Sign and Magnitude Subtract

Suppose we must subtract two positive numbers, x and y to get x−y. We 1’s complement y getting −y−1 and add x getting x−y−1. If our adder produces (both/either) p+q and p+q+1 from p and q then in the case at hand we will also have (x−y−1)+1 = x−y which is what we wanted.