[https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html](https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html) +[https://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.html](https://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.html) +[https://riptutorial.com/mips/example/29993/mars-mips-simulator](https://riptutorial.com/mips/example/29993/mars-mips-simulator) +[https://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf](https://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf) diff --git a/docs/fsm.md b/docs/fsm.md new file mode 100644 index 0000000..5910a81 --- /dev/null +++ b/docs/fsm.md @@ -0,0 +1,798 @@ +# **Introduction To Finite State Machines** + +## **Basic Definition And Formulations:** + +An FSM is a digital sequential circuit that can follow a number of predefined +states under the control of one or more inputs. Each state is a stable entity that +the machine can occupy. It can move from this state to another state under the +control of an outside-world input. + + + +Some FSMs have a clock input and are called synchronous FSMs, i.e. those that +do not belong to a type of FSM called asynchronous FSMs. +Each state of the FSM needs to be identifiable. This is achieved by using a +number of internal (to the FSM block) flip-flops. An FSM with four states +would require two flip-flops, since two flip-flops can store 22 =4 state numbers. +Each state has a unique state number, and states are usually assigned numbers +as s0 (state 0), s1, s2, and s3 (for the four-state example). +The rule here is + +**Number of states = 2(number of flip-flops)** + or +**Number of flip-flops = log2(number of states)** + +### **State Table** +The time sequence of inputs, outputs, and flip-flop states may be enumerated in +a state table. The state table for the circuit of Fig. 1.2 is shown in Table 1.1. It +consists of three sections labeled present state, next state, and output. The +present state designates the states of flip-flops before the occurrence of a clock +pulse. The next state shows the states of flip-flops after the application of a +clock pulse, and the output section lists the values of the output variables during +the present state. Both the next state and output sections have two columns, one +for x = 0 and the other for x = 1. + + + + + +### **State Equations** +A state equation (also known as an application equation) is an algebraic +expression that specifies the conditions for a flip-flop state transition. The left +side of the equation denotes the next state of a flip-flop and the right side, a +Boolean function that specifies the present state conditions that make the next +state equal to 1. A state equation is similar in form to a flip-flop characteristic +equation, except that it specifies the next state conditions in terms of external +input variables and other flip-flop values. The state equation is derived directly +from a state table. For example, the state equation for flip-flop A is derived +from inspection of Table 1-1. From the next state columns, we note that flip- +flop A goes to the 1 state four times: when x = 0 and AB = 01 or 10 or 11, or +when x = 1 and AB = 11. This can be expressed algebraically in a state equation +as follows: +**A(t + 1) = (A′B + AB′ + AB) x′ + Abx** + +### **State Diagram** +The information available in a state table may be represented graphically in a +state diagram. In this diagram, a state is represented by a circle, and the +transition between states is indicated by directed lines connecting the circles. +The state diagram of the sequential circuit give in the [Section 1.1](#11-state-table) is shown below. The +binary number inside each circle identifies the state the circle represents. +The directed lines are labeled with two binary numbers separated by a /. The +input value that causes the state transition is labeled first; the number after the symbol / gives the value of the output during the present state. For example, the +directed line from state 00 to 01 is labeled 1/0, meaning that the sequential +circuit is in a present state 00 while x = 1 and x = 0, and that on the +termination of the next clock pulse, the circuit goes to next state 01. A directed +line connecting a circle with itself indicates that no change of state occurs. The +state diagram provides the same information as the state table and is obtained +directly from table in [Section 1.1](#11-state-table) + + + +--- + +## **Types of Finite State Machines:** + +### **Mealy Model** +n this model, the FSM has a number of inputs that connect to the Next State +Decoder (combinational) logic. The Q outputs of the memory element Flip- +Flops connect to the Output Decoder logic, which in turn connects to the +Outside World Outputs. The Flip-Flops outputs are used as Next State inputs to +the Next State Decoder, and it is these that determine the next state that the +FSM will move to. Once the FSM has moved to this Next State, its Flip-Flops +acquire a new Present State, as dictated by the Next State Decoder. +Note that some of the Outside World Inputs connect directly to the Output +Decoder logic. This is the main feature of the Mealy-type FSM. + + + +### **Moore Model** +Another architectural form for an FSM is the Moore FSM. +The Moore FSM [Section 2.2](#22-moore-model) differs from the Mealy FSM in that it does not +have the feed-forward paths. This type of FSM is very common. Note that the +Outside World Outputs are a function of the Flip-Flops outputs only (unlike the +Mealy FSM architecture, where the Outside World Outputs are a function of +Flip-Flops outputs and some Outside World Inputs). + + + +--- + +## **Pre-Requisite Verilog Commands:** +### **Initial** +A set of Verilog statements are usually executed sequentially in a simulation. +These statements are placed inside a procedural block. Initial is one of the two +main types of procedural block statements. An initial block is not synthesizable +and hence cannot be converted into a hardware schematic with digital elements. +Hence initial blocks do not serve much purpose than to be used in simulations. +These blocks are primarily used to initialize variables and drive design ports +with specific values.This block will be executed only once during the entire +simulation. Execution of an initial block finishes once all the statements within +the block are executed. +The syntax is shown below: +```v +initial + [single statement] + +initial begin + [multiple statement] +end +``` +### **Always** +An always block is one of the procedural blocks in Verilog. Statements inside +an always block are executed sequentially. The always block is executed at +some particular event defined in the sensitivity list. +A sensitivity list is the expression that defines when the always block should be +executed and is specified after the @ operator within parentheses ( ) . This +list may contain either one or a group of signals whose value change will +execute the always block. +An always block can be used to realize combinational or sequential elements. A +sequential element like flip flop becomes active when it is provided with a clock +and reset. Similarly, a combinational block becomes active when one of its nput values change. These hardware blocks are all working concurrently +independent of each other. The connection between each is what determines the +flow of data. To model this behavior, an always block is made as a continuous +process that gets triggered and performs some action when a signal within the +sensitivity list becomes active. The syntax is displayed in [Section 2.2](#22-moore-model) +```v +always @ (event) + [statement] + +always @ (event) begin + [multiple statement] +end +``` + +### **Begin..End** +Statements are wrapped using begin and end keywords and will be executed +sequentially in the given order, one after the other. Delay values are +treated relative to the time of execution of the previous statement. After all the +statements within the block are executed control may be passed elsewhere. The +syntax is shown in [Section 3.3](#33-beginend) +```v +begin : name_seq + [statements] +end +``` +### **Fork..Join** +Statements are launched in parallel by wrapping them within the join and fork +keywords. A parallel block can execute statements concurrently and delay +control can be used to provide time-ordering of the assignments. The syntax is +shown in [Section 3.4](#34-forkjoin) +```v +fork : name_fork + [statements] +join +``` +### **Blocking Statements** +Blocking assignment statements are assigned using = and are executed one after +the other in a procedural block. However, this will not prevent execution of +statments that run in a parallel block. For eg +```v +module tb; + reg[7:0] a, b, c, d, e; + + initial begin + a = 8'hDA; + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + + b = 8'hF1; + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + + c = 8'h30 + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + end + + initial begin + d = 8'hAA; + $display("[%0t] d=0x0%h e=0x0%h", $time, d, e); + + e = 8'h55; + $display("[%0t] d=0x0%h e=0x0%h", $time, d, e); + end +endmodule +``` +In the above example, there are two initial blocks which are executed in parallel +when simulation starts. Statements are executed sequentially in each block +and both blocks finish at time 0ns. To be more specific, variable a gets assigned +first, followed by the display statement which is then followed by all other +statements. + +### **Non-Blocking Statements** +Non-blocking assignment allows assignments to be scheduled without blocking +the execution of following statements and is specified by a <= symbol. It's +interesting to note that the same symbol is used as a relational operator in +expressions, and as an assignment operator in the context of a non-blocking +assignment. The following code snippet is written by replacing all the blocking +statements in the previous example by non blocking statements. Try out for +yourself and compare the difference in the outputs :-) . +```v +module tb; + reg[7:0] a, b, c, d, e; + + initial begin + a <= 8'hDA; + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + + b <= 8'hF1; + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + + c <= 8'h30 + $display("[%0t] a=0x%0h b=0x0%h c=0x0%h", $time); + end + + initial begin + d <= 8'hAA; + $display("[%0t] d=0x0%h e=0x0%h", $time, d, e); + + e <= 8'h55; + $display("[%0t] d=0x0%h e=0x0%h", $time, d, e); + end +endmodule +``` + +### **Posedge and Negedge** +Simply speaking, +posedge means the transition from 0 to 1 +negedge the oposit transition from 1 to 0 +In synchronous sequential circuits, changes in flip-flops +occur only in response to a transition of a clock pulse. The transition may be +either a positive edge or a negative edge of the clock, but not both. Verilog HDL +takes care of these conditions by providing these two keywords viz. posedge +and negedge. The syntax is shown in [Section 3.7](#37-posedge-and-negedge) +```v +always@(posedge clock, negedge reset); +``` + +### **Case Statement** +The case statement checks if the given expression matches one of the other +expressions in the list and branches accordingly. It is typically used to +implement a multiplexer. The if-else construct may not be suitable if there are +many conditions to be checked and would synthesize into a priority encoder +instead of a multiplexer. +```v +// Here 'expression' should match one of the lines +case() + case_item1 : + case_item2, + case_item3 : begin + + end + default : +endcase +``` +The syntax is shown in [Section 3.8](#38-case-statement). A Verilog case statement starts with the +keyword case and ends with the endcase keyword. The expression within +parantheses will be evaluated exactly once and is compared with the list of +alternatives in the order they are written and the statements for which the +alternative matches the given expression are executed. A block of multiple +statements must be grouped and be within begin and end. +If none of the case items match the given expression, statements within the +default item is executed. The statement is optional, and there can be only one +default statement in a case statement. + +--- + +## **Examples of Implementing State Machines in Verilog:** +Now that we are all set and armed with the required amunition of verilog +commands, let’s dive headfirst into implementing state machines using verilog. +This section will consist of four examples. Each example will consist of the +problem statement, the state diagram, the verilog code and testbench and +finally,the output of the code. +Try implementing these problems on your own first without referring to this +manual. If yoou get stuck at any point, you can come back and take a peek ;-) +Remember, the key lies in understanding the state diagram thoroughly!! + +### **Mealy Machine Implementations** +Let’s start our dive with a simple example of implementing a mealy machine. +Recall that in a Mealy machine, the output is a function of both, the present +state as well as the input. Let’s consider the example of a Mealy Zero Detector +shown in [Section 4.1](#41-mealy-machine-implementations) + +### **Verilog Code:** +```v +module mealy_zero_det( + output reg y_out, + input x_in,clk,reset); + + reg [1:0] state,next_state; + parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11; + + always@(posedge clk,negedge reset) + if (reset==0) state <= S0; + else state<=next_state; + + always @ (state, x_in) + case (state) + S0: + if (x_in) next_state = S1; else next_state =S0; + S1: + if (x_in) next_state = S3; else next_state =S0; + S2: + if (~x_in) next_state = S0; else next_state = S2 + S3: + if (x_in) next_state = S2; else next_state=S0 + endcase + + always @ (state, x_in) + case (state) + S0: + y_out = 0; + S1, S2, S3: + y_out = ~x_in; + endcase + +endmodule +``` + +### **TestBench:** +```v +module mealy_zero_det_tb(); + wire t_y_out; + reg t_x_in,t_clock,t_reset; + mealy_zero_det uut(t_y_out,t_x_in,t_clock,t_reset);initial #200 $finish; + initial + begin + $dumpfile("dump.vcd"); + $dumpvars(1); + t_clock = 0; + forever #5 t_clock = ~t_clock; + end + initial + fork + t_reset = 0; + #2 t_reset = 1; + #87 t_reset = 0; + #89 t_reset = 1; + #10 t_x_in = 1; + #30 t_x_in = 0; + #40 t_x_in = 1; + #50 t_x_in = 0; + #52 t_x_in = 1; + #54 t_x_in = 0; + #70 t_x_in = 1; + #80 t_x_in = 1; + #70 t_x_in = 0; + #90 t_x_in = 1; + #100 t_x_in = 0; + #120 t_x_in = 1; + #160 t_x_in = 0; + #170 t_x_in = 1; + join +endmodule +``` +### **Simulation Waveform:** + + +### **Moore Machine Implememtation** +Let’s try implementing the above example in Moore Model. The state diagram +needs to be modified as in the Moore Model, the output depends only on the +initial state. The state diagram will be as shown in [Section 4.2](#42-moore-machine-implememtation) + + + +### **Verilog Code:** +```v +module moore_zero_det ( + output [1:0] y_out, + input x_in, clock, reset + ); + + reg [1:0] state; + parameter S0 = 2'b00, S1 = 2'b01, S2 = 2'b10, S3 = 2'b11; + + always @ (posedge clock, negedge reset) + if (reset == 0) + state <= S0; + else + case (state) + S0: + if (~x_in) + state <= S1; + else + state <= S0; + S1: + if (x_in) + state <= S2; + else + state <= S3; + S2: + if (~x_in) + state <= S3; + else + state <= S2; + S3: + if (~x_in) + state <= S0; + else + state <= S3; + endcase + + assign y_out = state; +endmodule +``` + +### **Testbench:** +```v +module moore_zero_det_tb(); +wire [1:0] t_y_out; +reg t_x_in,t_clock,t_reset; +moore_zero_det uut(t_y_out,t_x_in,t_clock,t_reset);initial #200 $finish; +initial + begin + // Dump waves + $dumpfile("dump.vcd"); + $dumpvars(1); + t_clock = 0; + forever #5 t_clock = ~t_clock; + end + initial + fork + t_reset = 0; + #2 t_reset = 1; + #87 t_reset = 0; + #89 t_reset = 1; + #10 t_x_in = 1; + #30 t_x_in = 0; + #40 t_x_in = 1; + #50 t_x_in = 0; + #52 t_x_in = 1; + #54 t_x_in = 0; + #70 t_x_in = 1; + #80 t_x_in = 1; + #70 t_x_in = 0; + #90 t_x_in = 1; + #100 t_x_in = 0; + #120 t_x_in = 1; + #160 t_x_in = 0; + #170 t_x_in = 1; + join +endmodule +``` +### **Simulation Waveform:** + + +### **Chess Clock Controller** +**Background:** At the start of a new game, the Reset input is asserted to initialize +the system and clear both timers to zero time. This is achieved by means of the +Clr output of the Chess Clock FSM being driven high, thereby asserting the +reset (rst) input of both timers. Each chess player has a push-button, which +when pressed applies a logic 1 to their respective inputs, Pa and Pb, of the +Chess Clock FSM. After resetting the timers, the player who is not making the +first move presses their push-button in order to enable the other player’s timer +to commence timing. +For example, if Player-A is to make the first move, then Player-B starts the +game by pressing their push-button. This has the effect of activating the Ta +output of the Chess Clock FSM block in order to enable TIMER-A to record the +time taken by Player-A to make the first move. Once Player-A completes the +first move, Player-A’s button is pressed in order to stop their own timer and start +Player-B’s timer (Ta is negated and Tb is asserted) +The state diagram of this machine is given in [Section 4.3](#43-chess-clock-controller) + + +As shown, the FSM makes use of four states having the names shown in the +upper half of the state circles. The states of the FSM outputs Ta, Tb and Clr are +listed in the lower half of every state circle; those outputs preceded by ‘/’ are +forced to logic 0, whereas those without ‘/’ are forced to logic 1. The presence +of the output states within each of the state circles indicates that the Chess +Clock FSM is of the Moore variety. The values of the inputs, Pa and Pb, are +shown alongside each corresponding state transition path (arrow) using a format +similar to that used to show the state of the outputs. The movement from one +state to another occurs on the rising edge of the Clock input. Where the number +of transitions shown originating from a given state is less than the total number +possible, the remaining input conditions result in a so-called sling, i.e. the next +state is the same as the current state. + +### **Verilog Code:** +```v +module chess_clk_cntrl( + output time_a,time_b,clr, + input player_a,player_b,clk,reset); + + localparam run_a=0,run_b=1,stop=2,Wait=3; + reg [1:0] state; + always@(posedge clk,posedge reset) + begin + if(reset) + state<=stop; + else + case(state) + run_a: + casex({player_a,player_b}) + 2'b0x: state<=run_a; + 2'b10: state<=run_b; + 2'b11: state<=Wait; + endcase + run_b: + casex({player_a,player_b}) + 2'bx0: state<=run_b; + 2'b01: state<=run_a; + 2'b11: state<=Wait; + endcase + stop: + case({player_a,player_b}) + 2'b00: state<=stop; + 2'b01: state<=run_a; + 2'b10: state<=run_b; + 2'b11: state<=Wait; + endcase + Wait: + if(player_a==player_b) + state<=Wait; + else + if(player_a==1'b1) + state<=run_b; + else + state<=run_a; + endcase + end + assign time_a=state==run_a; + assign time_b=state==run_b; + assign clr=state==stop; +endmodule +``` + +### **Testbench:** +```v +module chess_clk_cntrl_tb(); + wire time_a,time_b,clr; + reg player_a,player_b,clk,reset; + chess_clk_cntrl uut(time_a,time_b,clr,player_a,player_b,clk,reset); + initial + begin + $dumpfile("dump.vcd"); + $dumpvars(1); + clk=1'b0; + forever + #50 clk=~clk; + end + + initial + begin + reset=1'b1;player_a=1'b0;player_b=1'b0; + #100 reset=1'b0; + #101 player_a=1'b1; + #167 player_a=1'b0; + #215 player_b=1'b1; + #289 player_b=1'b0; + #350 player_a=1'b1;player_b=1'b1; + #478 player_a=1'b0;player_b=1'b0; + #513 player_b=1'b1; + #550 $stop; + end +endmodule +``` + +### **Simulation Waveform:** + + +### **Vending Machine** +Our vending machine is based on the following state diagram: + + +The machine has the following states: +•State 1: Reset +•State 2: Five +•State 3: Ten +•State 4: Fifteen +•State 5: Twenty +•State 6: Twenty Five +The machine only accepts the following coins +•Rs. 5 (nickel) +•Rs. 10 (dime) +•Rs. 25 (quarter) +Whenever we get a coin we jump to the next state. So for example, if we get a +coin from the reset state, say a Rs. 5 coin, then we jump to the next state Five . +Otherwise we stay in the same state. When we get Extra amount we come back +to the reset state and the difference is given back to the user. + +### **Verilog Code** +```v +module vending_machine( + output reg vend, + output reg [2:0] change,state, + input [2:0] coin, + input clk,rst); + + parameter [2:0]rs_5= 3'b001; + parameter [2:0]rs_10= 3'b010; + parameter [2:0]rs_15= 3'b011; + parameter [2:0]rs_20= 3'b100; + parameter [2:0]rs_25= 3'b101; + + parameter [2:0]idle= 3'b000; + parameter [2:0]five= 3'b001; + parameter [2:0]ten= 3'b010; + parameter [2:0]fifteen= 3'b011; + parameter [2:0]twenty= 3'b100; + parameter [2:0]twenty_five=3'b101; + + reg[2:0] next_state; + + always@(coin or state) + begin + next_state=0; + case(state) + idle: + case(coin) + rs_5: next_state=five; + rs_10: next_state=ten; + rs_25: next_state=twenty_five; + default: next_state=idle; + endcase + five: + case(coin) + rs_5: next_state= ten; + rs_10: next_state=fifteen; + rs_25: next_state=twenty_five; + default: next_state=five; + endcase + ten: + case(coin) + rs_5: next_state=fifteen; + rs_10: next_state=twenty; + rs_25: next_state=twenty_five; + default: next_state=ten; + endcase + fifteen: + case(coin) + rs_5: next_state=twenty; + rs_10: next_state=twenty_five; + rs_25: next_state=twenty_five; + default: next_state=fifteen; + endcase + twenty: + case(coin) + rs_5: next_state=twenty_five; + rs_10: next_state=twenty_five; + rs_25: next_state=twenty_five; + default: next_state=twenty; + endcase + twenty_five: + next_state=idle; + default: next_state=idle; + endcase + end + + always@(clk) + begin + if(rst) + begin + change<=3'b000; + vend<=1'b0; + state<=idle; + end + else + state<=next_state; + case(state) + idle: + begin + vend<=1'b0; + change<=3'd0; + end + five: + begin + vend<=1'b0; + if(coin==rs_25) + change<=rs_5; + else + change<=3'd0; + end + ten: + begin + vend<=1'b0; + if(coin==rs_25) + change<=rs_10; + else + change<=3'd0; + end + fifteen: + begin + vend<=1'b0; + if(coin==rs_25) + change<=rs_15; + else + change<=3'd0; + end + twenty: + begin + vend<=1'b0; + if(coin==rs_10) + change<=rs_5; + else + if(coin==rs_25) + change<=rs_20; + else + change<=3'd0; + end + twenty_five: + begin + vend<=1'b1; + change<=3'd0; + end + default: state<=idle; + endcase + end +endmodule +``` + +### **TestBench:** +```v +module vending_machine_tb(); + wire vend; + wire [2:0] change,state; + reg [2:0] coin; + reg clk,rst; + + vending_machine uut(vend,change,state,coin,clk,rst); + + parameter [2:0]rs_5= 3'b001; + parameter [2:0]rs_10= 3'b010; + parameter [2:0]rs_15= 3'b011; + parameter [2:0]rs_20= 3'b100; + parameter [2:0]rs_25= 3'b101; + + parameter [2:0]idle= 3'b000; + parameter [2:0]five= 3'b001; + parameter [2:0]ten= 3'b010; + parameter [2:0]fifteen= 3'b011; + parameter [2:0]twenty= 3'b100; + parameter [2:0]twenty_five=3'b101; + + initial + begin + $dumpvars; + $dumpfile("file.vcd"); + clk=1'b0; rst=1'b1; + #2 rst=0; coin=rs_5; + #2 rst=1; coin=2'b00; + #2 rst=0;coin=rs_10; + #2 rst=1; coin=2'b00; + #2 rst=0; coin=rs_25; + #2 rst=1; coin=2'b00; + #2 rst=0; coin=rs_5; + #2 coin=rs_5; + #2 coin=rs_5; + #2 coin=rs_5; + #2 coin=rs_5; + #2 rst=1; coin=2'b00; + #2 rst=0; coin=rs_5; + #2 coin=rs_10; + #2 coin=rs_10; + #2 rst=1; coin=2'b00; + #2 rst=0; coin=rs_10; + #2 coin=rs_25; + #2 coin=rs_5; + #2 rst=1; coin=2'b00; + #2 rst=0; coin=rs_10; + #2 coin= rs_10; + #2 coin=rs_25; + #2 rst=1; coin=2'b00; + #2 $finish; + end + always + #1 clk=~clk; + initial + begin + if (rst) + coin=2'b00; + end +endmodule +``` + + + +And with this we have come to the end of the manual for Finite State Machines. +Up next, you will learning the implementation of a Single Cycle MIPS +Processor. Hopefully this manual helped in broadening your understanding of +Finite State Machines from a very basic to a fairly advanced level. You’ll be +required to implement these concepts again in the Practice Questions. + +--- +## **References** +1. Digital Design: With An Introduction to Verilog HDL (5th Edition), M. +Morris Mano, Michael D. Cilleti. +2. FSM-based Digital Design using Verilog HDL, Peter Minns and Ian Elliott. +3. [http://www.csun.edu/~ags55111/](http://www.csun.edu/~ags55111/) +4. [https://ocw.mit.edu/courses/6-111-introductory-digital-systems- +laboratory-spring-2006/](https://ocw.mit.edu/courses/6-111-introductory-digital-systems- +laboratory-spring-2006/) +5. 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In the Terminal window, navigate to the directory where you placed the +"mars4_5.jar" file. For example, if you placed it in the Applications folder, +you can use the following command: ``` cd/Applications``` +10. Once you are in the correct directory, execute the following command to +run the MIPS MARS simulator: ```java -jar mars4_5.jar``` +11. The MIPS MARS simulator should now launch on your macOS computer. + +##### **Downloading MIPS MARS Simulator on Windows:** +1. Open a web browser on your Windows computer. +2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ +kenvollmar/mars/]([http://courses.missouristate.edu/ +kenvollmar/mars/]) +3. On the homepage, click on the "MARS 4.5" link under the "Download +MARS" section. +4. A ZIP file named "mars4_5.jar.zip" will be downloaded to your computer. +5. Locate the downloaded ZIP file in your Downloads folder or the folder you +specified for downloads. +6. Right-click on the ZIP file and select "Extract All" to extract its contents. This +will create a JAR file named "mars4_5.jar". +7. Move the "mars4_5.jar" file to a suitable location on your computer, such as +the Program Files folder. +8. Open the Command Prompt on your Windows computer by pressing the +Windows key + R, typing "cmd," and hitting Enter. +9. In the Command Prompt window, navigate to the directory where you placed +the "mars4_5.jar" file. For example, if you placed it in the Program Files +folder, you can use the following command: ```cd "C:\Program Files"``` +10. Once you are in the correct directory, execute the following command to run +the MIPS MARS simulator: ```java -jar mars4_5.jar``` +11. The MIPS MARS simulator should now launch on your Windows computer. + +##### **Downloading MIPS MARS Simulator on Linux:** +1. Open a web browser on your Linux computer. +2. Go to the official website of MIPS MARS at [http://courses.missouristate.edu/ +kenvollmar/mars/](http://courses.missouristate.edu/ +kenvollmar/mars/) +3. On the homepage, click on the "MARS 4.5" link under the "Download +MARS" section. +4. A ZIP file named "Mars4_5.jar.zip" will be downloaded to your computer. +5. Open the terminal on your Linux system. You can typically find it in the +Applications menu or by using the shortcut Ctrl+Alt+T. +6. Navigate to the directory where you downloaded the ZIP file. For example, if +it's in the Downloads folder, you can use the following command: ```cd ~/Downloads``` +7. Unzip the ZIP file using the following command: ```unzip Mars4_5.jar.zip``` +8. This will extract the "Mars4_5.jar" file from the ZIP archive. +9. Move the "Mars4_5.jar" file to a suitable location on your computer. For +instance, you can move it to the /opt directory using the following command: +```sudo mv Mars4_5.jar /opt``` +10. To run the MIPS MARS simulator, open the terminal and navigate to the +directory where you placed the JAR file. For example, if you moved it to the / +opt directory, use the following command: +```cd /opt``` +11. Execute the following command to launch the MIPS MARS simulator +```java -jar Mars4_5.jar``` +12. The MIPS MARS simulator should now launch on your Linux computer. + +### **MARS ASSEMBLY AND SYSTEM CALLS** +Before assembling, the environment of this simulator can be simplisticly split to three +segments: the editor at the upper left where all of the code is being written, the +compiler/output right beneath the editor and the list of registers that represent the +"CPU" for our program. + +After assembling (by simply pressing F3) the environment changes, with two new +segments getting the position of the editor: the text segment where + +i) each line of assembly code gets cleared of "pseudoinstructions" (we'll talk about +those in a sec) at the "basic" column and + +ii) the machine code for each instruction at the "code" column, +and the data segment where we can have a look at a representation of the memory of +a processor with little-endian order. + +After assembling, we can execute our code either all at once (F5) or step by step (F7), +as well as rewinding the execution several steps backwards to the back (F8). + +_**MARS accepts and exports files with the .asm filetype**_ + +##### **Pseudo instructions** + +Before looking at the instruction set , let us look at a few pseudo instructions that’ll +help you understand the IS better. + +_**Here's a list of useful pseudo-instructions.**_ + +`mov $t0, $t1`: Copy contents of register t1 to register t0. + +`li $s0, immed`: Load immediate into to register s0. +The way this is translated depends on whether immed is 16 bits or 32 bits. + +`la $s0, addr`: Load address into to register s0. + +`lw $t0, address`: Load a word at address into register t0 + +_**Given below are some standard arithmetic and logical instructions standard to +the MIPS Instruction Set Architecture.**_ + +_**MARS provides a small set of operating system-like services through the system +call (syscall) instruction **_ + +_**To request a service, a program loads the system call code into register $v0 and +arguments into registers $a0~$a3 **_ + +_**System calls that return values put their results in register $v0**_ + +##### **Arithmetic Instructions** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| add | add $1,$2,$3 | $1=$2+$3 | | +| subtract | sub $1,$2,$3 | $1=$2-$3 | | +| add immediate | addi $1,$2,100 | $1=$2+100 | "Immediate" means a constant number | +| add unsigned | addu $1,$2,$3 | $1=$2+$3 | Values are treated as unsigned integers,not two's complement integer| +| subtract unsigned | subu $1,$2,$3 | $1=$2-$3 | Values are treated as unsigned integers,not two's complement integers| +| add immediate unsigned | addiu $1,$2,100 | $1=$2+100 | Values are treated as unsigned integers,not two's complement integers| +| multiply (without overflow) | mul $1,$2,$3 | $1=$2*$3 | Result is only 32 bits! | +| multiply | mult $1,$2,$3 | $hi, $low=$2*$3 | Upper 32 bits stored in special register ``hi``. Lower 32 bits stored in special register ``lo``| +| divide | div $1,$2,$3 | $hi,$low=$2/$3 |Remainder stored in special register ``hi``. Quotient stored in special register ``lo`` | + +#### **Logical** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| and | and $1,$2,$3 | $1=$2&$3 | Bitwise AND| +| or | or $1,$2,$3 | $1=$2|$3 | Bitwise OR| +| and immediate | andi $1,$2,100 | $1=$2&100 | Bitwise AND with immediate value | +| or immediate | ori $1,$2,100 | $1=$2|100 | Bitwise OR with immediate value| +| shift left logical | sll $1,$2,10 | $1=$2<<10 | Shift left by constant number of bits| +| shift right logical | srl $1,$2,10 | $1=$2>>10 | Shift right by constant number of bits| + +#### **Data Transfer** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| load word | lw $1,100($2) | $1=Memory[$2+100] | Copy from memory to register| +| store word | sw $1,100($2) | Memory[$2+100]=$1 | Copy from register to memory| +| load upper immediate | lui $1,100 | $1=100x2^16 | Load constant into upper 16 bits. Lower 16 bits are set to zero| +| load address | la $1,label | $1=Address of the label | Pseudo-instruction (provided by assembler). Loads computed address of label (not it's contents) into register| +| load immediate | li $1,100 | $1=100 | Pseudo instruction (provided by assembler). Loads immediate value into the register.| +| move from hi | mfhi $2 | $2=hi | Copy from special register ``hi`` to general register| +| move from lo | mflo $2 | $2=lo | Copy from special register ``lo`` to general register| +| load word | lw $1,100($2) | $1=Memory[$2+100] | Copy from memory to register| +| move | move $1,$2 | $1=$2 | Pseudo instruction (provided by assembler). Copy from register to register| + +#### **Conditional Branch** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| branch on equal | beq $1,$2,100 | if($1==$2) go to PC+4+100 | Test if registers are equal| +| branch on not equal | bne $1,$2,100 | if($1!=$2) go to PC+4+100 | Test if registers are not equal| +| branch on greater than | bgt $1,$2,100 | if($1>$2) go to PC+4+100 | Pseudo-instruction | +| branch on greater than or equal | bge $1,$2,100 | if($1>=$2) go to PC+4+100 | Pseudo-instruction| +| branch on less than | blt $1,$2,100 | if($1<$2) go to PC+4+100 | Pseudo-instruction| +| branch on less than or equal | ble $1,$2,100 | if($1<=$2) go to PC+4+100 | Pseudo-instruction| + +#### **Comparison** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| set on less than | slt $s1,$s2,$s3 | if($2<$3) $1 = 1;else $1 = 0 | Test if less than. If true set $1 to 1. Otherwise set $1 to 0. +| set on less than immediate | slti $s1,$s2,100 | if($2<100) $1 = 1;else $1 = 0 | Test if less than. If true set $1 to 1. Otherwise set $1 to 0. + +#### **Unconditional Jump** +|Instruction | Example | Meaning | Comments | +|---|---|---|---| +| jump | j 1000 | go to address 1000 | Jump to target address| +| jump register | jr $1 | go to address stored in $1 | For switch procedure return| +| jump and link | jal 1000 | $ra=PC+4 go to address 1000 | Use when making procedure call. This saves the return address in $ra| + +#### **System Calls** +| Service | Operation | Code(in $v0) | Arguments | Results | +|---|---|---|---|---| +| print_int | Print integer number (32 bit) | 1 | $a0 = integer to be printed | None | +| print_float | Print floating-point number (32 bit) | 2 | $f12 = float to be printed | None | +| print_double | Print floating-point number (64 bit) | 3 | $f12 = integer to be printed | None | +| print_string | Print null-terminated character string | 4 | $a0 = address of string in memory | None | +| read_int | Read integer number from user | 5 | None | Integer returned in $v0 | +| read_float | Read floating-point number from user | 6 None | Float returned in $f0| +| read_double | Read double floating-point number from user | 7 |None | Double returned in $f0| +| read_string | Works the same as Standard Clibrary fgets() | 8 | $a0 = memory address of string input buffer $a1 = length of string buffer (n) | None | +| sbrk | Returns the address to a block of memory containing n additional bytes (Useful for dynamic memory allocation) | 9 | $a0=amount | address in $v0 | +| exit | Stop program from running | 10 | None | None | +| print_char | Print character | 11 | $a0 = character to be printed | None | +| read_char | Read character from user | 12 | None | Char returned in $v0 | +| exit2 | Stops program from running and returns an integer | 17 | $a0 = result(integer number) | None | + +The complete list of syscalls can be accessed at +[https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html](https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html ) + +#### **Assembler Directives** +| Directive | Result | +|---|---| +| .word w1, ..., wn| Store n 32-bit values in successive memory words | +| .half h1, ..., hn| Store n 16-bit values in successive memory words | +| .byte b1, ..., bn| Store n 8-bit values in successive memory words | +| .ascii str| Store the ASCII string str in memory. Strings are in double-quotes, i.e. "Computer Science" | +| .asciiz str| Store the ASCII string str in memory and null terminate it. Strings are in double-quotes, i.e. "Computer Science" | +| .space n| Leave an empty n-byte region of memory for later use | +| .align n| Align the next datum on a 2^n byte boundary. For example, .align 2 aligns the next value ona word boundary | + +#### **Registers** +|Register Number | Register Name| Description| +|---|---|---| +| 0 | $zero | The value 0 | +| 2-3 | $v0-$v1 | Values from expression evaluation and function results | +| 4-7 | $a0-$a3 | (arguments) First four parameters for subroutine | +| 8-15, 24-25 | $t0-$t9 | Temporary variables | +| 16-23 | $s0-$s7 | Saved values representing final computed results | +| 31 | $ra | Return address | + +#### **MARS(MIPS Assembler/Simulator) Tutorial** +**1. Input the Tutorial program** + +1.1) Open the MARS program and click from the file menu choose “File...New”. A +black document will open which you can enter your assembly code into. Click +“File...Save As” and save the file as “Tutorial1.asm ”. + +1.2) Enter the code as shown below into the editor and save the file. + +```v +# Program File: Tutorial1.asm +# Written by: MoSaad +# Date Created: 10/05/2023 +# Description: Tutorial program to introduce MARS simulator including: breakpoints, single- +stepping, and register and memory windows. +#----------------------------------------------------------- +#----------------------- +# Declare some constants +#----------------------- +.data +string1: .asciiz "Welcome to Hardware Lab at NIT Calicut\n" +string2: .asciiz "Hello World \n" +string3: .asciiz "\nLoop #" +#------------------ +# Main program body +#------------------ +.text +main: +li $v0,4 +la $a0,string1 +syscall +la $a0,string2 +syscall +li $t0, 1 +loop: +li $v0, 4 +la $a0,string3 +syscall +li $v0,1 +move $a0,$t0 +syscall +addi $t0,$t0,1 +bne $t0,4,loop +#----- +# Halt +#----- +li $v0, 10 +syscall +``` + + + +1.4) From the menu, choose “Run...Assemble”. The “Mars Messages” window at the +bottom of the screen will indicate if any errors occurred. No errors should occur. + + + +**2. Simulate the tutorial program** + +2.1) From the menu, choose “Run...Go” to execute the program. The program will +execute displaying two lines of text and three iterations of a loop to the Run /IO +window. + +2.2) The buttons at the top of the window can be used as shortcuts for the run menu. +Use the “Reset” button to reset the program, and then try tracing through the +program by clicking the step button. + +2.3) You can adjust the speed the program runs by moving the slider to the right of the +buttons. If you have an infinite loop in your program, it may be necessary to adjust +(slow down) the speed of the simulator to prevent the MARS program from +crashing. + + +Run the program. If a breakpoint has been set the program will stop at the next breakpoint. + + +Trace (Step) Into. Executes a single instruction. If +the instruction is a procedure call (jal) the simulator will stop at the first instruction of the procedure. + + +Backstep. Undo the last step taken in the code. + + +Pause the currently running program. Press the run button to continue execution. + + +Stop the currently running program. You will need to reset the simulator to execute the program again after stopping it. + + +Reset. Resets the simulator, reinitializing the registers, program counter, and memory. + + +Adjusts the speed that the simulator runs at. + +**3. Using the Debugging Tools** + +3.1) When a program does not work as expected you will need to use the debugging +tools provided with the simulator. + +3.2) One of the primary tools used to debug a program is setting a breakpoint. You can +break before execution of an instruction by clicking on the checkbox associated +with each instruction on the far left of the execute window. Set a breakpoint at +the instruction: addi $t0,$t0,1 + +3.3) Run the program until the breakpoint by clicking “Run”. At this point in the +program only the first loop iteration has been printed. (You will need to click +back to the Run/IO window to see the output.) + +3.4) Now use the “Trace Into” button to step through the loop that prints out the next line +of text one character at a time. Step through the instructions until “Loop #2” is +printed to the output window. Stop and find the value of the registers “t0” and +“pc” at that point? Has the line of code that the program counter points to executed +yet? + +3.5) The simulator also allows you to view the memory contents. The memory window +appears in the middle of the screen and is titled “Data Segment”. Remove the +earlier breakpoint and add a breakpoint to line 33, “syscall”. Click the run button +so that the program executes up until the new breakpoint. We are now in the code +right before “Loop #” is about to be printed for the third iteration. Notice that the $a0 register is now a pointer to the address where the “Loop #” text is stored. What +is the memory location the register is pointing to? + +3.6) Now look in the data segment area, and find the address $a0 points to. This is the +memory section where the characters of the text “Loop #” is stored. Using an +ASCII table find the address where the ‘p’ in “Loop” is located? + +3.7) Exercise: Can you find where the word “Welcome” is stored in the memory? + + + +## **Integer Handling** + +Unlike NASM where numbers are stored as characters, MIPS can store single or multiple digit +integers directly. This chapter describes how to read and print integers. Basic operations in integer +handling (add, sub, mul, div) will also be covered. + +**1. Declaring an integer** + +Integers can be declared as constants in the ‘.data’ section as shown below: + +*Code to declare constants ‘x’ and ‘y’ with values 30 and 40 respectively:* + +```v +.data +x: .word 30 +y: .word 40 +``` + +**2. Loading an integer value into a register** + +Another way of using integers in MIPS is to read their values into temporary registers +using ‘I’ type instructions. +The two commonly used methods of reading integer values are: + +1. Loading a value into a temporary register. +2. Adding the value of the zero register and any value into a temporary register. + +*Code to enter integer values 5 and 10 using add and load instructions respectively into temporary +registers:* +```v +.text +addi $t0, $0, 5 +li $t1, 10 +``` +**3. Reading integers as input from the user** + +Integers can be read from the user using _syscall_ (system call) instructions. +The system call code for reading an integer is ‘5’. This syscall code value must be +loaded into the register $v0 in order to perform its designated function. The input is +then stored in $v0. + +_Code to read an integer input from the user:_ +```v +.text +li $v0, 5 +syscall +``` +**4. Printing integers** + +Integers stored in registers can also be printed using syscall instructions. The system call +code for printing an integer is ‘1’. This syscall code value must be loaded into the +register $v0 in order to perform its designated function. The integer to be printed must +be stored in the $a0 register. + +_Code to print the integer ‘5’ after storing it in a register:_ +```v +.text +li $a0, 5 +li $v0, 1 +syscall +``` +We have now learnt how to store single and multi digit integers and how to print their +values. We shall now combine all of these into a single program for a more robust +understanding of the covered concepts. + +_Code to declare a constant x with value 10, load values 20 and 30 into two registers and read +an integer value from the user and print all these values:_ + +```v +.data +x: .word 10 +.text +addi $t0, $0, 20 #load value 20 +li $t1, 30 #load value 30 +li $v0, 5 #read integer input +syscall +move $t2, $v0 #move integer input +lw $a0, x #print x +li $v0, 1 +syscall +move $a0, $t0 +li $v0, 1 #print value of $t0 +syscall +move $a0, $t1 #print value of $t1 +li $v0, 1 +syscall +move $a0, $t2 #print integer input +li $v0, 1 +syscall +li $v0, 10 #exit program +syscall +``` + +_Output:_ +_Assume the value ‘5’ is entered by the user as input._ +```v +5 +1020305 +-- program is finished running -- +``` + +**5. Adding integers** + +Integers can be added in two ways, either by adding fixed or immediate values to an +integer value stored in a register, or by adding two integers that are both stored in registers. +Both methods to add integers are demonstrated below: + +_Code to add integer values stored in registers:_ +```v +.text +addi $t0, $t1, 5 #t0=t1+5 +add $t2, $t2, $t1 #t2=t2+t1 +addi $t1, $zero, 5 #t1=0+5 +add $t2, $zero, $t1 #t2=0+t1 +``` + +**6. Subtracting integers** + +Unlike addition, values can only be subtracted if they are stored in a register. + +_Code to subtract integer values stored in registers:_ +``` +.text +sub $t2, $t2, $t1 #t2=t2-t1 +sub $t2, $zero, $t1 #t2=0-t1 +``` +**7. Multiplying integers** + +MIPS allows you to multiply the values present in two registers and stores the 32 most +significant bits in the HI special register and the 32 least significant bits in the LO special +register. + +The value obtained in the HI and LO registers can be accessed using the mfhi and mflo +instructions respectively. + +_Code to multiply two integers values and access the result after multiplication:_ +``` +.text +mult $t0, $t1 #signed mult +mflo $s0 #s0=t0*t1 +multu $t2, $t3 #unsigned mult +mflo $s1 #s1=t2*t3 +``` + +**8. Dividing integers** + +Division in MIPS is similar to multiplication except for a key difference, the HI special +register stores the remainder while the LO special register will hold the quotient of the +division. + +_Code to divide to integers and access the remainder and quotient after division:_ + +``` +.text +div $t1, $t2 #signed div +mfhi $s0 #s0=t1%t2 +mflo $s1 #s1=t1/t2 +divu $t3, $t4 #unsigned div +mfhi $s2 #s2=t3%t4 +mflo $s3 #s3=t3/t4 +``` + +### **Points To Note** + +**1.** Entering number of size larger than 32 bits + The largest integer that can be entered in 32 bit space is 2,147,483,647. Entering a + number larger than that results in the following error: + + ``` Runtime exception at 0x0040002c: invalid integer input (syscall 5)``` + +**2.** Changing the value of $zero register + It is not possible to change the value of the $zero register, any instructions that attempt + to alter the value have no effect. + +**3.** Multiplying numbers of size 32 bits + In MIPS, all integer values must be 32 bits. So if there is a valid answer, it must be + contained in the lower 32 bits of the answer. Thus to implement multiplication in MIPS, + the two numbers must be multiplied using the mult operator, and the valid result moved + from the lo register. + +**4.** Division by zero + If the divisor is zero, then the MIPS divide instructions do not compute any result in the + HI and LO registers. Division by zero is ignored and no exception is produced. + +**5.** Meaning of the _.word_ directive +The _.word_ directive allocates 4 bytes of space in the data region. The .word directive can +then be given an integer value, and it will initialize the allocated space to that integer +value. Be careful as it is incorrect to think of a the .word directive as a declaration for an +integer, as this directive simply allocates and initializes 4 bytes of memory, it is not a +data type. What is stored in this memory can be any type of data. + +## **String Operations** + +Strings in MIPS can be declared as constant in the _.data_ part of the program. They are often stored +this way so that they can be used as user prompts or to format output of a program. Strings can also +be entered by the user during the runtime of the program. Both methods of using strings in MIPS +will be demonstrated below. + +**1. Entering string constants** + +Pre-determined strings enclosed by double quotes can be declared in the _.data_ section. + +_Code to store the string “enter an element:” in memory under the name “message”:_ + +``` +.data +message: .asciiz “enter an element:” +``` +**2. Enter strings as input from the user** + +To enter strings as input, the syscall code to be used is 8. Apart from that, the address of the +memory space into which the string must be entered, is loaded into the $a0 register. The +maximum size of the string must also be loaded into the $a1 register before performing the +syscall. + +_Code to read a string as input from the user:_ + +``` +.data +input: .space 100 +inputsize: .word 100 +.text +li $v0, 8 +la $a0, input +lw $a1, inputsize +syscall +``` +**3. Printing strings stored in memory** + +To print the required string, the syscall to be used is 4. The address of the string has to be +loaded into the $a0 register. + +_Code to print a string named ‘message’ stored in memory:_ +``` +.text +li $v0, 4 +la $a0, output +syscall +``` +We have now learnt how to declare strings constants as well as how to store strings entered +by the user. We shall now write a program combining both the concepts for a more robust +understanding of basic string operations. + +_Code to read a string, with prompts instructing the user:_ + +``` +.text +main: + # Prompt for the string to enter + li $v0, 4 + la $a0, prompt + syscall + + # Read the string. + li $v0, 8 + la $a0, input + lw $a1, inputSize + syscall + + # Output the text + li $v0, 4 + la $a0, output + syscall + + # Output the number + li $v0, 4 + la $a0, input + syscall + + # Exit the program + li $v0, 10 + syscall + +.data +input: .space 81 +inputSize: .word 80 +prompt: .asciiz "Please enter a string: " +output: .asciiz "\nYou typed the string: " +``` + +### **Points To Note** + +- The _.space_ directive allocates n bytes of memory in the data region of the program, where + n=81 in this program. Since the size of a character is 1 byte, this is equivalent to saving 80 + characters for data. 81 was used here because in MIPS a sequence of ASCII characters is + terminated by a null value (byte containing 0). This is known as a null terminator. + +- If the string the user enters is larger than the maximum size of the string, it is truncated to + the maximum size. This is to prevent the program from accessing memory not allocated to + the string. + +## **Floating Point Numbers** + +Floating point numbers are stored according to the IEEE 754 Standard. There are 2 types +of floating point numbers, single precision and double precision. + +### **Floating point number representation** + +According to IEE 754 Standard, floating point numbers follow the given representation. + +```Sign Exponent Fraction``` + +- The sign bit is 0 or 1, for positive or negative respectively. + +- The exponent stores the exponent of the number in scientific notation of its binary +representation, plus a bias. + +- The fraction stores the fractional part of the binary representation of the number. + + +| Data | Single Precision | Double Precision | +|----|----|----| +|Size | 32 bits | 64 bits | +|Exponent size | 8 bits | 11 bits | +|Fraction size | 23 bits| 52 bits | +|Bias |127| 1023| + +Note + +- Since there are some numbers with non-ending decimal part in there binary representation + ( For Example- ( 1 /3) 10 = (0.01 0011 0011 0011 ....) 2 ) and we have only limited bits to store + the fraction part, there will be some slight inaccuracy while storing certain floating point + numbers. Therefore, it is recommended to always use double, as it has a higher precision due + to its increased no. of bits. + +### **MIPS floating point architecture** + +In MIPS, all floating point calculations are computed in a separate processor, called co- +processor 1. + +The coprocessor contains 32 floating point registers, each of width 32 bits. The registers +are numbered from $f 0 to $f3 1. + +Each register is can store a single precision floating point number, while double precision is +stored in 2 registers in an even-odd pair. For instructions concerning double precision numbers, the +even numbered register is used in the instruction. Using an odd numbered register will throw an +error. + +In addition to the registers, there are 8 condition flags, which are used in floating point +compare and branch instructions. + + +#### **Floating point registers in MIPS** + +|Registers | Usage | +|---|---| +|$f0 - $f3 | Used for results of floating point procedures | +| $f4 - $f11 | Temporary floating point registers, whose values are NOT preserved across procedure calls| +|$f12 - $f15 | Floating point parameters, whose values are NOT preserved across procedure calls | +| $f16 - $f19 | More temporary floating point registers, whose values are NOT preserved across procedure calls | +|$f20 - $f31 | Saved floating point registers, whose values are preserved across procedure calls | + +Among the 32 registers, only $f 4 - $f 11 , $f 16 - $f 19 and $f 20 - $f 31 can +be used by the programmer for storing values, as the others are reserved for special purposes. + +Note + +- Unlike the general purpose register $ 0 , $f 0 is not hardwired to be zero, and is used for storing results of procedures. + +### **Declaring a Floating point number** + +``` +.data + num1: .float 3. + num2: .double 4.5 3 + + .align 2 # Since float has 2^2 bytes + float_arr: .space 100 it has to be aligned to 2 + + .align 3 # Since double has 2^3 bytes it has to be aligned to 3 + double_arr: .space 100 +``` + +### **Reading and Printing Floating point numbers** + +Reading and printing a floating point number is similar to that of an integer, using syscall, +only difference being in the $v0 value and parameter registers. + +#### **Single precision** + +The $v0 value for reading a single precision floating point number is 6 while that of printing is 2. + +``` +main: + li $v0, 6 + syscall # The number is stored in $f0 + + li $v0, 2 + mov.s $f12, $f0 # The number to be printed is moved to $f12 + syscall +``` + +#### **Double precision** + +The $v0 value for reading a double precision floating point number is 7 while that of +printing is 3. + +``` +main: + li $v0, 7 + syscall # The number is stored in $f0/$f1 + + li $v0, 3 + mov.d $f12, $f0 # The number to be printed is + syscall moved to $f12/$f13 +``` + +### **Data Movement Instructions** + +|Instruction | Syntax | Remarks | +|---|---|---| +|Load single/double| l.s fdest, address l.d fdest, address | The single/double floating-point stored in address is loaded onto register fdest | +|Store single/double | s.s fsrc, address s.d fsrc, address | The single/double floating-point stored in register fsrc is stored to address | +| Move single/double | mov.s fdest, fsrc mov.d fdest, fsrc | The single/double floating-point stored in register fsrc is moved to register fdest | +|Move from coprocessor 1 |mfc1 dest, fsrc | The 32 - bit data from floating register fsrc is copied to general purpose register dest | +| Move to coprocessor 1 | mtc1 src, fdest | The 32 - bit data from general purpose register src is copied to floating point register fdest | + +Note + +- There is no load immediate for floating point. So if a constant is needed, it has to be stored in + the data segment and loaded to the required register. +- For the move to/from coprocessor 1 instructions, the first operand is a general purpose + register and the second one is the floating point register. + +### **Arithmetic Instructions** + +|Instruction | Syntax | Remarks| +|:----|------|-----| +|Addition | add.s fdest, fsrc1, fsrc2
add.d fdest, fsrc1, fsrc |The single/double floating-point numbers stored in fsrc1 and fsrc2
are added and stored in register fdest | +|Subtraction | sub.s fdest, fsrc1, fsrc2
sub.d fdest, fsrc1, fsrc2 |The single/double floating-point number stored in fsrc
subtracted from fsrc1 and stored in register fdest | +| Multiplication | mul.s fdest, fsrc1, fsrc2
mul.d fdest, fsrc1, fsrc2 |The single/double floating-point numbers stored in fsrc1 and fsrc2
are multiplied and stored in register fdest | +|Division | div.s fdest, fsrc1, fsrc2
div.d fdest, fsrc1, fsrc |The single/double floating-point number stored in fsrc1 is divided by fsrc2
and the quotient is stored in register fdest | +|Negation | neg.s fdest, fsrc
neg.d fdest, fsrc | The single/double floating-point number stored in fsrc
is negated (Sign changed) and stored in register fdest | +| Absolute value | abs.s fdest, fsrc
abs.d fdest, fsrc | Absolute value (Magnitude) of the single/double floating-point number stored in fsrc
is stored in register fdest | +| Square root | sqrt.s fdest, fsrc
sqrt.d fdest, fsrc | Square root of the single/double floating-point number stored in fsrc
is stored in register fdest + +### **Sample Question 1** + +Given a temperature in Fahrenheit, convert it into Celsius (Input and output has to be floating point values). + +Temperature in degrees Celsius = (Temperature in degrees Fahrenheit - 32 ) * 5 / 9. +``` +data + # Constants used for calculation + const1: .double 32.0 + const2: .double 5.0 + const3: .double 9.0 + + # User prompts + msg1: .asciiz "Enter the temperature in Fahrenheit: " + msg2: .asciiz "The temperature in Celsius is: " + + +.text +.globl main +main: + + li $v0, 4 # Printing msg1 + la $a0, msg1 + syscall + + li $v0, 7 # Reading user input + syscall + + mov.d $f12, $f0 # $f12 = User Input + l.d $f14, const1 # $f12 = $f12 - 32 + sub.d $f12, $f12, $f14 + + l.d $f14, const2 # $f12 = $f12 * 5 + mul.d $f12, $f12, $f14 + + l.d $f14, const3 # $f12 = $f12 / 9 + div.d $f12, $f12, $f14 + + li $v0, 4 # Printing msg2 + la $a0, msg2 + syscall + + li $v0, 3 # Printing final answer + syscall + + li $v0, 10 # Exit + syscall +``` + +## **Comparison/Branch Instructions** + +|Instruction | Syntax | Remarks| +|---|---|---| +| Compare equal | c.eq.s cc, fsrc1, fsrc2
c.eq.s fsrc1, fsrc2
c.eq.d cc, fsrc1, fsrc2
c.eq.d fsrc1, fsrc2 |Sets the condition flag cc as 1 if the numbers in fsrc1
and fsrc2 are equal, 0 otherwise.| +|Compare less than | c.lt.s cc, fsrc1, fsrc2
c.lt.s fsrc1, fsrc2
c.lt.d cc, fsrc1, fsrc2
c.lt.d fsrc1, fsrc2 | Sets the condition flag cc as 1 if the number in fsrc1
is less than that in fsrc2, 0 otherwise. | +| Compare less than or equal to | c.le.s cc, fsrc1, fsrc2
c.le.s fsrc1, fsrc2
c.le.d cc, fsrc1, fsrc2
c.le.d fsrc1, fsrc|Sets the condition flag cc as 1 if the number in fsrc1
is less thanor equal to that in fsrc2, 0 otherwise. | +|Branch if true | bc1t cc, label
bc1t label | Jumps to label if the condition flag cc is set as 1 | +|Branch if false | bc1f cc, label
bc1f label | Jumps to label if the condition flag cc is set as 0 | + +Note + +- The condition flag can be omitted in the above instructions, in which case condition flag 0 is + taken as default. +- As there is no comparison instruction for “Not equal to”, it has to be implemented by + reversing the required branch condition + Ex. We need to branch to label if $f4 and $f6 are not equal. This can be written as + ``` + c.eq.d $f4, $f6 + bc1.f label + ``` +- For greater than and greater than and equal to, it is simpler to reverse the input registers. + Ex. We need to branch to label if $f4 if greater than $f6. This can be written as + ``` + c.le.d $f6 , $f4 + bc1.t label + ``` + +### **Sample Question 2** +Given an array of floating numbers of size n, print the maximum and minimum element + + +``` +data + # Array + .align 3 + arr: .space 1000 + + # Characters + newline: .asciiz "\n" + + # User Prompts + msg1: .asciiz "Enter n: " + msg2: .asciiz "Enter no. " + msg3: .asciiz ": " + msg4: .asciiz "The maximum no. is: " + msg5: .asciiz "The minimum no. is: " + +.text +.globl main +main: + + li $v0, 4 # Print msg1 + la $a0, msg1 + syscall + + li $v0, 5 # Read n + syscall + move $t0, $v0 + + li $t1, 0 # $t1 will be the loop variable + # going from 0,1,2.. + li $t2, 0 # $t2 will be the element indices + # going from 0,8,16.. + loop1: # Loop to read n elements + beq $t0, $t1, end_loop1 # Termination condition + + li $v0, 4 # Print msg2 + la $a0, msg2 + syscall + + li $v0, 1 # Print position of + move $a0, $t1 # number to be inputted + addi $a0, $a0, 1 + syscall + + li $v0, 4 # Print msg3 + la $a0, msg3 + syscall + + li $v0, 7 # Read input and + syscall # store in arr + s.d $f0, arr($t2) + + addi $t1, $t1, 1 # Increamenting #t1 + addi $t2, $t2, 8 # and $t2 + j loop1 + + end_loop1: + + li $t1, 0 # Resetting $t1 and $t2 + li $t2, 0 + l.d $f4, arr($zero) # $f4 stores the max value + l.d $f6, arr($zero) # $f6 stores the min value + + loop2: # Loop to compute max and min + beq $t0, $t1, end_loop2 # Termination Condition + + l.d $f8, arr($t2) # Load a number from arr + + c.lt.d $f4, $f8 # Compare if the number is + # greater than current max + bc1f not_max + mov.d $f4, $f8 # If yes then update new max + not_max: + + c.lt.d $f8, $f6 # Compare if the number is + # less than current min + bc1f not_min + mov.d $f6, $f8 # If yes then update new min + not_min: + + addi $t1, $t1, 1 # Incrementing $t1 and $t2 + addi $t2, $t2, 8 + j loop2 + + end_loop2: + + li $v0, 4 # Print msg4 + la $a0, msg4 + syscall + + li $v0, 3 # Print max number + mov.d $f12, $f4 + syscall + + i $v0, 4 # Print newline + la $a0, newline + syscall + + li $v0, 4 # Print msg5 + la $a0, msg5 + syscall + + li $v0, 3 # Print min number + mov.d $f12, $f6 + syscall + + li $v0, 10 # Exit + syscall +``` + +### **Data Conversion Instructions** + +#### **Conversion within floating point** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert single to double | cvt.d.s fdest, fsrc |The single floating-point stored in fsrc is converted to double and stored in fdest | +|Convert double to single | cvt.s.d fdest, fsrc| The double floating-point stored in fsrc is converted to single and stored in fdest | + +### **Conversion to integers** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert single to integer | cvt.w.s fdest, fsrc |The single floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point)
and stored in 2 ’s compliment form in fdest | +|Convert double to integer | cvt.w.d fdest, fsrc | The double floating-point stored in fsrc is converted to 32 bit integer (Ignoring the part after decimal point) and
stored in 2 ’s compliment form in fdest | + + Note + +- The output of the above two instructions is in 2 ’s compliment form, which should not be + used with any other instructions other than mfc1. Other instructions always assume the data + in registers are according to IEEE standards, which can cause errors. + +#### **Conversion from integers** + +| Instruction | Syntax | Remarks| +|---|---|---| +|Convert integer to single | cvt.s.w fdest, fsrc |The data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to single precision floating point and is stored in fdest | +| Convert integer to double | cvt.d.w fdest, fsrc | The data stored in fsrc is considered as an integer in 2 ’s compliment form and
is converted to double precision floating point and is stored in fdest | + +### **Special Instructions** + +| Instruction | Syntax | Remarks | +|---|---|---| +| Ceiling | ceil.w.s fdest, fsrc
ceil.w.d fdest, fsrc | The smallest integer not greater than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form | +|Floor | floor.w.s fdest, fsrc
floor.w.d fdest, fsrc | The greatest integer not smaller than the floating point number in fsrc
is stored in fdest in 2 ’s compliment form | +|Round to nearest integer |round.w.s fdest, fsrc
round.w.d fdest, fsrc | The floating-point stored in fsrc is rounded off to
nearest integer and stored in fdest in 2 ’s compliment form | + +### **Sample Question 3** + +Given a floating point number and an integer n, round off the floating point number to n +digits. + + Hint- + +Multiplty then given number with 10^n, and round off using round.w.d instruction. +Divide the result by 10^n to obtain the final result. + +``` +data + # Constants used for calculation + const1: .double 0.0 + const2: .double 1.0 + const3: .double 10.0 + + # User prompts + msg1: .asciiz "Enter the number : " + msg2: .asciiz "Enter number of digits to round off to: " + msg3: .asciiz "The rounded off number is: " + +.text +.globl main +main: + + li $v0, 4 # Print msg1 + la $a0, msg1 + syscall + + li $v0, 7 # Read number to round off + syscall + + mov.d $f12, $f0 # $f12 = user input + + li $v0, 4 # Print msg2 + la $a0, msg2 + syscall + + li $v0, 7 # Read n + syscall + + mov.d $f16, $f0 # $f16 = n + l.d $f4, const1 # $f4 used as a loop varibale + # initialised to 0 + l.d $f6, const2 # $f6 used to store 10^n + l.d $f8, const3 # $f8 used to store 10 for + # calculating power + l.d $f10, const2 # $f10 used to store 1 for + # incrementing loop variable + loop1: # Loop to compute 10^n + c.eq.d $f4, $f16 # Ternminaltion Condition + bc1t end_loop1 + + mul.d $f6, $f6, $f8 # $f6 = $f6 * 10 + add.d $f4, $f4, $f10 # $f4 = $f4 + 1 + + j loop1 + end_loop1: + + mul.d $f12, $f12, $f6 # $f12 = $f12 * (10^n) + round.w.d $f12, $f12 # $f12 is rounded to nearest + # integer + cvt.d.w $f12, $f12 # Output after rounding, + # which is a word, is + # converted back to double + div.d $f12, $f12, $f6 # $f12 = $f12 / (10^n) + + li $v0, 4 # Print msg3 + la $a0, msg3 + syscall + + li $v0, 3 # Print final answer + syscall + + li $v0, 10 # Exit + syscall +``` + +## Integer Arrays + +An Integer Array is continuous storage block in memory in which each element is an integer. Each +element of an array is accessed using the base address of the array and the index of the element we +must access. + +### **Declaration and Initialization** + +Integer arrays can be initialized using .word or an empty array can be declared using +the .space keyword inside the .data section of the program + +``` +data: +arr: .word 3,4,-5,6 #initialized an array arr=[3,4,-5,6] +arr2: .space 40 # empty array with 40 bytes reserved for arr2 +``` + +### **Array Traversal** + +Array traversal refers to accessing each element of the array using its index. + +Each integer element of an array occupies a word (4 bytes). Therefore,4 bytes needed to be added to the current address to obtain the address of the following element. + +_Address of arr [k] = base address of arr + 4 * k_ + +Eg: To access arr[3] and store it to $t + +``` +a $s0,arr # base add address of array is stored in $s0 +addi $s0,$s0,12 # $s0 = address of arr[3] = arr + 4 * 3 +lw $t2,0($s0) # $t2=arr[3] +``` +or +``` +a $s0,arr # base add address of array is stored in $s0 +lw $t2,12($s0) # $t2=value of (arr + 12) +``` + +### **Array Input** + +The elements of an integer array can be received from the user using the syscall for +integer input and a for loop. + +_An empty array must be declared in the .data by allocating the necessary space as shown before._ + +_Each integer element of an array occupies 4 bytes. Therefore, 4 bytes needed to be added to the current address after each insertion._ + +The following code segment can be used to create an array of size n by receiving inputs from the user: + +Assume $s1 contains n, $s0 contains base address of an empty array and $t0 is the loop counter + +``` +for: + beq $t0,$s1,exit # loop termination condition + sll $t1,$t0,2 # $t1=i*4 + add $t1,$t1,$s0 # $t1 = arr + i * 4 + + li $v0,5 # input integer and store in $t2 + syscall + move $t2,$v0 + sw $t2,0($t1) # $t2 = arr[i] + addi $t0,$t0,1 # increment loop counter i + j for +``` + +### **Printing an Integer Array** + +Integer Array can be printed by traversing each element by using array traversal rules (as discussed above) and integer printing (code 1 is loaded to $v0). + +Consider the following code snippet to print the array created in the previous example in which every element is provided by the user: + +``` +la $s0,arr # store base address of array in $s0 +li $t0,0 +print: + beq $t0,$s1,end + sll $t1,$t0,2 # array traversal to access arr[i] + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + li $v0,1 # 1 is the syscall number to print integers + move $a0,$t2 # print $t2 + syscall + + li $a0, 32 # 32 is the ASCII code for space + li $v0, 11 # syscall number for printing character + syscall + addi $t0,$t0,1 # increment loop counter + j print +end: +li $v0,10 #end program +syscall +``` + +### **Negative Numbers as Elements** + +All integer operations in MIPS support both positive and negative numbers. No changes are required to the program for the input and output of positive integers. + +``` +enter array element: -5 +enter array element: -6 +enter array element: 8 +enter array element: -2 +The elements of the array are: -5.0 -6.0 8.0 -2.0 +-- program is finished running -- +``` + +### **Floating Point Numbers as Elements** + +An array of floating-point numbers can be created by replacing all the integer +operations with floating-point operations. The following changes need to be made to +convert an integer array into an array of floating-point numbers: + +1) Replace the integer code loaded to $v0 by floating-point code +2) Replace the load, store and move operation by l.s , s.s and mov.s where floating point data type is used + +``` +# program to input array +for: + beq $t0,$s1,exit + sll $t1,$t0,2 + add $t1,$t1,$s0 + li $v0,6 # code for floating point input + syscall + s.s $f0,0($t1) # arr[i]=$f0 + addi $t0,$t0,1 + j for +exit: + +# print array +print: + beq $t0,$s1,end + sll $t1,$t0,2 + add $t1,$t1,$s0 + l.s $f0,0($t1) # $f0=arr[i] + li $v0,2 # code for printing floating point + mov.s $f12,$f0 + syscall + li $a0, 32 + li $v0, 11 + syscall + addi $t0,$t0,1 + j print +end +``` + +### **One Dimensional Arrays** + +#### **To calculate the sum of n numbers in an n sized array** + +``` +li $t0,0 +la $s0,arr +li $t3,0 #t3 stores the sum +sum: #for loop + beq $t0,$s1,end # $s1 contains n + sll $t1,$t0,2 + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + add $t3,$t3,$t2 # $t3=$t3+$t2 + addi $t0,$t0,1 # increment loop counter + j sum +end: +li $v0,1 # print sum +move $a0,$t3 +syscall +``` + +#### **To find the largest element in an n sized array** + +``` +la $s0,arr +li $t0,0 +li $t3,-1000 # $t3=max + # initialized to -1000 +max: + beq $t0,$s1,end # $s1 contains n + sll $t1,$t0,2 + add $t1,$t1,$s0 + lw $t2,0($t1) # $t2=arr[i] + ble $t2,$t3,inc_i # if arr[i]<=max, jump to inc_count + move $t3,$t2 # if arr[i]>max, max=arr[i] + inc_count: + addi $t0,$t0,1 # increment loop counter + j max +end: +li $v0,1 # print max +move $a0,$t3 +syscall +``` + +## **String Operations (Advanced)** + +### **Null Character and Newline** + +When strings are created by using user input (code 8 passed to $vo), it forms a sequence of ASCII +characters that are terminated by a newline character, followed by a NULL character. The newline +character is triggered by the pressing of enter key during user input. + +_The ASCII code for newline is 10. Hence_ beq, $t1,10,label _can be used as a comparing instruction_ + +_MIPS treats NULL character as a zero. Hence_ beqz, $t1, label _can be used as a comparing instruction_ + +### **String Traversal** + +Strings are made up of characters, in which each character occupies a byte. Hence, unlike an Integer +Array, each character must be traversed byte by byte. + +Eg: + +To find the length of a string (newline character need not be included) + +``` +# assume string is input to str1 +li $s1,0 #loop counter (i) + +len: + lb $t1,str1($s1) # $t1=str[i] + beq $t1,10,start # termination condition + addi $s1,$s1,1 # i=i+1 + j len +start: + li $v0,1 # print len=i + move $a0,$s1 + syscall +``` + +_If the newline character needs to be included in the length, beq should be replaced with beqz_ + +### **String Concatenation** + +Concatenation of two strings can be done using 2 loops. The presence of newline and null character +at the end of each string should be considered. + +Consider two strings, str1 and str2. The following is the pseudocode and the code snippet for +concatenating str2 to str1: +_Pseudo Code:_ + +```c +i=0 + +j=0 + +while str1[i]!='\n' + +i++ + +while str2[j]!='\0' + +str1[i]=str2[j] + +i++ + +j++ +``` +_MIPS:_ + +```mips +i $s1,0 # i=0 +li $s2,0 # j=0 +loop1: + lb $t1,str1($s1) + beq $t1,10,loop2 + addi $s1,$s1,1 # i++ + j loop1 +loop2: + lb $t1,str2($s2) + beqz $t1,end + sb $t1,str1($s1) # str1[i]=str[j] + addi $s1,$s1,1 # i++ + addi $s2,$s2,1 # j++ + j loop2 +end: +``` + +### **Palindrome Checking** + +A palindrome sequence that reads the same backwards as forwards. Palindrome checking uses two +pointer method. + +Assume a string str, whole length is n. Length of the string is calculated by previous method and +stored in $s1. The following code snippet shows the while loop necessary for checking whether the +string is palindrome + +``` +addi $s1,$s1,-1 # j=n-1 +li $s0,0 # i=0 +for: + lb $t1,str($s0) + lb $t2,str($s1) + bge $s0,$s1,true # if i>=j,exit loop. return True + bne $t1,$t2,false # if str[i]!=str[j], return False + addi $s0,$s0,1 # i++ + addi $s1,$s1,-1 # j-- + j for +``` + +## **Two Dimensional Arrays** + +2-DArrays/Matrices/Tables aren’t stored in memory the way it is normally visualized; rather it is stored as a single array in either row major form or column major form. Let’s see how a matrix is represented in memory in both the forms with a starting address of 1230. (Remember:In an array each element is 4 bytes long). + +a) Row Major form : Here elements are stored row wise. First we store the first row, then the second and soon. + + + +b) Column Major form: Here elements are stored column wise. First we store the first column, then the second and soon. + +Row Major form ( starting address 1000 ) + + + +Column Major form ( starting address 1000 ) + + + +### **Sample code** + +_->Insertion of elements and printing the 2D-array_ + +_**We are using row major form to input the elements as a string_ + +_**NOTE: all characters need to be space separated, the end of the sequence also need to have a space_ + +### **Pseudo code->** + +``` +Prompt user for number of rows and columns +Initialize 2D array +Prompt user to enter matrix values as a string +Loop through input string: +- Extract numbers delimited by spaces +- Convert each substring to integer and store in the 2D array +Print the matrix: +- Loop through rows: +- Loop through columns: +- Print each element of the matrix +- Print a space between elements +- Print a newline after each row +Exit the program +``` +### **MIPS Code->** + +``` +.data +newline: .asciiz "\n" +space: .asciiz " " +msg_rows: .asciiz "Enter number of rows : " +msg_columns: .asciiz "Enter number of columns : " +msg_input: .asciiz "Enter matrix ( row major form ) : " +mat1: .space 100 +input: .space 100 + +.text +main: + li $v0, 4 + la $a0, msg_rows + syscall + + li $v0, 5 + syscall + move $t0, $v0 # $t0 = number of rows + + li $v0, 4 + la $a0, msg_columns + syscall + + li $v0, 5 + syscall + move $t1, $v0 # $t1 = number of columns + + li $v0, 4 + la $a0, msg_input + syscall + + li $v0, 8 # syscall for read_str + la $a0, input # Load address of input buer + li $a1, 100 # Maximum length + syscall + + la $t2, input + la $t3, mat1 + + li $t5, 0 + + # t2 - address of input string + # t3 - address of matrix + # t4 - used to iterate through string + # t5 - used to calculate number + +input_loop: + lb $t4, 0($t2) + beq $t4, 32, store + +# when a space is detected add the number calculated to the array and continue + + beq $t4, $zero , end_input + +#In ASCII encoding, the decimal value 32 corresponds to the space character (' ') + +#This loop exist to calculate numbers that have more than one digit , since our input is a string. + +# We need to iterate and add the characters until we detect a space + + sub $t6 , $t4, 48 # converts character to integer + +# for calculating the number + + mul $t5, $t5, 10 + add $t5, $t5, $t6 + addi $t2, $t2, 1 + + j input_loop +store: + sw $t5, 0($t3) #store the number obtained in the 2D-array + + addi $t3, $t3, 4 #increment the address to next memory block + li $t5, 0 + + add $t2 , $t2 , 1 #increment the index of string + j input_loop #loop back to the input to continue iteration of string + +end_input : + li $t6 , 0 # Initialize row index + la $t8, mat1 # Load address of array for printing + + li $v0, 4 + la $a0, newline + syscall + +print_loop: + beq $t6 , $t0 , end_programme + li $t7 , 0 # Initialize column index + +print_column_loop: + lw $t9 , 0($t8) # Load number from array + li $v0, 1 # syscall for print_int + move $a0, $t9 # Load number to print + syscall + + li $v0, 4 # syscall for print_str + la $a0, space # Load address of space + syscall + + addi $t7, $t7, 1 # Increment column index + addi $t8 , $t8 , 4 # Increment base address + blt $t7, $t1 , print_column_loop # Print all elements in the row + +# Print newline after each row + + li $v0 , 4 + la $a0 , newline + syscall + +# Reset column index for next row + li $t7 , 0 + +# Increment row index + addi $t6 , $t6 , 1 + + j print_loop + +end_programme : + li $v0, 10 # syscall for exit + syscall +``` +### **Output** +``` + Enter number of rows:3 + Enter number of columns:3 + Enter matrix(row major form) : 1 2 3 4 5 6 7 8 9 + + 1 2 3 + 4 5 6 + 7 8 9 +``` + +### **->To find maximum and minimum element in a 2-D array** + +**We are using row major form to input the elements as a string + +**same process of taking the input as the above + +__**NOTE: all characters need to be space separated, the end of the sequence also need to have a space__ + +#### **Pseudo code->** + +``` +Prompt user for number of rows and columns +Initialize 2D array +Prompt user to enter matrix values as a string +Loop through input string: +- Extract numbers delimited by spaces +- Convert each substring to integer and store in the 2D +array +Find minimum and maximum elements in the matrix: +- Initialize minimum element to maximum possible value +and maximum element to 0 +- Loop through each element of the matrix: +- Update minimum and maximum elements if necessary +Print the maximum element message: +- Print "The maximum element is: " +- Print the maximum element +Print the minimum element message: +- Print "The minimum element is: " +- Print the minimum element +Exit the program +``` + +### **MIPS Code->** + +``` +.data +newline: .asciiz "\n" +space: .asciiz " " +msg_rows: .asciiz "Enter number of rows : " +msg_columns: .asciiz "Enter number of columns : " +msg_input: .asciiz "Enter matrix ( row major form ) : " +maximum : .asciiz"The maximum element is : " +minimum : .asciiz"The minimum element is : +mat1: .space 100 +input: .space 100 +.text +main: + li $v0, 4 + la $a0, msg_rows + syscall + + li $v0, 5 + syscall + move $t0, $v0 # $t0 = number of rows + + li $v0, 4 + la $a0, msg_columns + syscall + + li $v0, 5 + syscall + move $t1, $v0 # $t1 = number of columns + + li $v0, 4 + la $a0, msg_input + syscall + + li $v0, 8 # syscall for read_str + la $a0, input # Load address of input buer + li $a1, 100 # Maximum length + syscall + + la $t2, input + la $t3, mat1 + + li $t5, 0 + + # t2 - address of input string + # t3 - address of matrix + # t4 - used to iterate through string + # t5 - used to calculate number + +input_loop: + lb $t4, 0($t2) + beq $t4, 32, store + + # when a space is detected add the number calculated to the array and continue + + beq $t4, $zero , end_input + + #In ASCII encoding, the decimal value 32 corresponds to the space character (' ') + + #This loop exist to calculate numbers that have more than one digit , since our input is a string + # we need to iterate and add the characters until we detect a space + + sub $t6 , $t4, 48 # converts character to integer + + # for calculating the number + mul $t5, $t5, 10 + add $t5, $t5, $t6 + addi $t2, $t2, 1 + j input_loop + +store: + sw $t5, 0($t3) #store the number obtained in the 2D-array + addi $t3, $t3, 4 #increment the address to next memory block + li $t5, 0 + add $t2 , $t2 , 1 #increment the index of string + j input_loop #loop back to the input to continue iteration of string + +end_input : + li $t6 , 0 # Initialize row index + la $t8, mat1 # Load address of array for printing + li $v0, 4 + la $a0, newline + syscall + +find_min_max: + li $t3 , 0 # Initialize max element to 0 + li $t2 , 0xffffffff + li $t6 , 0 # Initialize row index to 0 + la $a0 , mat1 + +row_loop: + beq $t6, $t0 , end # If all rows have been checked, exit + + li $t7, 0 # Initialize column index to 0 + +column_loop: + beq $t7, $t1 , end_column_loop # If all columns have been checked, move to next row + + lw $t8, 0($a0) # Load current element from array + +# Compare current element with max element and the min element + bgt $t8, $t3, update_max # if element greater than max element , update max + + min : + blt $t8 , $t2 , update_min # if element smaller than min element, update min + + increment : + addi $a0, $a0, 4 # Move to next column + addi $t7, $t7, 1 # Increment column index + j column_loop + +update_max: + move $t3 , $t8 # Update max element + j min # control goes back to checking for the conditional statement of min element + +update_min: + move $t2 , $t8 # Update min element + j increment # control goes back to incrementing the looping values + +End_column_loop: + addi $t6, $t6, 1 # Increment row index + j row_loop + +end : + li $v0 , 4 + la $a0 , maximum + syscall + + li $v0 , 1 + move $a0 , $t3 # printing the maximum element + syscall + + li $v0 , 4 + la $a0 , newline + syscall + + li $v0 , 4 + la $a0 , minimum # printing the minimum element + syscall + + li $v0 , 1 + move $a0 , $t2 + syscall + + li $v0 , 10 + syscall +``` +### **Output** +``` + Enter number of rows :3 + Enter number of columns :3 + Enter matrix ( row major form ) : 1 2 34 5 6 7 300 9 22 + + The maximum element is : 300 + The minimum element is : 1 +``` + +### **More Questions** + + _->Searching in Matrix: Write a MIPS assembly program to search for a given element in a matrix and return its position if found._ + + _->Matrix Addition: Write a MIPS program to add two matrices of the same size_ + + _->Transpose of a Matrix: Write a MIPS assembly program to find the transpose of a given matrix._ + + +★ **MIPS code for if statements** + ● Iftheconditionisanequalityusebeq,bne + ● Iftheconditionisacomparisoncombinebeq/bnewithset-on-less-than + + +**Why not blt or bge?** + While blt and bge (pseudo-instructions) are available in MIPS, beq and bne are favoured inconditional statements for their efficiency making them the common choice. + +**Example 1)** Given,f:$s0, g:$s1, h:$s2, i:$s3, j:$s4 +``` + if(i==j) + f = g + h; + else + f = g - h; +``` + +**Solution 1 :-** Corresponding MIPS code +``` + bne $s3, $s4, else + add $s0, $s1, $s2 + j endif +else: sub $s0, $s1, $s2 +endif: ........... +``` +**Example 2)** Given,f:$s0 ,g:$s1 ,h:$s2 ,i:$s3 ,j:$s4 +``` + if(i + +➢ Stack allocation (refer Recursion in MIPS(non-leaf procedure) for detailed explanation) + + + +(a) before, (b) during, and (c) after a procedure call. + +There are two types of procedure calling- + +**1) Leaf Procedures:** These procedures do not call other procedures. + +When a leaf procedure is called: + +● There turn address is saved on the stack. +● A stack frame/procedure frame/activation record is setup to store local variables. +● Arguments may be passed in registers or on the stack. +● The procedure executes its code. + +Upon completion,it restores the stack pointer and returns to the saved return address. + +**2) Non-leaf Procedures(NestedProcedures):** These procedures call other procedures, eg.- **Recursive Functions/Procedures.** + +In addition to the steps for leaf procedures, non-leaf procedures must manage: + +● Saving and restoring additional registers beyond there turn address. +● Managing multiple levels of procedure calls and returns. +● Ensuring that data in registers is preserved a cross nested calls. +● Properly handling there turn value from called procedures. + +★ **Function (Procedure) calling in MIPS** + + +In MIPS assembly language, passing parameters to functions involves using +registers. Unlike high-level languages where parameters are often passed on the stack,MIPS typically uses specific registers for passing arguments. + +● $a0 to $a3 :These are argument registers and are used to pass the first four arguments to a function. If a function has more than four parameters,additional parameters are typically passed on the stack. + +● $v0 and $v1: These are value registers and are used to return values from functions. Functions can return up to two values using these registers. + + + +(Note:-i) Register 1, called $at, is reserved for the assembler. + ii) Registers 26–27, called $k0–$k1 are reserved for the operating system.) + +➢ **Steps in calling a procedure (function)** + +In MIPS assembly language, procedure calling follows a similar structure to function calls in high-level languages like C. + +The following steps typically occur in both leaf and non-leaf functions but there are some nuances in how they're implemented, especially regarding the handling of the stack: + +● **Arguments Passing** :.Arguments to the function can be passed via registers or the stack, depending on the calling convention. In register-based passing, arguments are loaded in to designated argument registers like $a0-$a3. If there are more arguments than available registers, excess arguments are typically passed on the stack. + +● **Jump and Link (jal)** :jal makes the control jump to the given address while storing there turn address at PC+4 in the $ra register This effectively sets up the return mechanism for the function call. + +● **Function Prologue (Non-leaf functions):** Non-leaf functions need to setup a stack frame. This involves: Saving the return address($ra) +on to the stack, saving any callee- saved registers on to the stack(these are typically $s0-$s7),setting up the frame pointer($fp) to establish a reference point for accessing local variables and saved registers. + +● **Function Execution** :The function performs its task, accessing arguments, local variables, and performing computations. + +**● Function Epilogue (Non-leaf functions):** Before returning, non-leaf functions need to cleanup the stack frame and restore the state of callee-saved registers.This involves restoring callee-saved registers from the stack, restoring the return address($ra) from the stack resetting the stack pointer($sp) to deallocate the stack frame, jumping back to the return address using the jr $ra instruction. + +● Return: Upon completing its task, the function returns control to the caller. If it's a leaf function, it typically involves jumping back to the return address stored in $ra using the jr $ra instruction. For non-leaf + functions, the return sequence includes restoring the stack frame and registers before jumping back to the caller. + +(Note:-For simplicity we will only use $sp and extend the stack at procedure entry/exit) + +**Example 1)** Calling a procedure which prints a string +```asm +//code +printFunction(); +a=a+2; +//code +``` + +**Solution 1 :-** Corresponding MIPS code +```asm +data +hello_string: .asciiz "Hello, world!\n" # String definition + +.text +main: +....previous code +jal printFunction #jump to printFunction +addi $s2, 2 +....further code +li $v0, 10 # Set syscall code 10 for exit +syscall # Perform syscall to exit the program + +printFunction: +li $v0, 4 # Set syscall code 4 to print a string +la $a0, hello_string # Load the address of the string +syscall # Perform syscall to print +jr $ra # Return control to PC + 4 +``` + +● When jal is used, the control moves to the address specified in the instruction and the address of the next instruction is stored in $ra. + +● When the procedure ends jr $ra is used to return control back to the +next address from where it jumped. + +● These procedures are usually placed after the “main” procedure to avoid instruction overlap. + +**Example 1)** Calling a function with parameters +```asm +//code +result=addNumbers(5,7); +//code +``` + + +**Solution 1 :-** Corresponding MIPS code +```asm +text +main: + li $a0, 5 # Load first parameter (5) into $a0 + li $a1, 7 # Load second parameter (7) into $a1 + jal addNumbers # Jump to addNumbers function + move $s0, $v0 # Store the result returned by addNumbers in $s0 + # Further code + li $v0, 10 # Set syscall code 10 for exit + syscall # Perform syscall to exit the program + +addNumbers: + add $v0, $a0, $a1 # Add the values of $a0 and $a1 and store the result in $v0 + jr $ra # Return control to the next instruction after jal +``` + +● In the main function, parameters are passed to the addNumbers function by loading values into registers $a0 and $a1. + +● The jal instruction is used to jump to the addNumbers function. + +● Inside the addNumbers function, the parameters are accessed from the $a0 and $a1 registers. + +● The result of the addition is stored in register $v0, which is commonly used to return function results in MIPS. + +● Finally, jr $ra is used to return control back to the instruction after the jal in the main function. + +★ **Recursion in MIPS (non-leaf procedure)** + +In MIPS assembly language, implementing recursion involves understanding function calls and stack manipulation. + +**The Stack in MIPS Assembly** + +● The stack is a crucial data structure used in MIPS assembly language for managing function calls, local variables, and return addresses. +● It operates based on the Last-In-First-Out (LIFO) principle, meaning the +last item pushed onto the stack is the first item to be popped off. + +**Stack Operations:** + +**Stack Pointer ($sp):** +● The stack pointer register, $sp, points to the top of the stack. It keeps track of the current position in memory where new items are pushed onto or popped off the stack. + +**Push Operation:** +● To push data onto the stack, the stack pointer is decremented to reserve space for the new item, and then the data is stored at the memory location pointed to by the stack pointer. + +**Pop Operation:** +● To pop data off the stack,the data is retrieved from the memory location +pointed to by the stack pointer, and then the stack pointer is incremented to remove the item from the stack. + +**Stack Usage in Function Calls:** +**Function Prologue:** +● When a function is called, the current contents of relevant registers (such as there turn address and callee-saved registers) are typically saved on the stack to ensure they are preserved. +● This process is often referred to as the function prologue. + +**Function Epilogue:** +● Upon completion of the function, the saved values on the stack are restored to their original registers. +● This process is known as the function epilogue. + + +**Example)** Function Call and Stack Usage + +● When main calls my Function using jal, the return address (the address of the instruction following the function call) is automatically saved in register $ra. +● Inside my Function, the function prologue allocates space on the stack +to save the return address. +● The function body executes the desired operations. +● Finally, in the function epilogue, the return address is restored, and the stack space allocated in the prologue is deallocated before returning control to the caller. + +To understand recursion in MIPS, a good understanding of the stack pointer and how it operates on memory is imperative. Recursion involves careful management of the function call stack, ensuring that return addresses and local variables are properly saved and restored. This example illustrates the process of calculating the factorial of a number using recursion in MIPS assembly language. + +**Example) Calculating the factorial of a number using recursion** + +```asm +//code +result = factorial(5); +//code +``` + +**Solution 1 :-** Corresponding MIPS code +```asm +text +main: + li $a0, 5 # Load the value 5 (number whose factorial is to be calculated) into $a0 + jal factorial # Jump to the factorial function + move $s0, $v0 # Store the result returned by factorial in $s0 + + # Further code using the result stored in $s0 + # ... + + li $v0, 10 # Set syscall code 10 for exit + syscall # Perform syscall to exit the program + +factorial: + # Function prologue + addi $sp, $sp, -4 # Allocate space on the stack for local variables + sw $ra, 0($sp) # Save the return address on the stack + + # Check for base case: if n <= 1, return 1 + li $t0, 1 # Load the value 1 into $t0 + ble $a0, $t0, base_case # Branch to base_case if $a0 (n) <= $t0 (1) + + # Recursive case: n * factorial(n - 1) + addi $a0, $a0, -1 # Decrement $a0 (n) by 1 + jal factorial # Recursive call to factorial function + lw $ra, 0($sp) # Restore the return address from the stack + addi $sp, $sp, 4 # Deallocate space on the stack for local variables + mul $v0, $a0, $v0 # Multiply n by the result of factorial(n - 1) + jr $ra # Return control to the caller + +base_case: + # Base case: n <= 1, return 1 + li $v0, 1 # Load the value 1 into $v0 + lw $ra, 0($sp) # Restore the return address from the stack + addi $sp, $sp, 4 # Deallocate space on the stack for local variables + jr $ra # Return control to the caller +``` + +● In the main function, the value 5 is loaded into register $a0 to calculate its factorial. +● The factorial function is then called using the jal instruction. +● Inside the factorial function, the base case checks if the input value n is less than or equal to 1.If so,it returns 1. +● Otherwise,the function decrements n by 1 and recursively calls itself +with the decremented value. +● The result of the recursive call is then multiplied by n to compute the factorial. +● Finally,the result is returned to the caller using register $v0. + + + + +### **References** +J.L.Hennessy and D.A.Patterson Computer Organization and Design:The Hardware/Software Interface, Fifth Edition +“Digital Logic and Computer Design” by M.Morris Mano +“Digital Fundamentals” by Thomas L.Flyod +[http://www.cs.missouristate.edu/MARS/](http://www.cs.missouristate.edu/MARS/) +[https://www.d.umn.edu/~gshute/mips/directives-registers.pdf](https://www.d.umn.edu/~gshute/mips/directives-registers.pdf) +[https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html](https://courses.missouristate.edu/KenVollmar/mars/Help/SyscallHelp.html) +[https://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.html](https://courses.missouristate.edu/KenVollmar/mars/Help/MarsHelpIntro.html) +[https://riptutorial.com/mips/example/29993/mars-mips-simulator](https://riptutorial.com/mips/example/29993/mars-mips-simulator) +[https://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf](https://bytes.usc.edu/files/ee109/documents/MARS_Tutorial.pdf) diff --git a/docs/public/NITC_Logo.png b/docs/public/NITC_Logo.png new file mode 100644 index 0000000000000000000000000000000000000000..4795af64edc12a304e6abd64057097195ba7782b GIT binary patch literal 105936 zcmdSAg;$i{7cY!bQi4dQfFm%Vz-HnpcFm%JvA>E;O`2ODa z{ttI8*2B!1v+J|>IeVXY!j%-HaWKg+k&uvZWWGqKAR(b-At9mGzd}K@u>qys}Fq>m{`NW_jAt;#}(A6^>EN=qR93yU4; zLVQDam64Z3-$O$~W9A;uJpv<|UN|@_sJ$4^^GHK*L6VUWRr6dt%5+;M?3?@9HGVO% zg7Y#WB$}0psd4_%*4DPBrmx@c`5{(QBl!8V=m)|d$Dv{LtDn9NuV$@euGHPEUI=He zJ-j^56nHDhCFrt4p+q35{QvUbAZ0`Wp%MWgwiqORpcK-IG+juhBtK}a)nw)|pcR+BM6^w2Y}ChTbaP^z zTT{y`L%uO2X?#|OWE6a#JGb9Qi7uh92+U)clqOb;$n)HgxK7Y`kM}>Gmy^$e^qb{% z0=_AgA=uaEJquZ`<4Kn(!^1l$N3bd1gUcur+#CTbJ{vxN{Qn#3lQrJ4KWh)t_|FD! z1WP=UR!iL_d7dDe1s_7xtvT0}>9w%da|l#wny 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zAxxb4uS8zo71Kuh8hPkqUtYlbZxq$(6|??X_y)s@4>%H$S*~_a{3#I_ zMjgNpwJwnIPnXJ}{(5Cvtl`IJ>f&9qQT=^^!Xz5-Aq=oy4CME=J>PTVjx3crXV=DA~%bs}?gX`$aLX+OKK%cs0-NQ!#sHy5#a}Va{uF zI=a{r4@8vA^p~z!u=;~a@?h{6K90}EbokB1R!~(>Cyc_}whOfy{SzXNR>m(c0GD7} zZOg*#G=(d0qDaWVnoa4g5XsO=eUXAHbSL->jcQS`OoOI;E=Xi(fLhKKCzTo{yssM!RvUx zKC_uO$-Qf*_hP&K7(fg95&YOBLvu2kM^-?Nu8=_wv-~WwQ3k`Mj(AB>I)rA9{Fx7| znA7sXlh!iQtvGZO9_NYux9phRTIWw;Q7hyA;ZOf1vHJhG@mwAgPp|SHmTv`ce77~!vDP4zfn;Aw|9l$tJ6e0`cLWGMY@+ + +`5`. Output port: read_data, write to it when the read/write signal is high and +read its value when the read/write signal is low. + +```v +module register(input clk, rst, rw, + input [3:0] write_data, + output [3:0] read_data); + + reg [3:0] block; + always@(posedge clk) begin + if(!rst) block <= 0; + else begin + if(rw==1) block <= write_data; + else read_data <= block; + end + end +endmodule +``` +Since we have written our read logic in the else block, even if the rw +signal is any value other than 0 or 1 at the beginning we just read the +register displaying its contents, which is ‘x’ initially. This is to avoid +unintentionally writing a value, giving read operation a higher priority +over write. You can initialize the block reg to 0 too (it can depend on the +question). + +If we have a register with multiple read and write ports, the question will +mention certain specifications for e.g. reads can occur parallelly but not +writes. To demonstrate how to go about coding for such a question, let +us see an example of a 4-bit register with 1 read ports and 2 write ports. +A read and write operation cannot occur simultaneously but we can have +2 such writes and every time we write to the register, we alternately use +either of the write ports. Initially, when we perform a write operation, we write into the register with write_data_1, the next time with +write_data_2, etc. + +```v +module reg_wr(input clk, + input rst, + input rw, + input[15:0] data1, data2, + output reg [15:0] read); + // perform writ1 & writ2 alternatively + reg [15:0] block; + reg track=0; + always@(posedge clk) begin + if(rst==0) begin // reset is active low + read <= 0; + end + else if(rw==0) begin // write + if(track==0) begin + block <= data1; + track <= 1; + end + else begin + block <= data2; + track <= 0; + end + end + else begin // read + read <= block; + end + end +endmodule +``` +To design a register using flip-flops, let’s consider the first example +wherein we had a 4-bit register with one read and write port. +We instantiate four D flip-flops and assign the incoming input as input to +the flip-flops if the rw signal is high, else we assign the contents of the +flip-flop to the output variable. Note that in case of the write operation, +the output variable reflects the previously read/stored value. + +```v +module dflfl(output reg op, input ip, input clk); + always @(posedge clk) begin + op <= ip; + end +endmodule + +module four_bit_reg(output reg [3:0] out, input [3:0] ip, input clk, input rw); + reg [3:0]intermed; + reg [3:0]temp; + + dflfl g1(temp[3], rw ? ip[3]:temp[3], clk); + dflfl g2(temp[2], rw ? ip[2]:temp[2], clk); + dflfl g3(temp[1], rw ? ip[1]:temp[1], clk); + dflfl g4(temp[0], rw ? ip[0]:temp[0], clk); + + always @(*) begin + if(rw==1'b1) intermed <= temp; // storing previous value in intermed + end + + always @(posedge clk) begin + if(rw==1'b1) out <= intermed; // if a write occurs then previously read value is displayed + else out <= temp; // else in case of a read + end +endmodule +``` + +When we instantiate the D flip-flops, we check whether the rw signal is +high i.e. whether a write is occurring to pass the input to it. Since we +cannot mix case and if else statements with our combinational block i.e. +we cannot instantiate the dffs conditionally (Verilog does not support +this), the dffs will therefore be instantiated at every rising edge transition +and so for a read operation, we pass it dummy data which would be the +previously written (currently stored) value. + +## **Register Files** +Register Files contain an array of registers. Hence there is a need for read +and write address inputs to ascertain which register to read from or write data into. +Ports are input and output signals. When a question mentions that the +register has to have multiple read ports or multiple write ports- this +means that there are several read_address, write_address and +write_data ports- we can perform more than 1 operation at the same +time on different registers within the register file. There are several cases +to consider in such questions- if a question permits multiple writes at the +same time, you need to think of the possibility of more than one +operation attempting to write to the same register, or if a read and write +can occur together, you need to think of the possibility of an operation +attempting to read from and another attempting to write to the same +register. So assigning priorities is important. More than one read +operation occurring simultaneously won’t create a problem. +Let’s look at the code for a register file with 8 registers capable of storing +8-bit data each. It has 2 read ports and 1 write port. Two reads are permitted simultaneously, however only read or write is allowed at a +time. +```v +module reg_file(input clk, rst, + input [1:0]r1r2w, + input[2:0] port1, + input[2:0] port2, + input [2:0] port3, + input [7:0] data, + output reg [7:0] read1, read2); + + reg [WIDTH-1:0] block[WIDTH-1:0]; + // 2 read ports, 1 write port + always@(posedge clk) begin + // r1r2w- 0: write case + // r1r2w- 1: read1 case + // r1r2w- 2: read2 case + // r1r2w- 3: read1 & read2 case + if(rst==0) begin + read1 <= 0; + read2 <= 0; + end + else if(r1r2w == 0) begin // write + block[port1] <= data; + end + else if(r1r2w == 1) begin + read1 <= block[port2]; + end + else if(r1r2w == 2) begin + read2 <= block[port3]; + end + else begin + read1 <= block[port2]; + read2 <= block[port3]; + end + end +endmodule +``` +We declare a r1r2w signal because we are permitted to perform two +reads but a read and write cannot occur simultaneously. Besides the +ports, we declare an array of eight eight-bit registers in Verilog in this +format: reg [x:0] block [y:0] where you declare the number of bits of +each register before the variable name ‘block’ and the number of array +elements i.e. registers after block. + +Here's a pictorial representation of the register file: + +If we are permitted to perform multiple write operations, then we must assign +priorities to the write ports. We can do this by structuring our if else blocks in a +favourable manner. + +Let’s assume that we have eight eight-bit registers contained in a register file +that has 1 read port and 2 write ports. Similar to the last example, we cannot +have a read and write operation at once but we can perform both write +operations simultaneously. In case two writes try to access the same register, +give priority to write_data_1. + +```v +module reg_file(input clk, rst, + input [1:0] rw1w2, + input [2:0] write_add_1, + input [2:0] write_add_2, + input [2:0] read_add, + input [7:0] write_data_1, + input [7:0] write_data_2, + output reg [7:0] read_data); + + parameter WIDTH=8; + reg [WIDTH-1:0] block[WIDTH-1:0]; + + always@(posedge clk) begin + // rw1w2- 0: read case + // rw1w2- 1: write1 case + // rw1w2- 2: write2 case + // rw1w2- 3: write1 & write2 case + if(rst==0) begin + read_data <= 0; + end + else if(rw1w2 == 0) begin // read + read_data <= block[read_add]; + end + else if(rw1w2 == 1) begin // write1 + block[write_add_1] <= write_data_1; + end + else if(rw1w2 == 2) begin // write2 + block[write_add_2] <= write_data_2; + end + else begin + if (write_add_1 == write_add_2) + block[write_add_1] <= write_data_1; + else begin + block[write_add_1] <= write_data_1; + block[write_add_2] <= write_data_2; + end + end + end +endmodule +``` +**Q:** Can you take the previous example and modify it such that the register file +now has 2 read ports and 2 write ports and any pair of operations can occur +simultaneously? Let the read operation be of higher priority when a read and +write occur simultaneously, and if two operations attempt to write to the same +register, let the one with the lower serial number e.g. write_data_1 over +write_data_2 be of higher priority. + +## **Shift Registers** +Shift registers are a cascade of flip-flops used to store values which are +passed on to the consecutive register at every edge triggering. They are +used for temporary data storage, data transfer and data manipulation. +Here is an example of a SISO (Serial In, Serial Out) type shift register: +Assuming that the ffs are initialized to store a value of 0. Data can be +serially shifted to the left or right, in this example we shift to the right. + + +|CLK Transition | D | Q1 | Q2 | Q_out| +|---|---|---|---|---| +|↑|1|1|0|0| +|↑|1|1|1|0| +|↑|0|0|1|1| +|↑|0|0|0|1| +|↑|1|1|0|0| +|↑|0|0|1|0| + +This example shown above is that of a SISO shift register wherein there is only +1 (serial) input and 1 output each such that the data is stored and shifted bit by +bit sequentially either leftwards or rightwards. + +Other types of shift registers include: +`1.` **SIPO: Serial In, Parallel Out (One input, outputs Qi where i=1,2,..,n for +each of the n flipflops)** + + +|CLK Transition | D | Q1 | Q2 | Q_out| +|---|---|---|---|---| +|↑|1|1|0|0| +|↑|1|1|1|0| +|↑|0|0|1|1| +|↑|0|0|0|1| +|↑|1|1|0|0| +|↑|0|0|1|0| + + +`2.`**PISO: Parallel In, Serial Out (Multiple inputs fed separately to each ff, one +output Q_out)** + + +[Image Credit: GeeksForGeeks](https://www.geeksforgeeks.org/piso-shift-register/) + +`3.` **PIPO: Parallel In, Parallel Out (Separate inputs for each ff, separate +outputs at each ff)** + + +|CLK Transition | D1 | D2 | D3 | Q1 | Q2 | Q3| +|---|---|---|---|---|---|---| +|↑|1|0|1|1|0|1| +|↑|1|0|0|1|0|0| +|↑|0|0|1|0|0|1| +|↑|0|0|0|0|0|0| +|↑|1|1|1|1|1|1| +|↑|0|1|0|0|1|0| + +Let’s look at the design of a 4-bit shift register (SISO) in Verilog: + +```v +module shift_reg(input clk, en, in, output reg out); + reg [3:0] sreg; + integer i; + + always@(posedge clk) begin + if(en) begin + for(i=0; i<3; i++) begin + sreg[i+1] <= sreg[i]; + sreg[0] <= in; + end + out <= sreg[15]; + end + end +endmodule +``` + +When the EN signal is active, the shift register operates according to SISO logic; +however, when the EN signal is inactive, no shifting or alteration occurs. +If we were to implement a 4-bit shift register (SISO) with D flip-flops +(hierarchical modelling), it would look like this: + +```v +module dflfl(output reg op, input ip, input clk); + always @(posedge clk) begin + op <= ip; + end +endmodule + +module siso(output reg [3:0] out, + input ip, + input clk,en); + reg [3:0] temp; + + dflfl g1(out[3], en ? ip:out[3], clk); + dflfl g2(out[2], en ? out[3]:out[2], clk); + dflfl g3(out[1], en ? out[2]:out[1], clk); + dflfl g4(out[0], en ? out[1]:out[0], clk); + + endmodule +``` + +This is an example of a shift right SISO shift register wherein the input gets +serially shifted to the right at every positive edge triggering. The combinational +block involves instantiation of four D flip-flops and applying the serial shifting +logic by passing the input to the MSB flip-flop. The inputs to the other flip-flops +are the outputs of the flip-flops preceding them. If the enable signal is low, we +freeze the current values and we don’t make any changes. + +**Q:** Attempt to design a bidirectional shift register in Verilog. +We need to have two modes- shift left and shift right, and so we have an +additional input control signal. +Try it out and see if you can implement it in code. +**Q.** Attempt to design a 4-bit SIPO shift register in Verilog. What changes would +you have to make to the SISO code and what additional input and output +signals would you have to include? + +## **Some useful short notes** +**1. A note on parameterization:** +The code that we write for n-bit registers is limited for registers which are +strictly n-bits. In order to write code and design registers that are more +reusable, that can accommodate an arbitrary number of bits for each +instantiation, we can utilize instantiation parameters. We can pass the required +value of the parameter at the time of instantiation and we can also specify a +default value. + +```v +module register #(parameter WIDTH=4) ( + input clk, rst, rw, + input [WIDTH-1:0] write_data, + output [WIDTH-1:0] read_data); + reg [WIDTH-1:0] block; + + always@(posedge clk) begin + if(!rst) block <= 0; + else begin + if(rw==1) block <= write_data; + else read_data <= block; + end + end +endmodule +``` + +The syntax for parametrizing a module is: +*module module_name #(parameter PARAMETER_NAME =default_value) +(declare input and output signals)* + +## **References** +1. [https://my.eng.utah.edu/~cs6710/handouts/verilog-xl-behavioral.pdf](https://my.eng.utah.edu/~cs6710/handouts/verilog-xl-behavioral.pdf) +2. [https://www.realdigital.org/doc/43c79714a7f3d0bbb8098d60c63fde48](https://www.realdigital.org/doc/43c79714a7f3d0bbb8098d60c63fde48) +3. PISO Shift Register: [https://www.geeksforgeeks.org/piso-shift-register/](https://www.geeksforgeeks.org/piso-shift-register/) +

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Hardware Lab NITC

Appearance

INTRODUCTION ​

Table of Contents ​

TopicPage
Introduction1
Verilog Syntax2
Basic Logic Gates3
Binary Adders and Subtractors4
Latches5
Flip Flops6
Multiplexers7
Demultiplexers8
Parity Generator9
Code converter10
Comparators11
Registers12
Counters13
Arithmetic Logic Unit14
Encoders15
Decoders16
How ro make a verilog program17
Bibliography18

Verilog is a Hardware Description Language (HDL). They resemble programming languages specifically oriented to describe hardware structures and their behavior. This language describes an interconnection of components. Such a structural description, a netlist, can be used as input to logic simulation just as a schematic is used.

A typical procedure is used in employing an HDL description as simulation input. The steps in the procedure are analysis, elaboration, and initialization, followed by the simulation.
Analysis checks the description for violations of the syntax and semantic rules for the HDL and produces an intermediate representation of the design.

Elaboration traverses the design hierarchy represented by the description; in this process, the design hierarchy is flattened to an interconnection of modules described only by their behaviors.
The result of the analysis and elaboration performed by the compiler is a simulation model of the original HDL description. This model is then passed to the simulator for execution. Initialization sets all of the variables in the simulation model to specified or default values.
Simulation executes the simulation model in either batch or interactive mode with inputs specified by the user.

The testbench is a description that includes the design to be tested, typically referred to as the Device Under Test (DUT). The testbench describes a collection of hardware and software functions that apply inputs to the DUT and analyze the outputs for correctness.
Verilog supports a design at many levels of abstraction. The primary three kinds of abstraction in Verilog are

  • Behavioral level
  • Register-transfer level
  • Gate level

Behavioral: ​

This is the highest level of abstraction provided by Verilog HDL. It describes the circuit using procedural statements (the "always" block, case, and if statements). At the behavioral level, the circuit is described using an algorithm consisting of a set of instructions executed one after the other sequentially.

Data-Flow: ​

This is the second highest level of abstraction. It specifies the circuit as a combination of operations and data transfer between the registers. In this approach, the 'assign' statement is used. An assign statement is a continuous statement where any signal changes on the right-hand side will update the output signal. Changes in the inputs are continuously monitored. Any synthesizable code is called RTL code. Gate-Level: This is the lowest level of abstraction. Here, the circuit is described by logical links and their timing properties. The module is implemented in terms of logic gates and interconnections between these gates. It resembles a schematic drawing with components connected with signals.

Functional Differences ​

Behavioral Level ​

Pros ​

  • Easy to write and understand, especially for complex algorithms and high-level functionality.
  • Portability: the same behavioral code can be synthesized into different hardware architectures.
  • Enables early verification, allowing designers to test system functionality before committing to a particular hardware architecture.

Cons ​

  • Less control over the hardware implementation details.
  • Can be less efficient in terms of area, power, and performance than lower levels of abstraction.
  • More difficult to optimize for timing and power.

Register Transfer Level (RTL) ​

Pros ​

  • Offers greater control over the hardware implementation details.
  • Can be optimized for timing, power, and area, allowing for more efficient designs.
  • Can be used for both simulation and synthesis. Cons
  • More difficult to write and understand than the behavioral level.
  • Can be less portable than the behavioral level, since the same code may not synthesize correctly across different architectures.
  • Can be more difficult to verify than the behavioral level, since the design is more complex.

Gate Level ​

Pros ​

  • Provides the most detailed view of the hardware implementation.
  • Highly optimized for area, power, and performance.
  • Ideal for final verification of the design. Cons
  • Very difficult to write and understand.
  • Not portable: The code is specific to a particular hardware architecture.
  • Verification can be very time-consuming and difficult, especially for complex designs.

VERILOG SYNTAX ​

CODE: ​

v
module half_adder(output s, c, input a, b);
+    
Hardware Lab NITC
Appearance
INTRODUCTION ​
Table of Contents ​
TopicPage
Introduction1
Verilog Syntax2
Basic Logic Gates3
Binary Adders and Subtractors4
Latches5
Flip Flops6
Multiplexers7
Demultiplexers8
Parity Generator9
Code converter10
Comparators11
Registers12
Counters13
Arithmetic Logic Unit14
Encoders15
Decoders16
How ro make a verilog program17
Bibliography18
Verilog is a Hardware Description Language (HDL). They resemble programming languages specifically oriented to describe hardware structures and their behavior. This language describes an interconnection of components. Such a structural description, a netlist, can be used as input to logic simulation just as a schematic is used.
A typical procedure is used in employing an HDL description as simulation input. The steps in the procedure are analysis, elaboration, and initialization, followed by the simulation.
 Analysis checks the description for violations of the syntax and semantic rules for the HDL and produces an intermediate representation of the design.
Elaboration traverses the design hierarchy represented by the description; in this process, the design hierarchy is flattened to an interconnection of modules described only by their behaviors.
 The result of the analysis and elaboration performed by the compiler is a simulation model of the original HDL description. This model is then passed to the simulator for execution. Initialization sets all of the variables in the simulation model to specified or default values.
 Simulation executes the simulation model in either batch or interactive mode with inputs specified by the user.
The testbench is a description that includes the design to be tested, typically referred to as the Device Under Test (DUT). The testbench describes a collection of hardware and software functions that apply inputs to the DUT and analyze the outputs for correctness.
 Verilog supports a design at many levels of abstraction. The primary three kinds of abstraction in Verilog are
  • Behavioral level
  • Register-transfer level
  • Gate level
Behavioral: ​
This is the highest level of abstraction provided by Verilog HDL. It describes the circuit using procedural statements (the "always" block, case, and if statements). At the behavioral level, the circuit is described using an algorithm consisting of a set of instructions executed one after the other sequentially.
Data-Flow: ​
This is the second highest level of abstraction. It specifies the circuit as a combination of operations and data transfer between the registers. In this approach, the 'assign' statement is used. An assign statement is a continuous statement where any signal changes on the right-hand side will update the output signal. Changes in the inputs are continuously monitored. Any synthesizable code is called RTL code. Gate-Level: This is the lowest level of abstraction. Here, the circuit is described by logical links and their timing properties. The module is implemented in terms of logic gates and interconnections between these gates. It resembles a schematic drawing with components connected with signals.
Functional Differences ​
Behavioral Level ​
Pros ​
  • Easy to write and understand, especially for complex algorithms and high-level functionality.
  • Portability: the same behavioral code can be synthesized into different hardware architectures.
  • Enables early verification, allowing designers to test system functionality before committing to a particular hardware architecture.
Cons ​
  • Less control over the hardware implementation details.
  • Can be less efficient in terms of area, power, and performance than lower levels of abstraction.
  • More difficult to optimize for timing and power.
Register Transfer Level (RTL) ​
Pros ​
  • Offers greater control over the hardware implementation details.
  • Can be optimized for timing, power, and area, allowing for more efficient designs.
  • Can be used for both simulation and synthesis. Cons
  • More difficult to write and understand than the behavioral level.
  • Can be less portable than the behavioral level, since the same code may not synthesize correctly across different architectures.
  • Can be more difficult to verify than the behavioral level, since the design is more complex.
Gate Level ​
Pros ​
  • Provides the most detailed view of the hardware implementation.
  • Highly optimized for area, power, and performance.
  • Ideal for final verification of the design. Cons
  • Very difficult to write and understand.
  • Not portable: The code is specific to a particular hardware architecture.
  • Verification can be very time-consuming and difficult, especially for complex designs.
VERILOG SYNTAX ​
CODE: ​
v
module half_adder(output s, c, input a, b);
     assign s = a ^ b;
     assign c = a & b;
 endmodule
module is always terminated by endmodule. Always specify output first and then input.
TESTBENCH: ​
v
module half_adder_test;
@@ -33,8 +33,8 @@
         #20;
         end
     end
-endmodule
reg: store input values
wire: store output values begin end is used to specify a block of code.
BASIC LOGIC GATES ​
Logic gates are basic building blocks of digital electronics circuits that perform logical operations on one or more binary inputs and produce a binary output. In other words, a logic gate is an electronic device that operates on logical signals (digital signals) to perform a Boolean function.
There are several types of logic gates, including:
AND gate: It has two or more input signals and produces a HIGH output only if all inputs are HIGH. The AND gate symbol is the dot or multiplication symbol.
OR gate: It has two or more input signals and produces a HIGH output if at least one input is HIGH. The OR gate symbol is the plus symbol.
NOT gate (Inverter): It has one input signal and produces the complement of the input signal at its output. The NOT gate symbol is a triangle with a circle at the output.
NAND gate: It is a combination of an AND gate and a NOT gate. It produces a LOW output only if all inputs are HIGH. The NAND gate symbol is an AND gate with a small circle at its output.
NOR gate: It is a combination of an OR gate and a NOT gate. It produces a HIGH output only if all inputs are LOW. The NOR gate symbol is an OR gate with a small circle at its output.
XOR gate: It has two input signals and produces a HIGH output if the two inputs are different (i.e., one input is HIGH and the other is LOW). The XOR gate symbol is the addition symbol with a circle around it.
XNOR gate: It is a combination of an XOR gate and a NOT gate. It produces a HIGH output if the two inputs are the same (i.e., both inputs are HIGH or both inputs are LOW). The XNOR gate symbol is an XOR gate with a small circle at its output.
Binary Adders and Subtractors ​
HALF ADDER ​
A half-adder is an arithmetic circuit that generates the sum of two binary digits. The circuit has two inputs and two outputs. The input variables are the augend and addend bits to be added, and the output variables produce the sum and carry.
The Boolean functions for the two outputs, easily obtained from the truth table, are
S = XY + XY = X ⊕ Y
C = XY
xyCS
0000
0101
1001
1110
FULL ADDER ​
A full adder is a combinational circuit that forms the arithmetic sum of three input bits. Two input variables, denoted by X and Y, represent the two significant bits to be added. The third input, Z, represents the carry from the previous lower significant position.
 The simplified sum-of-product functions for the two outputs are :
S = XYZ + XYZ + XY Z + XYZ
C = XY + XZ + YZ
S = (X ⊕ Y) ⊕ Z
C = XY + Z(X ⊕ Y)
RIPPLE CARRY ADDER ​
A parallel binary adder is a digital circuit that produces the arithmetic sum of two binary numbers using only combinational logic. The parallel adder uses n full adders in parallel, with all input bits applied simultaneously to produce the sum.
 The full adders are connected in cascade, with the carry output from one full adder connected to the carry input of the next full adder. Since a 1 carry may appear near the least significant bit of the adder and yet propagate through many full adders to the most significant bit, just as a wave ripples outward from a pebble dropped in a pond, the parallel adder is referred to as a ripple carry adder.
CARRY LOOK AHEAD ADDER ​
Define two new binary variables
Pi = Ai XOR Bi
Gi = Ai AND Bi
the output sum and carry can respectively be expressed as
Si = Pi XOR Ci
Ci+1 = Gi + (Pi AND Ci)
Each sum output requires two exclusive-OR gates. The output of the first exclusive-OR gate generates the Pi variable, and the AND gate generates the Gi variable. The carries are propagated through the carry lookahead generator and applied as inputs to the second exclusive-OR gate. All output carries are generated after a delay through two levels of gates. Thus, outputs S1 through S3 have equal propagation delay times.
HALF SUBTRACTOR ​
A half subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) and produces two output bits: the difference (D) and the borrow (B). The half subtractor is called "half" because it can only subtract two single-bit binary numbers, unlike a full subtractor that can subtract two multi-bit binary numbers. D= A XOR B B’ = Abar AND B
 
FULL SUBTRACTOR ​
A full subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) along with a borrow (Bin) and produces two output bits: the difference (D) and the borrow (Bout). The full subtractor is an extension of the half subtractor, which can only subtract two single-bit binary numbers.
D = A XOR B XOR Bin
 B’ = Abar AND B OR ((A XOR B)bar)Bin
BINARY ADDER AND SUBTRACTOR ​
M-N where M-minuend and N is subtrahend When performing a subtraction we complement the subtrahend N, and when performing an addition we do not complement N.
The 2s complement can be obtained by taking the 1s complement and adding 1 to the least significant bit. The 1s complement can be implemented easily with inverter circuits, and we can add 1 to the sum by making the input carry of the parallel adder equal to 1. The input carry C0 must be equal to 1. The operation that is performed becomes A plus the 1s complement of B plus 1. This is equal to A plus the 2s complement of B. For unsigned numbers, it gives A - B if A >= B or the 2s complement of B - A if A []( B
LATCHES ​
SR LATCH ​
The SR latch is a circuit constructed from two cross- coupled NOR gates. The latch has two inputs, labeled S for set and R for reset, and two useful states. When output Q = 1 and Q = 0, the latch is said to be in the set state. When Q = 0 and Q = 1, it is in the reset state. Outputs Q and Q are normally the complements of each other. When both inputs are equal to 1 at the same time, an undefined state with both outputs equal to 0 occurs.
S̅R̅ LATCH ​
The SR latch with two cross- coupled NAND gates. It operates with both inputs normally at 1, unless the state of the latch has to be changed. The application of a 0 to the S input causes output Q to go to 1, putting the latch in the set state. When the S input goes back to 1, the circuit remains in the set state. With both inputs at 1, the state of the latch is changed by placing a 0 on the R input. This causes the circuit to go to the reset state and stay there, even after both inputs return to 1. The condition that is undefined for this NAND latch is when both inputs are equal to 0 at the same time, an input combination that should be avoided. When the NAND latch requires a 0 signal to change its state, it is referred to as an SR latch.
SR LATCH WITH CONTROL INPUT ​
It consists of the basic NAND latch and two additional NAND gates. The control input C acts as an enable signal for the other two inputs. The output of the NAND gates stays at the logic- 1 level as long as the control input remains at 0.
 When the control input goes to 1, information from the S and R inputs is allowed to affect the S R latch. The set state is reached with S = 1, R = 0, and C = 1. To change to the reset state, the inputs must be S = 0, R = 1, and C = 1. In either case, when C returns to 0, the circuit remains in its current state. Control input C = 0 disables the circuit so that the state of the output does not change, regardless of the values of S and R. Moreover, when C = 1 and both the S and R inputs are equal to 0, the state of the circuit does not change.An undefined state occurs when all three inputs are equal to 1. This condition places 0s on both inputs of the basic S R latch, giving an undefined state.
D LATCH ​
One way to eliminate the undesirable undefined state in the SR latch is to ensure that inputs S and R are never equal to 1 at the same time. This is done in the D latch, shown in Figure 4-8. This latch has only two inputs: D (data) and C (control). The complement of the D input goes directly to the S input, and D is applied to the R input.
 As long as the control input is 0, the S R latch has both inputs at the 1 level, and the circuit cannot change state regardless of the value of D. The D input is sampled when C = 1. If D is 1, the Q output goes to 1, placing the circuit in the set state. If D is 0, output Q goes to 0, placing the circuit in the reset state. The D latch receives its designation from its ability to hold data in its internal storage. The binary information present at the data input of the D latch is transferred to the Q output when the control input is enabled (1). The output follows changes in the data input, as long as the control input is enabled. When the control input is disabled (0), the binary information that was present at the data input at the time the transition in C occurred is retained at the Q output until the control input C is enabled again.
FLIP FLOPS ​
There are basically 4 types of flip-flops:
  1. SR Flip-Flop
  2. JK Flip-Flop
  3. D Flip-Flop
  4. T Flip-Flop
SR FLIP-FLOP ​
SR flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, SR latch operates with an enable signal. The circuit diagram of SR flip-flop is shown in the following figure.This circuit has two inputs S & R and two outputs QN and Qn+1, present and next state respectively. The operation of the SR flip-flop is similar to SR Latch. But, this flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. Qn+1 = S + R’Qn
JK FLIP-FLOP ​
JK flip-flop is the modified version of SR flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has two inputs J & K and two outputs Qn and Qn+1, present and next state respectively, JK flip-flop can be used for one of these four functions such as Hold, Reset, Set & Complement of present state based on the input conditions, when positive transition of clock signal is applied.
Qn+1 = J(Qn)’ + K’(Qn)
D FLIP-FLOP ​
D flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, D latch operates with an enable signal. That means, the output of D flip-flop is insensitive to the changes in the input, D except for active transition of the clock signal. This circuit has single input D and two outputs Qn and Qn+1. This flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. D flip-flop always holds the information, which is available on data input, D of earlier positive transition of clock signal. Next state of D flip-flop is always equal to data input, D for every positive transition of the clock signal.
Qn+1 = D
T FLIP-FLOP ​
T flip-flop is the simplified version of JK flip-flop. It is obtained by connecting the same input ‘T’ to both inputs of JK flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has single input T and two outputs Qn and Qn+1. The operation of the T flip-flop is the same as that of the JK flip-flop. Here, we considered the inputs of JK flip-flop as J = T and K = T in order to utilize the modified JK flip-flop for 2 combinations of inputs. So, we eliminated the other two combinations of J & K, for which those two values complement each other in a T flip-flop.
Qn+1 = T’Q(n) + (Q(n))’T = T XOR Q(n)
MULTIPLEXERS ​
2-1 MUX ​
It selects binary information from one of many input lines and directs the information to a single output line. The selection of a particular input line is controlled by a set of input variables, called selection inputs. there are 2^n input lines and n selection inputs whose bit combinations determine which input is selected. , if the select input S = 0, the output of the multiplexer takes on the values of I 0 , and, if input S = 1, the output of the multiplexer takes on the values of I 1 . Thus, S selects either input I 0 or input I 1 to appear at output Y.
 We can see that the equation for the 2–to–1-line multiplexer output Y is
 Y = S’I0 + SI1
4-1 MUX ​
The function Y depends on four inputs I 0 , I 1 , I 2 , and I 3 and two select inputs S1 and S0 . By placing the values of I 0 through I 3 in the Y column. Since there are six variables, and only S1 and S0 are fixed, this single row represents 16 rows of the corresponding full truth table. From the table, we can write the equation for Y as
 Y = S1’S0’ I0 + S1’S0 I1 + S1S0’I2 + S1S0 I3
S1S2Y
00I0
01I1
10I2
11I3
DEMULTIPLEXERS ​
1:2 DEMUX ​
A 1-to-2 demultiplexer consists of one input line, two output lines and one select line. The signal on the select line helps to switch the input to one of the two outputs. When the select input is LOW, then the input will be passed to Y0 and if the select input is HIGH, then the input will be passed to Y1
 Y0 = S’ D
 Y1 = S D
PARITY GENERATOR ​
Many systems use a parity bit as a means for bit error detection. Any group of bits contains either an even or an odd number of 1s. A parity bit is attached to a group of bits to make the total number of 1s in a group always even or always odd. An even parity bit makes the total number of 1s even, and an odd parity bit makes the total odd. A parity bit provides for the detection of a single bit error (or any odd number of errors, which is very unlikely) but cannot check for two errors in one group. For instance, let’s assume that we wish to transmit the BCD code 0101. (Parity can be used with any number of bits; we are using four for illustration.) The total code transmitted, including the even parity bit, is
Now let’s assume that an error occurs in the third bit from the left (the 1 becomes a 0)
When this code is received, the parity check circuitry determines that there is only a single 1 (odd number), when there should be an even number of 1s. Because an even number of 1s does not appear in the code when it is received, an error is indicated.
CODE CONVERTER ​
BCD to Binary Code converter ​
The binary numbers representing the weights of the BCD bits are summed to produce the total binary number. The binary equivalent of each BCD bit is a binary number representing the weight of that bit within the total BCD number.
Binary to Gray ​
Conversion between binary code and Gray code is sometimes useful. The following rules explain how to convert from a binary number to a Gray code word:
  1. The most significant bit (left-most) in the Gray code is the same as the corresponding MSB in the binary number.
  2. Going from left to right, add each adjacent pair of binary code bits to get the next Gray code bit. Discard carries
Gray to Binary ​
To convert from Gray code to binary, use a similar method; however, there are some differences. The following rules apply:
  1. The most significant bit (left-most) in the binary code is the same as the corresponding bit in the Gray code.
  2. Add each binary code bit generated to the Gray code bit in the next adjacent position. Discard carries.
COMPARATORS ​
The exclusive-NOR gate can be used as a basic comparator because its output is a 0 if the two input bits are not equal and a 1 if the input bits are equal. The basic comparator can be expanded to any number of bits. The AND gate sets the condition that all corresponding bits of the two numbers must be equal if the two numbers themselves are equal. To determine an inequality of binary numbers A and B, you first examine the highest order bit in each number. The following conditions are possible: 1. If A3 = 1 and B3 = 0, number A is greater than number B. 2. If A3 = 0 and B3 = 1, number A is less than number B. 3. If A3 = B3, then you must examine the next lower bit position for an inequality. These three operations are valid for each bit position in the numbers. The general procedure used in a comparator is to check for an inequality in a bit position, starting with the highest-order bits (MSBs). When such an inequality is found, the relationship of the two numbers is established, and any other inequalities in lower-order bit positions must be ignored because it is possible for an opposite indication to occur; the highest-order indication must take precedence.
Registers ​
A register is a group of flip‐flops, each one of which shares a common clock and is capable of storing one bit of information. An n ‐bit register consists of a group of n flip‐flops capable of storing n bits of binary information. In addition to the flip‐flops, a register may have combinational gates that perform certain data‐processing tasks.
Four‐bit register ​
The common clock input triggers all flip‐flops on the positive edge of each pulse, and the binary data available at the four inputs are transferred into the register. The value of (I3 , I2 , I1 , I0) immediately before the clock edge determines the value of (A3 , A2 , A1 , A0) after the clock edge. The four outputs can be sampled at any time to obtain the binary information stored in the register. The input Clear_b goes to the active‐low R (reset) input of all four flip‐flops. When this input goes to 0, all flip‐flops are reset asynchronously. The Clear_b input is useful for clearing the register to all 0’s prior to its clocked operation. The R inputs must be maintained at logic 1 (i.e., de-asserted) during normal clocked operation. Note that, depending on the flip‐flop, either Clear, Clear_b, reset, or reset_b can be used to indicate the transfer of the register to an all 0’s state.
Four bit register with parallel load**Gi = Ai AND Bi ** ​
A four‐bit data‐storage register with a load control input that is directed through gates and into the D inputs of the flip‐flops. The additional gates implement a two‐channel mux whose output drives the input to the register with either the data bus or the output of the register. The load input to the register determines the action to be taken with each clock pulse.
SHIFT REGISTERS ​
SERIAL IN/SERIAL OUT REGISTERS ​
The serial in/serial out shift register accepts data serially—that is, one bit at a time on a single line. It produces the stored information on its output also in serial form .
Serial In/Parallel Out Shift Registers ​
Data bits are entered serially (least-significant bit first) into a serial in/parallel out shift register in the same manner as in serial in/serial out registers. The difference is the way in which the data bits are taken out of the register; in the parallel output register, the output of each stage is available. Once the data is stored, each bit appears on its respective output line, and all bits are available simultaneously, rather than on a bit-by-bit basis as with the serial output.
Parallel In/Serial Out Shift Registers ​
For a register with parallel data inputs, the bits are entered simultaneously into their respective stages on parallel lines rather than on a bit-by-bit basis on one line as with serial data inputs.
Parallel In/Parallel Out Shift Registers ​
Parallel entry and parallel output of data have been discussed. The parallel in/parallel out register employs both methods. Immediately following the simultaneous entry of all data bits, the bits appear on the parallel outputs.
COUNTERS ​
A register that goes through a prescribed sequence of states upon the application of input pulses is called a counter. The input pulses may be clock pulses, or they may originate from some external source and may occur at a fixed interval of time or at random. The sequence of states may follow the binary number sequence or any other sequence of states.
BINARY RIPPLE COUNTER ​
A binary ripple counter consists of a series connection of complementing flip‐flops, with the output of each flip‐flop connected to the C input of the next higher order flip‐flop. The flip‐flop holding the least significant bit receives the incoming count pulses. A complementing flip‐flop can be obtained from a JK flip‐flop with the J and K inputs tied together or from a T flip‐flop. A third possibility is to use a D flip‐flop with the complement output connected to the D input.The output of each flip‐flop is connected to the C input of the next flip‐flop in sequence. The flip‐flop holding the least significant bit receives the incoming count pulses. The bubble in front of the dynamic indicator symbol next to C indicates that the flip‐flops respond to the negative‐edge transition of the input. The negative transition occurs when the output of the previous flip‐flop to which C is connected goes from 1 to 0.
BCD RIPPLE COUNTER ​
A decimal counter follows a sequence of 10 states and returns to 0 after the count of 9. Such a counter must have at least four flip‐flops to represent each decimal digit, since a decimal digit is represented by a binary code with at least four bits. The sequence of states in a decimal counter is dictated by the binary code used to represent a decimal digit. The four outputs are designated by the letter symbol Q, with a numeric subscript equal to the binary weight of the corresponding bit in the BCD code. Note that the output of Q1 is applied to the C inputs of both Q2 and Q8 and the output of Q2 is applied to the C input of Q4. The J and K inputs are connected either to a permanent 1 signal or to outputs of other flip‐flops.
4 BIT SYNCHRONOUS BINARY COUNTER ​
The flip‐flop in the least significant position is complemented with every pulse. A flip‐flop in any other position is complemented when all the bits in the lower significant positions are equal to 1 . Synchronous binary counters have a regular pattern and can be constructed with complementing flip‐flops and gates. The C inputs of all flip‐flops are connected to a common clock. The counter is enabled by Count_enable. If the enable input is 0, all J and K inputs are equal to 0 and the clock does not change the state of the counter. The first stage, A0, has its J and K equal to 1 if the counter is enabled. The other J and K inputs are equal to 1 if all previous least significant stages are equal to 1 and the count is enabled. The chain of AND gates generates the required logic for the J and K inputs in each stage. The counter can be extended to any number of stages, with each stage having an additional flip‐flop and an AND gate that gives an output of 1 if all previous flip‐flop outputs are 1. Note that the flip‐flops trigger on the positive edge of the clock.
FOUR BIT UP-DOWN BINARY COUNTER ​
The two operations can be combined in one circuit to form a counter capable of counting either up or down. It has an up control input and a down control input. When the up input is 1, the circuit counts up, since the T inputs receive their signals from the values of the previous normal outputs of the flip‐flops.
BINARY COUNTER WITH PARALLEL LOAD ​
When equal to 1, the input load control disables the count operation and causes a transfer of data from the four data inputs into the four flip‐flops. If both control inputs are 0, clock pulses do not change the state of the register. The carry output becomes a 1 if all the flip‐flops are equal to 1 while the count input is enabled. This is the condition for complementing the flip‐flop that holds the next significant bit. The carry output is useful for expanding the counter to more than four bits. The speed of the counter is increased when the carry is generated directly from the outputs of all four flip‐flops, because the delay to generate the carry bit is reduced. A counter with a parallel load can be used to generate any desired count sequence.the Count control is set to 1 to enable the count through the CLK input. Also, recall that the Load control inhibits the count and that the clear operation is independent of other control inputs.
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ARITHMETIC LOGIC UNIT (ALU) ​
The ALU, or arithmetic logic unit, is a crucial component of the CPU (central processing unit) in a computer system. It is responsible for carrying out arithmetic and logic operations. Also referred to as the integer unit (IU), it is an integrated circuit found in both CPUs and GPUs. The ALU is the final stage in the processor where calculations are performed. It possesses the capability to handle various tasks related to arithmetic and logic operations, including addition, subtraction, shifting operations, as well as Boolean comparisons such as XOR, OR, AND, and NOT operations. It operates on binary numbers and can execute mathematical and bitwise operations. The ALU consists of two units: the arithmetic unit (AU) and the logic unit (LU). By utilizing operands and codes, the ALU determines which operations to perform based on the input data provided. Once the ALU completes processing the input, the resulting information is sent to the computer's memory.
Here are the main functions of an ALU:
Arithmetic Operations: The ALU performs various arithmetic operations on binary numbers, such as addition, subtraction, multiplication, and division. It uses binary addition and subtraction circuits to handle these operations efficiently.
Logical Operations: The ALU executes logical operations on binary data, including AND, OR, XOR (exclusive OR), and NOT. These operations manipulate individual bits or binary values to determine logical relationships and produce logical results.
Comparison Operations: The ALU performs comparison operations to determine the relationship between two binary values. It can compare if two values are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other. The result of these comparisons is typically represented by setting specific flags or registers in the CPU.
Bitwise Operations: The ALU carries out bitwise operations, which manipulate individual bits in binary numbers. These operations include shifting the bits left or right, rotating bits, and masking operations. Bitwise operations are commonly used in tasks such as data manipulation, encryption, and signal processing.
Conditional Operations: The ALU supports conditional operations, enabling the CPU to execute different instructions based on certain conditions. For example, it can perform conditional branching, where the CPU jumps to a specific instruction address based on the result of a comparison operation.
Data Movement: The ALU may also handle data movement operations within the CPU. This involves transferring data between registers, memory, and other CPU components.
ENCODER ​
An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n (or fewer) input lines and n output lines.
PRIORITY ENCODER ​
A priority encoder is an encoder circuit that includes the priority function. The operation of the priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence. In addition to the two outputs x and y , the circuit has a third output designated by V ; this is a valid bit indicator that is set to 1 when one or more inputs are equal to 1. If all inputs are 0, there is no valid input and V is equal to 0. The other two outputs are not inspected when V equals 0 and are specified as don’t-care conditions.
x = D2+ D3
 y = D3 + D1 D 2
 V = D0 + D1 + D2 + D3
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DECODER ​
A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines.The decoders presented here are called n -to- m -line decoders, where m … 2^n.
3-8 LINE DECODER ​
The three inputs are decoded into eight outputs, each representing one of the minterms of the three input variables. The three inverters provide the complement of the inputs, and each one of the eight AND gates generates one of the minterms.
2-4 LINE DECODER WITH ENABLE INPUT ​
The circuit operates with complemented outputs and a complement enable input. The decoder is enabled when E is equal to 0 (i.e., active-low enable). As indicated by the truth table, only one output can be equal to 0 at any given time; all other outputs are equal to 1. The output whose value is equal to 0 represents the minterm selected by inputs A and B . The circuit is disabled when E is equal to 1, regardless of the values of the other two inputs. When the circuit is disabled, none of the outputs are equal to 0 and none of the minterms are selected.
HOW TO MAKE A VERILOG PROGRAM ​
Create a New Project in your own version of Quartus Prime. ​
Select an appropriate directory for your Verilog project files and create an empty project file template. ​
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Use the 10M50DAF484C7G Board from the MAX 10 Family. ​
Set ModelSim as your Simulation Tool (ModelSim must be installed prior) and finish the initialization of the project. ​
Click on the file icon in the top left corner and create a new Verilog HDL file. ​
When you wish to save your program, simply use Ctrl+S or click the Save icon in the top left corner. ​
Before running your program, you must first set a testbench for it. Do this by going into the Assignments menu and clicking Settings. ​
Create a new Test Bench if you are creating one for a new program that has not been made before. ​
Name your Test Bench appropriately (usually just the name of the test bench file) and add it to the list of Test Benches. ​
After setting your testbench, you can now run and compile your program by clicking on the third play button. ​
You will be able to view your circuit design and how it is structured, and simulate results using the test bench by going to the Tools menu. ​
BIBLIOGRAPHY ​
  1. Digital Design, 5th Edition by M Morris Mano and Michael Ciletti
  2. Digital Fundamentals by Floyd and Jain
  3. electronicshub.org/demultiplexerdemux
  4. tutorialspoint.com/digital_circuits/digital_circuits_flip_flops
  5. tutorialspoint.com/digital_circuits/digital_circuits_demultiplexers
Copyright © 2024 National Institute of Technology Calicut

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+endmodule

reg: store input values
wire: store output values begin end is used to specify a block of code.

BASIC LOGIC GATES ​

Logic gates are basic building blocks of digital electronics circuits that perform logical operations on one or more binary inputs and produce a binary output. In other words, a logic gate is an electronic device that operates on logical signals (digital signals) to perform a Boolean function.

There are several types of logic gates, including:

AND gate: It has two or more input signals and produces a HIGH output only if all inputs are HIGH. The AND gate symbol is the dot or multiplication symbol.

OR gate: It has two or more input signals and produces a HIGH output if at least one input is HIGH. The OR gate symbol is the plus symbol.

NOT gate (Inverter): It has one input signal and produces the complement of the input signal at its output. The NOT gate symbol is a triangle with a circle at the output.

NAND gate: It is a combination of an AND gate and a NOT gate. It produces a LOW output only if all inputs are HIGH. The NAND gate symbol is an AND gate with a small circle at its output.

NOR gate: It is a combination of an OR gate and a NOT gate. It produces a HIGH output only if all inputs are LOW. The NOR gate symbol is an OR gate with a small circle at its output.

XOR gate: It has two input signals and produces a HIGH output if the two inputs are different (i.e., one input is HIGH and the other is LOW). The XOR gate symbol is the addition symbol with a circle around it.

XNOR gate: It is a combination of an XOR gate and a NOT gate. It produces a HIGH output if the two inputs are the same (i.e., both inputs are HIGH or both inputs are LOW). The XNOR gate symbol is an XOR gate with a small circle at its output.

Binary Adders and Subtractors ​

HALF ADDER ​

A half-adder is an arithmetic circuit that generates the sum of two binary digits. The circuit has two inputs and two outputs. The input variables are the augend and addend bits to be added, and the output variables produce the sum and carry.

The Boolean functions for the two outputs, easily obtained from the truth table, are

S = XY + XY = X ⊕ Y

C = XY

xyCS
0000
0101
1001
1110

FULL ADDER ​

A full adder is a combinational circuit that forms the arithmetic sum of three input bits. Two input variables, denoted by X and Y, represent the two significant bits to be added. The third input, Z, represents the carry from the previous lower significant position.
The simplified sum-of-product functions for the two outputs are :

S = XYZ + XYZ + XY Z + XYZ
C = XY + XZ + YZ

S = (X ⊕ Y) ⊕ Z
C = XY + Z(X ⊕ Y)

RIPPLE CARRY ADDER ​

A parallel binary adder is a digital circuit that produces the arithmetic sum of two binary numbers using only combinational logic. The parallel adder uses n full adders in parallel, with all input bits applied simultaneously to produce the sum.
The full adders are connected in cascade, with the carry output from one full adder connected to the carry input of the next full adder. Since a 1 carry may appear near the least significant bit of the adder and yet propagate through many full adders to the most significant bit, just as a wave ripples outward from a pebble dropped in a pond, the parallel adder is referred to as a ripple carry adder.

CARRY LOOK AHEAD ADDER ​

Define two new binary variables

Pi = Ai XOR Bi
Gi = Ai AND Bi

the output sum and carry can respectively be expressed as

Si = Pi XOR Ci
Ci+1 = Gi + (Pi AND Ci)

Each sum output requires two exclusive-OR gates. The output of the first exclusive-OR gate generates the Pi variable, and the AND gate generates the Gi variable. The carries are propagated through the carry lookahead generator and applied as inputs to the second exclusive-OR gate. All output carries are generated after a delay through two levels of gates. Thus, outputs S1 through S3 have equal propagation delay times.

HALF SUBTRACTOR ​

A half subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) and produces two output bits: the difference (D) and the borrow (B). The half subtractor is called "half" because it can only subtract two single-bit binary numbers, unlike a full subtractor that can subtract two multi-bit binary numbers. D= A XOR B B’ = Abar AND B

FULL SUBTRACTOR ​

A full subtractor is a combinational circuit that subtracts two single-bit binary numbers (A and B) along with a borrow (Bin) and produces two output bits: the difference (D) and the borrow (Bout). The full subtractor is an extension of the half subtractor, which can only subtract two single-bit binary numbers.

D = A XOR B XOR Bin
B’ = Abar AND B OR ((A XOR B)bar)Bin

BINARY ADDER AND SUBTRACTOR ​

M-N where M-minuend and N is subtrahend When performing a subtraction we complement the subtrahend N, and when performing an addition we do not complement N.

The 2s complement can be obtained by taking the 1s complement and adding 1 to the least significant bit. The 1s complement can be implemented easily with inverter circuits, and we can add 1 to the sum by making the input carry of the parallel adder equal to 1. The input carry C0 must be equal to 1. The operation that is performed becomes A plus the 1s complement of B plus 1. This is equal to A plus the 2s complement of B. For unsigned numbers, it gives A - B if A >= B or the 2s complement of B - A if A []( B

LATCHES ​

SR LATCH ​

The SR latch is a circuit constructed from two cross- coupled NOR gates. The latch has two inputs, labeled S for set and R for reset, and two useful states. When output Q = 1 and Q = 0, the latch is said to be in the set state. When Q = 0 and Q = 1, it is in the reset state. Outputs Q and Q are normally the complements of each other. When both inputs are equal to 1 at the same time, an undefined state with both outputs equal to 0 occurs.

S̅R̅ LATCH ​

The SR latch with two cross- coupled NAND gates. It operates with both inputs normally at 1, unless the state of the latch has to be changed. The application of a 0 to the S input causes output Q to go to 1, putting the latch in the set state. When the S input goes back to 1, the circuit remains in the set state. With both inputs at 1, the state of the latch is changed by placing a 0 on the R input. This causes the circuit to go to the reset state and stay there, even after both inputs return to 1. The condition that is undefined for this NAND latch is when both inputs are equal to 0 at the same time, an input combination that should be avoided. When the NAND latch requires a 0 signal to change its state, it is referred to as an SR latch.

SR LATCH WITH CONTROL INPUT ​

It consists of the basic NAND latch and two additional NAND gates. The control input C acts as an enable signal for the other two inputs. The output of the NAND gates stays at the logic- 1 level as long as the control input remains at 0.
When the control input goes to 1, information from the S and R inputs is allowed to affect the S R latch. The set state is reached with S = 1, R = 0, and C = 1. To change to the reset state, the inputs must be S = 0, R = 1, and C = 1. In either case, when C returns to 0, the circuit remains in its current state. Control input C = 0 disables the circuit so that the state of the output does not change, regardless of the values of S and R. Moreover, when C = 1 and both the S and R inputs are equal to 0, the state of the circuit does not change.An undefined state occurs when all three inputs are equal to 1. This condition places 0s on both inputs of the basic S R latch, giving an undefined state.

D LATCH ​

One way to eliminate the undesirable undefined state in the SR latch is to ensure that inputs S and R are never equal to 1 at the same time. This is done in the D latch, shown in Figure 4-8. This latch has only two inputs: D (data) and C (control). The complement of the D input goes directly to the S input, and D is applied to the R input.
As long as the control input is 0, the S R latch has both inputs at the 1 level, and the circuit cannot change state regardless of the value of D. The D input is sampled when C = 1. If D is 1, the Q output goes to 1, placing the circuit in the set state. If D is 0, output Q goes to 0, placing the circuit in the reset state. The D latch receives its designation from its ability to hold data in its internal storage. The binary information present at the data input of the D latch is transferred to the Q output when the control input is enabled (1). The output follows changes in the data input, as long as the control input is enabled. When the control input is disabled (0), the binary information that was present at the data input at the time the transition in C occurred is retained at the Q output until the control input C is enabled again.

FLIP FLOPS ​

There are basically 4 types of flip-flops:

  1. SR Flip-Flop
  2. JK Flip-Flop
  3. D Flip-Flop
  4. T Flip-Flop

SR FLIP-FLOP ​

SR flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, SR latch operates with an enable signal. The circuit diagram of SR flip-flop is shown in the following figure.This circuit has two inputs S & R and two outputs QN and Qn+1, present and next state respectively. The operation of the SR flip-flop is similar to SR Latch. But, this flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. Qn+1 = S + R’Qn

JK FLIP-FLOP ​

JK flip-flop is the modified version of SR flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has two inputs J & K and two outputs Qn and Qn+1, present and next state respectively, JK flip-flop can be used for one of these four functions such as Hold, Reset, Set & Complement of present state based on the input conditions, when positive transition of clock signal is applied.

Qn+1 = J(Qn)’ + K’(Qn)

D FLIP-FLOP ​

D flip-flop operates with only positive clock transitions or negative clock transitions. Whereas, D latch operates with an enable signal. That means, the output of D flip-flop is insensitive to the changes in the input, D except for active transition of the clock signal. This circuit has single input D and two outputs Qn and Qn+1. This flip-flop affects the outputs only when positive transition of the clock signal is applied instead of active enable. D flip-flop always holds the information, which is available on data input, D of earlier positive transition of clock signal. Next state of D flip-flop is always equal to data input, D for every positive transition of the clock signal.

Qn+1 = D

T FLIP-FLOP ​

T flip-flop is the simplified version of JK flip-flop. It is obtained by connecting the same input ‘T’ to both inputs of JK flip-flop. It operates with only positive clock transitions or negative clock transitions. This circuit has single input T and two outputs Qn and Qn+1. The operation of the T flip-flop is the same as that of the JK flip-flop. Here, we considered the inputs of JK flip-flop as J = T and K = T in order to utilize the modified JK flip-flop for 2 combinations of inputs. So, we eliminated the other two combinations of J & K, for which those two values complement each other in a T flip-flop.

Qn+1 = T’Q(n) + (Q(n))’T = T XOR Q(n)

MULTIPLEXERS ​

2-1 MUX ​

It selects binary information from one of many input lines and directs the information to a single output line. The selection of a particular input line is controlled by a set of input variables, called selection inputs. there are 2^n input lines and n selection inputs whose bit combinations determine which input is selected. , if the select input S = 0, the output of the multiplexer takes on the values of I 0 , and, if input S = 1, the output of the multiplexer takes on the values of I 1 . Thus, S selects either input I 0 or input I 1 to appear at output Y.
We can see that the equation for the 2–to–1-line multiplexer output Y is
Y = S’I0 + SI1

4-1 MUX ​

The function Y depends on four inputs I 0 , I 1 , I 2 , and I 3 and two select inputs S1 and S0 . By placing the values of I 0 through I 3 in the Y column. Since there are six variables, and only S1 and S0 are fixed, this single row represents 16 rows of the corresponding full truth table. From the table, we can write the equation for Y as
Y = S1’S0’ I0 + S1’S0 I1 + S1S0’I2 + S1S0 I3

S1S2Y
00I0
01I1
10I2
11I3

DEMULTIPLEXERS ​

1:2 DEMUX ​

A 1-to-2 demultiplexer consists of one input line, two output lines and one select line. The signal on the select line helps to switch the input to one of the two outputs. When the select input is LOW, then the input will be passed to Y0 and if the select input is HIGH, then the input will be passed to Y1
Y0 = S’ D
Y1 = S D

PARITY GENERATOR ​

Many systems use a parity bit as a means for bit error detection. Any group of bits contains either an even or an odd number of 1s. A parity bit is attached to a group of bits to make the total number of 1s in a group always even or always odd. An even parity bit makes the total number of 1s even, and an odd parity bit makes the total odd. A parity bit provides for the detection of a single bit error (or any odd number of errors, which is very unlikely) but cannot check for two errors in one group. For instance, let’s assume that we wish to transmit the BCD code 0101. (Parity can be used with any number of bits; we are using four for illustration.) The total code transmitted, including the even parity bit, is

Now let’s assume that an error occurs in the third bit from the left (the 1 becomes a 0)

When this code is received, the parity check circuitry determines that there is only a single 1 (odd number), when there should be an even number of 1s. Because an even number of 1s does not appear in the code when it is received, an error is indicated.

CODE CONVERTER ​

BCD to Binary Code converter ​

The binary numbers representing the weights of the BCD bits are summed to produce the total binary number. The binary equivalent of each BCD bit is a binary number representing the weight of that bit within the total BCD number.

Binary to Gray ​

Conversion between binary code and Gray code is sometimes useful. The following rules explain how to convert from a binary number to a Gray code word:

  1. The most significant bit (left-most) in the Gray code is the same as the corresponding MSB in the binary number.
  2. Going from left to right, add each adjacent pair of binary code bits to get the next Gray code bit. Discard carries

Gray to Binary ​

To convert from Gray code to binary, use a similar method; however, there are some differences. The following rules apply:

  1. The most significant bit (left-most) in the binary code is the same as the corresponding bit in the Gray code.
  2. Add each binary code bit generated to the Gray code bit in the next adjacent position. Discard carries.

COMPARATORS ​

The exclusive-NOR gate can be used as a basic comparator because its output is a 0 if the two input bits are not equal and a 1 if the input bits are equal. The basic comparator can be expanded to any number of bits. The AND gate sets the condition that all corresponding bits of the two numbers must be equal if the two numbers themselves are equal. To determine an inequality of binary numbers A and B, you first examine the highest order bit in each number. The following conditions are possible: 1. If A3 = 1 and B3 = 0, number A is greater than number B. 2. If A3 = 0 and B3 = 1, number A is less than number B. 3. If A3 = B3, then you must examine the next lower bit position for an inequality. These three operations are valid for each bit position in the numbers. The general procedure used in a comparator is to check for an inequality in a bit position, starting with the highest-order bits (MSBs). When such an inequality is found, the relationship of the two numbers is established, and any other inequalities in lower-order bit positions must be ignored because it is possible for an opposite indication to occur; the highest-order indication must take precedence.

Registers ​

A register is a group of flip‐flops, each one of which shares a common clock and is capable of storing one bit of information. An n ‐bit register consists of a group of n flip‐flops capable of storing n bits of binary information. In addition to the flip‐flops, a register may have combinational gates that perform certain data‐processing tasks.

Four‐bit register ​

The common clock input triggers all flip‐flops on the positive edge of each pulse, and the binary data available at the four inputs are transferred into the register. The value of (I3 , I2 , I1 , I0) immediately before the clock edge determines the value of (A3 , A2 , A1 , A0) after the clock edge. The four outputs can be sampled at any time to obtain the binary information stored in the register. The input Clear_b goes to the active‐low R (reset) input of all four flip‐flops. When this input goes to 0, all flip‐flops are reset asynchronously. The Clear_b input is useful for clearing the register to all 0’s prior to its clocked operation. The R inputs must be maintained at logic 1 (i.e., de-asserted) during normal clocked operation. Note that, depending on the flip‐flop, either Clear, Clear_b, reset, or reset_b can be used to indicate the transfer of the register to an all 0’s state.

Four bit register with parallel load**Gi = Ai AND Bi ** ​

A four‐bit data‐storage register with a load control input that is directed through gates and into the D inputs of the flip‐flops. The additional gates implement a two‐channel mux whose output drives the input to the register with either the data bus or the output of the register. The load input to the register determines the action to be taken with each clock pulse.

SHIFT REGISTERS ​

SERIAL IN/SERIAL OUT REGISTERS ​

The serial in/serial out shift register accepts data serially—that is, one bit at a time on a single line. It produces the stored information on its output also in serial form .

Serial In/Parallel Out Shift Registers ​

Data bits are entered serially (least-significant bit first) into a serial in/parallel out shift register in the same manner as in serial in/serial out registers. The difference is the way in which the data bits are taken out of the register; in the parallel output register, the output of each stage is available. Once the data is stored, each bit appears on its respective output line, and all bits are available simultaneously, rather than on a bit-by-bit basis as with the serial output.

Parallel In/Serial Out Shift Registers ​

For a register with parallel data inputs, the bits are entered simultaneously into their respective stages on parallel lines rather than on a bit-by-bit basis on one line as with serial data inputs.

Parallel In/Parallel Out Shift Registers ​

Parallel entry and parallel output of data have been discussed. The parallel in/parallel out register employs both methods. Immediately following the simultaneous entry of all data bits, the bits appear on the parallel outputs.

COUNTERS ​

A register that goes through a prescribed sequence of states upon the application of input pulses is called a counter. The input pulses may be clock pulses, or they may originate from some external source and may occur at a fixed interval of time or at random. The sequence of states may follow the binary number sequence or any other sequence of states.

BINARY RIPPLE COUNTER ​

A binary ripple counter consists of a series connection of complementing flip‐flops, with the output of each flip‐flop connected to the C input of the next higher order flip‐flop. The flip‐flop holding the least significant bit receives the incoming count pulses. A complementing flip‐flop can be obtained from a JK flip‐flop with the J and K inputs tied together or from a T flip‐flop. A third possibility is to use a D flip‐flop with the complement output connected to the D input.The output of each flip‐flop is connected to the C input of the next flip‐flop in sequence. The flip‐flop holding the least significant bit receives the incoming count pulses. The bubble in front of the dynamic indicator symbol next to C indicates that the flip‐flops respond to the negative‐edge transition of the input. The negative transition occurs when the output of the previous flip‐flop to which C is connected goes from 1 to 0.

BCD RIPPLE COUNTER ​

A decimal counter follows a sequence of 10 states and returns to 0 after the count of 9. Such a counter must have at least four flip‐flops to represent each decimal digit, since a decimal digit is represented by a binary code with at least four bits. The sequence of states in a decimal counter is dictated by the binary code used to represent a decimal digit. The four outputs are designated by the letter symbol Q, with a numeric subscript equal to the binary weight of the corresponding bit in the BCD code. Note that the output of Q1 is applied to the C inputs of both Q2 and Q8 and the output of Q2 is applied to the C input of Q4. The J and K inputs are connected either to a permanent 1 signal or to outputs of other flip‐flops.

4 BIT SYNCHRONOUS BINARY COUNTER ​

The flip‐flop in the least significant position is complemented with every pulse. A flip‐flop in any other position is complemented when all the bits in the lower significant positions are equal to 1 . Synchronous binary counters have a regular pattern and can be constructed with complementing flip‐flops and gates. The C inputs of all flip‐flops are connected to a common clock. The counter is enabled by Count_enable. If the enable input is 0, all J and K inputs are equal to 0 and the clock does not change the state of the counter. The first stage, A0, has its J and K equal to 1 if the counter is enabled. The other J and K inputs are equal to 1 if all previous least significant stages are equal to 1 and the count is enabled. The chain of AND gates generates the required logic for the J and K inputs in each stage. The counter can be extended to any number of stages, with each stage having an additional flip‐flop and an AND gate that gives an output of 1 if all previous flip‐flop outputs are 1. Note that the flip‐flops trigger on the positive edge of the clock.

FOUR BIT UP-DOWN BINARY COUNTER ​

The two operations can be combined in one circuit to form a counter capable of counting either up or down. It has an up control input and a down control input. When the up input is 1, the circuit counts up, since the T inputs receive their signals from the values of the previous normal outputs of the flip‐flops.

BINARY COUNTER WITH PARALLEL LOAD ​

When equal to 1, the input load control disables the count operation and causes a transfer of data from the four data inputs into the four flip‐flops. If both control inputs are 0, clock pulses do not change the state of the register. The carry output becomes a 1 if all the flip‐flops are equal to 1 while the count input is enabled. This is the condition for complementing the flip‐flop that holds the next significant bit. The carry output is useful for expanding the counter to more than four bits. The speed of the counter is increased when the carry is generated directly from the outputs of all four flip‐flops, because the delay to generate the carry bit is reduced. A counter with a parallel load can be used to generate any desired count sequence.the Count control is set to 1 to enable the count through the CLK input. Also, recall that the Load control inhibits the count and that the clear operation is independent of other control inputs.

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ARITHMETIC LOGIC UNIT (ALU) ​

The ALU, or arithmetic logic unit, is a crucial component of the CPU (central processing unit) in a computer system. It is responsible for carrying out arithmetic and logic operations. Also referred to as the integer unit (IU), it is an integrated circuit found in both CPUs and GPUs. The ALU is the final stage in the processor where calculations are performed. It possesses the capability to handle various tasks related to arithmetic and logic operations, including addition, subtraction, shifting operations, as well as Boolean comparisons such as XOR, OR, AND, and NOT operations. It operates on binary numbers and can execute mathematical and bitwise operations. The ALU consists of two units: the arithmetic unit (AU) and the logic unit (LU). By utilizing operands and codes, the ALU determines which operations to perform based on the input data provided. Once the ALU completes processing the input, the resulting information is sent to the computer's memory.

Here are the main functions of an ALU:

Arithmetic Operations: The ALU performs various arithmetic operations on binary numbers, such as addition, subtraction, multiplication, and division. It uses binary addition and subtraction circuits to handle these operations efficiently.

Logical Operations: The ALU executes logical operations on binary data, including AND, OR, XOR (exclusive OR), and NOT. These operations manipulate individual bits or binary values to determine logical relationships and produce logical results.

Comparison Operations: The ALU performs comparison operations to determine the relationship between two binary values. It can compare if two values are equal, not equal, greater than, less than, greater than or equal to, or less than or equal to each other. The result of these comparisons is typically represented by setting specific flags or registers in the CPU.

Bitwise Operations: The ALU carries out bitwise operations, which manipulate individual bits in binary numbers. These operations include shifting the bits left or right, rotating bits, and masking operations. Bitwise operations are commonly used in tasks such as data manipulation, encryption, and signal processing.

Conditional Operations: The ALU supports conditional operations, enabling the CPU to execute different instructions based on certain conditions. For example, it can perform conditional branching, where the CPU jumps to a specific instruction address based on the result of a comparison operation.

Data Movement: The ALU may also handle data movement operations within the CPU. This involves transferring data between registers, memory, and other CPU components.

ENCODER ​

An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2n (or fewer) input lines and n output lines.

PRIORITY ENCODER ​

A priority encoder is an encoder circuit that includes the priority function. The operation of the priority encoder is such that if two or more inputs are equal to 1 at the same time, the input having the highest priority will take precedence. In addition to the two outputs x and y , the circuit has a third output designated by V ; this is a valid bit indicator that is set to 1 when one or more inputs are equal to 1. If all inputs are 0, there is no valid input and V is equal to 0. The other two outputs are not inspected when V equals 0 and are specified as don’t-care conditions.

x = D2+ D3
y = D3 + D1 D 2
V = D0 + D1 + D2 + D3

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DECODER ​

A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines.The decoders presented here are called n -to- m -line decoders, where m … 2^n.

3-8 LINE DECODER ​

The three inputs are decoded into eight outputs, each representing one of the minterms of the three input variables. The three inverters provide the complement of the inputs, and each one of the eight AND gates generates one of the minterms.

2-4 LINE DECODER WITH ENABLE INPUT ​

The circuit operates with complemented outputs and a complement enable input. The decoder is enabled when E is equal to 0 (i.e., active-low enable). As indicated by the truth table, only one output can be equal to 0 at any given time; all other outputs are equal to 1. The output whose value is equal to 0 represents the minterm selected by inputs A and B . The circuit is disabled when E is equal to 1, regardless of the values of the other two inputs. When the circuit is disabled, none of the outputs are equal to 0 and none of the minterms are selected.

HOW TO MAKE A VERILOG PROGRAM ​

Create a New Project in your own version of Quartus Prime. ​

Select an appropriate directory for your Verilog project files and create an empty project file template. ​

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Use the 10M50DAF484C7G Board from the MAX 10 Family. ​

Set ModelSim as your Simulation Tool (ModelSim must be installed prior) and finish the initialization of the project. ​

Click on the file icon in the top left corner and create a new Verilog HDL file. ​

When you wish to save your program, simply use Ctrl+S or click the Save icon in the top left corner. ​

Before running your program, you must first set a testbench for it. Do this by going into the Assignments menu and clicking Settings. ​

Create a new Test Bench if you are creating one for a new program that has not been made before. ​

Name your Test Bench appropriately (usually just the name of the test bench file) and add it to the list of Test Benches. ​

After setting your testbench, you can now run and compile your program by clicking on the third play button. ​

You will be able to view your circuit design and how it is structured, and simulate results using the test bench by going to the Tools menu. ​

BIBLIOGRAPHY ​

  1. Digital Design, 5th Edition by M Morris Mano and Michael Ciletti
  2. Digital Fundamentals by Floyd and Jain
  3. electronicshub.org/demultiplexerdemux
  4. tutorialspoint.com/digital_circuits/digital_circuits_flip_flops
  5. tutorialspoint.com/digital_circuits/digital_circuits_demultiplexers

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