How to Represent Signed Integers?

If you need to add one positive and one negative number, you'll perform subtraction.

Example: Adding the $6$-bit numbers $-6_{10} = 100110_2$ and $13_{10} = 001101_2$ requires to subtract $6_{10}$ from $13_{10}$:

0   01101
1 - 00110
    _____
0   00111

The result we got is $-6 + (+13) = +7$.

The sign bit of the resulting number is always the sign bit of the number with the bigger magnitude from those we are adding: since $|+13| > |-6|$, the sign is positive (= $0$.)