An (in my opinion) easier way to remember the bit representation is to remember that a positive number and its negative counterpart should add to 0. But zero is

An (in my opinion) easier way to remember the bit representation is to remember that a positive number and its negative counterpart should add to 0. But zero is congruent to 2^b (where b is the number of bits). So equivalently, a number and its negative counterpart should add up to 2^b (since bits can’t add to 0). Then, suppose we take a positive number x and invert all its bits to get y. Then x + y = 1111… = 2^b-1. So if we choose one of x or y to represent with +1 in its bit representation, they will be positive/negative counterparts. It’s easier to keep positive numbers having the same representation as unsigned, so we choose to represent the bit value of -x with +1.