Please clearly show the proof and the answer. thank you very much.

HW 17.4 Construct a FA using only HA's and one other gate. Solution Cout Design: using HA1 HA2 S1+ in in S1 S2 S2 AS S1 HA1 C1 HA2 B Cout C2 B Cout In Cout Note: We would think we need to add C and C2. Do we? Not if they may not be both -1. Let's see: A=1 Suppose C1- 1 --> & > Si 0 0 So:C1 and C2 may not be both 1--> use OR gate. > 2 We can also prove the diagram is correct by substituting the functions in the diagram: HA: S A'B AB Prove we qet: HW 18.1 - assigned Continue this proof. Show S = S2 and Cout CABAC+BC -1 + C2