diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde..112b236 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -5,61 +5,61 @@ 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 Convert the binary number 101101 to decimal: -Answer: +Answer: 45 Which is larger: 1000 or 0111? -Answer: +Answer: 1000 (We compare bit by bit from the left. First 1 > 0) Which is larger: 00100 or 01011? -Answer: +Answer: 01011 (We compare bit by bit from the left. Second 1 > 0) 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 (decimal system), 1111 (binary system) How many bits would you need in order to store the numbers between 0 and 255 inclusive? -Answer: +Answer: we need 8 bits (11111111(binary) = 255 (decimal)) How many bits would you need in order to store the numbers between 0 and 3 inclusive? -Answer: +Answer: we need 2 bits (11(binary) = 3(decimal)) How many bits would you need in order to store the numbers between 0 and 1000 inclusive? -Answer: +Answer: we need 10 bits (1111101000(binary) = 1000(decimal)) 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 only one '1' bit. Convert the decimal number 14 to hex. -Answer: +Answer: E Convert the decimal number 386 to hex. -Answer: +Answer: 182 Convert the hex number 386 to decimal. -Answer: +Answer: 902 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: dark gray 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: purple 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