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London | Elhadj Abdoul Diallo | Module-Tools | WEEK1- Number-systems #17

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London | Elhadj Abdoul Diallo | Module-Tools | WEEK1- Number-systems #17

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1b9d1aa
add answer for 14(decimal) to binary.
Feb 26, 2025
c733455
Add image for decimal to binary conversion of 14
Feb 26, 2025
bfa723c
Add conversion from binary 101101 to decimal and include correspondin…
Feb 26, 2025
eff9c73
Update README to correct answer for comparison between 1000 and 0111
Feb 26, 2025
4684c53
Update README to correct answer for comparison between 00100 and 01011
Feb 26, 2025
44b1b52
Update README to provide answer for addition of 10101 and 01010
Feb 26, 2025
0a98247
Update README to provide answer for addition of 10001 and 10001
Feb 26, 2025
f32f1d6
Update README to correct answer for largest number storable with 4 bits
Feb 26, 2025
c264635
Update README to provide answer for number of bits needed to store nu…
Feb 26, 2025
2631663
Update README to provide answer for number of bits needed to store nu…
Feb 26, 2025
39fad99
Update README to provide answer for number of bits needed to store nu…
Feb 26, 2025
071ae76
Update README to explain how to determine if a binary number is a pow…
Feb 26, 2025
d21ffbe
Add image and answer for converting decimal 14 to hex in README
Feb 26, 2025
d2955f8
Add image and answer for converting decimal 386 to hex in README
Feb 26, 2025
4829402
Add image and update answer for converting hex 386 to decimal in README
Feb 26, 2025
b810975
Update README with the decimal conversion answer for hex B
Feb 26, 2025
963ac76
Update README with the decimal conversion answer for byte 0x21
Feb 26, 2025
b3ce03f
Update README with ASCII character representation for byte 0x21
Feb 26, 2025
951f371
Update README with greyscale color interpretation for byte 0x21
Feb 26, 2025
15be59c
Update README with RGB color interpretation for bytes 0xAA00FF
Feb 26, 2025
05a80ca
Update README with decimal conversion for bytes 0xAA00FF
Feb 26, 2025
a1a5272
Update README with hex representation for decimal number 386
Mar 2, 2025
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47 changes: 26 additions & 21 deletions number-systems/README.md
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Expand Up @@ -5,61 +5,66 @@ Do not convert any binary numbers to decimal when solving a question unless the
The goal of these exercises is for you to gain an intuition for binary numbers. Using tools to solve the problems defeats the point.

Convert the decimal number 14 to binary.
Answer:
Answer: 1110
![answer-1](14-decimal-binary.png)
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praise: It is a real pleasure to see you include your working here, you've employed a very reliable method for working these out consistently!


Convert the binary number 101101 to decimal:
Answer:
Convert the binary number 101101 to decimal.
Answer: 45
![alt text](101101-to-decimal.png)

Which is larger: 1000 or 0111?
Answer:
Answer: 1000

Which is larger: 00100 or 01011?
Answer:
Answer: 01011

What is 10101 + 01010?
Answer:
Answer: 11111

What is 10001 + 10001?
Answer:
Answer: 100010

What's the largest number you can store with 4 bits, if you want to be able to represent the number 0?
Answer:
Answer: 15

How many bits would you need in order to store the numbers between 0 and 255 inclusive?
Answer:
Answer: 8

How many bits would you need in order to store the numbers between 0 and 3 inclusive?
Answer:
Answer: 2

How many bits would you need in order to store the numbers between 0 and 1000 inclusive?
Answer:
Answer: 10

How can you test if a binary number is a power of two (e.g. 1, 2, 4, 8, 16, ...)?
Answer:
Answer: A binary number is a power of two if it has exactly one '1' bit and all other bits are '0'. For example, 1 (0001), 2 (0010), 4 (0100), 8 (1000), etc.

Convert the decimal number 14 to hex.
Answer:
Answer: E
![alt text](14-to-hex.png)

Convert the decimal number 386 to hex.
Answer:
Answer: 182
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nitpick: One of the problems with hex numbers are that they often look like decimal ones, so we can avoid this ambiguity here by using 0x182

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I agree, thank you for bringing this up. I am going to update it.

![alt text](386-to-hex.png)
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praise: I've never done this manually so it's really useful to see this method illustrated!


Convert the hex number 386 to decimal.
Answer:
Answer: 902
![alt text](386-hex-to-decimal.png)

Convert the hex number B to decimal.
Answer:
Answer: 11

If reading the byte 0x21 as a number, what decimal number would it mean?
Answer:
Answer: 33

If reading the byte 0x21 as an ASCII character, what character would it mean?
Answer:
Answer: !

If reading the byte 0x21 as a greyscale colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
Answer:
Answer: A greyscale value of 0x21 corresponds to a dark grey colour.

If reading the bytes 0xAA00FF as an RGB colour, as described in "Approaches for Representing Colors and Images", what colour would it mean?
Answer:
Answer: The RGB colour would be a shade of magenta, with red at 170 (0xAA), green at 0 (0x00), and blue at 255 (0xFF).

If reading the bytes 0xAA00FF as a sequence of three one-byte decimal numbers, what decimal numbers would they be?
Answer:
Answer: 170, 0, 255