Question

Suppose A and B are signed numbers, find the logic expression of the overflow flag when A and B are added. R = result. (Hint: Recall that overflow happens to signed addition if and only if 1) adding two positives and getting a negative, or 2) adding two negatives and getting a positive.)

A = a₃₁a₃₀a₃₀…a₂a₁a₀

B = b₃₁b₃₀b₃₀…b₂b₁b₀

R = r₃₁r₃₀r₃₀…r₂r₁r₀

Answer 1

Recall that overflow happens to signed addition if and only if

1) adding two positives and getting a negative

if you assume carry of kth bit is ck, This case arises when ck-1 is 1 and ck is 0

2) adding two negatives and getting a positive.

If a ck-1 = 0 , then the only way that 1 can be carried out is if x_k-1 = 1 and y_k-1 = 1. That way, the sum is 0, and the carry out is 1. This is the case when you add two negative numbers, but the result is non-negative

from these two cases Overflow can be written as O =