(b) [1 mark] Let 3: and y be two numbers encoded in 71bit 2's complement, such that at lt; 0 and y 2 0. Clearly, the sum 3: + 3; cannot generate an...

(b) [1 mark] Let 3: and y be two numbers encoded in 71—bit 2’s complement, such that at < 0 andy 2 0. Clearly, the sum 3: + 3; cannot generate an overflow because the magnitude of the result ismoving closer to 0.Writing the binary equivalent of a: with an MSB of 1 and y with an MSB of 0, there are two casesto consider: 3::y: n—+ E.— 1+ 0 E Either (Case 1) the caer in to the MSB equals 0, or (Case 2) the carrz in to the MSB equals 1.Show that the overflow rule holds in either case, i.e., that the carry in equals the carry out. [2 marks] Continuing with the same notation in part (b), there are 4 more cases to consider:where a: and y are both negative or both positive, combined with whether or not the carry in tothe MSB equals 0 or 1.Prove that the overflow rule holds in all 4 cases, i.e., that the carry in equals the carry out if andonly if overflow did not occur.