What is “2's Complement”?

Question

I\'m in a computer systems course and have been struggling, in part, with Two\'s Complement. I want to understand it but everything I\'ve read hasn\'t brought the p

Answer 1

To bitwise complement a number is to flip all the bits in it. To two’s complement it, we flip all the bits and add one.

Using 2’s complement representation for signed integers, we apply the 2’s complement operation to convert a positive number to its negative equivalent and vice versa. So using nibbles for an example, 0001 (1) becomes 1111 (-1) and applying the op again, returns to 0001.

The behaviour of the operation at zero is advantageous in giving a single representation for zero without special handling of positive and negative zeroes. 0000 complements to 1111, which when 1 is added. overflows to 0000, giving us one zero, rather than a positive and a negative one.

A key advantage of this representation is that the standard addition circuits for unsigned integers produce correct results when applied to them. For example adding 1 and -1 in nibbles: 0001 + 1111, the bits overflow out of the register, leaving behind 0000.

For a gentle introduction, the wonderful Computerphile have produced a video on the subject.