Information Representation

Number bases

Computers store everything in binary (base 2), using only the digits 0 and 1. We also use denary (base 10) for humans and hexadecimal (base 16) as a compact way of writing binary — each hex digit represents exactly four bits (a nibble).

To convert binary → denary, add the place values where a 1 appears. For an 8-bit number the place values are 128 64 32 16 8 4 2 1. For example 01001011 = 64 + 8 + 2 + 1 = 75.

To convert denary → binary, repeatedly subtract the largest place value that fits, or repeatedly divide by 2 and read the remainders bottom-up.

To convert binary → hex, split into nibbles from the right and write each as one hex digit: 1011 0110 = B6. To convert hex → denary, multiply each digit by its power of 16: B6 = 11×16 + 6 = 176 + 6 = 182.