Binary Values and Ranges

A bit is a single binary digit, so it has only two patterns: 0 or 1. Adding a second bit lets each pattern so far be extended with a 0 or a 1, so the count of patterns doubles. Add a third bit and it doubles again. That is why the number of binary patterns grows by a factor of two with every extra bit.

Counting patterns and the largest value

For n bits, the number of different patterns is 2 to the power n. Counting starts at zero, so the largest value is 2 to the power n minus 1: one of the patterns is spent on zero, which puts the top value one below the total count.

For example, 12 bits give 2 to the power 12 = 4096 patterns, running from 0 to 4095, so 12 bits are enough for any whole number smaller than 4096.

The 8-bit range

With 8 bits there are 2 to the power 8 = 256 patterns, so the denary values run from 0 to 255. The same range written in binary is 00000000 to 11111111, and in hexadecimal it is 00 to FF.

Only positive whole numbers are covered here: negative numbers, two's complement, sign and magnitude and binary fractions are not required.