diff --git a/number-systems/101101-to-decimal.png b/number-systems/101101-to-decimal.png new file mode 100644 index 0000000..d136268 Binary files /dev/null and b/number-systems/101101-to-decimal.png differ diff --git a/number-systems/14-decimal-binary.png b/number-systems/14-decimal-binary.png new file mode 100644 index 0000000..98869bb Binary files /dev/null and b/number-systems/14-decimal-binary.png differ diff --git a/number-systems/14-to-hex.png b/number-systems/14-to-hex.png new file mode 100644 index 0000000..41c1e21 Binary files /dev/null and b/number-systems/14-to-hex.png differ diff --git a/number-systems/386-hex-to-decimal.png b/number-systems/386-hex-to-decimal.png new file mode 100644 index 0000000..58ca01e Binary files /dev/null and b/number-systems/386-hex-to-decimal.png differ diff --git a/number-systems/386-to-hex.png b/number-systems/386-to-hex.png new file mode 100644 index 0000000..4655298 Binary files /dev/null and b/number-systems/386-to-hex.png differ diff --git a/number-systems/README.md b/number-systems/README.md index 77a3bde..8d5c269 100644 --- a/number-systems/README.md +++ b/number-systems/README.md @@ -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) -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: 0x182 +![alt text](386-to-hex.png) 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