Why is the maximum value of an unsigned n-bit integer 2^n-1 and not 2^n?

Question

The maximum value of an n-bit integer is 2ⁿ-1. Why do we have the \"minus 1\"? Why isn\'t the maximum just 2ⁿ?

Answer 1

The numbers from 0 to N are not N. They are N+1. This is not obvious to the majority of people and as a result many programs have bugs because if this reason.