4.5 Ranges of numbers

Although modulo-2ⁿ implies that an n-bit number can be used to represent any range of 2ⁿ numbers, there are only two ranges that are practical.

For unsigned numbers, an n-bit number represents integers from 0 (all bits 0) to 2ⁿ - 1. This means that a 4-bit unsigned integer can represent 0 to 15.

For signed numbers, an n-bit number represents integers from -2^n-1 to 2^n-1 - 1. In our example, a 4-bit signed integer can represent -8 to 7. Note that it may seem that the non-negative side is missing a number. This is because 0 is considered non-negative.