In this problem, we guide you through the process of designing a circuit that computes S = 2X Y, where X and Y are 3-bit signed inputs represented in 2's complement.

(a) (1 point) What is the minimum value of S?

(b) (1 point) What is the maximum value of S?

(c) (1 point) What is the range of S?

(d) (1 point) How many bits should S be such that the circuit never overflows?

(e) (2 points) Show the implementation of this circuit using full adders. Remember to properly extend X and Y to avoid overflow of S.

(f) (1 point) Use design-by-contraction technique to reduce the hardware of the circuit you obtained in Part (e).

INSTRUCTIONS: Solve by hand (or using your tablet) and upload a scanned image of your answer. You scanned image MUST be crystal clear. If your image is not clear, you will get ZERO in this quiz. Check your image clarity before submission.