Question 1: Combinational Logic (15 points) Consider a combinational logic circuit which pets two 2-hit unsignedIntegers And 8-B, as inputs, and produce a single bit Fas the output The F is / if the absolute difference of A and B is an even integer, and otherwise. a) Construct the truth table for the output points) lapel Output F . . 0 1 0 . 1 0 1 1 1 0 0 1 0 + . 1 . 0 1 . 1 1 . . 1 1 1 . . 1 1 1 1 . 1 1 1 2 b) Derive the Boolean expeession for the output F in the inputs. A. A. Bund B. (Le. A A. B. B.) in both Sum-of-Product (SP) and Product-of-Sam Pos formats with minterms and masterms respectively (4 points) c) Use K-map below to simplify the SoP representation for the circuit. Show all the groups in the K-map clearly. Then write the expression in its simplest form. (3 points) 00 01 11 10 44 00 01 11 10 d) Implement the simplified logic equation using AND, OR, NOR gates only. Indicate clearly the inputs A1, A, B1, and B, and the output Fin the circuit. Note: You can use at most 3 gates. If you use more than that and your logic is correct, you will get 2 points. If you use gates other than the allowed AND, OR, NOR gates, or if the logic is incorrect, you will get zero point. You can draw the circuit yourself below. Alternatively you can also draw the circuit using the Logisim software we taught during the lab and paste the picture below. (4 points)