Q3 (60 pts):

Part A: Use the truth table to prove the validity of the expression: Overflow =

Part C: Prove the validity of the expression for the overflow flag in the addition of n-bit signed numbers:

Cn Cn-1 for addition of n-bit signed numbers. Hint: construct first the truth table for both Overflow and Cr, as a function of xn-1, Yn-1, and on-1. Part B: Please prove that the carry-out signal, ck, from bit position k 1 of a ripple-carry adder can be expressed as Ck = xk yksk, where xk and ykare the two inputs and sk is the sum bit, at the bit position k. Hint: consider the fact Sk = xx@yxOck when simplifying expression xx@yxOsk f = Xn-1 Oyn-10sn-10cn