1. Prove the consensus theorem: XY+ IZ+1Z- XY +X'Z 2. Please use algebraic method to get the product-of-sums format for the following expression: 3. Find F and simply: 4. Design a parallel 4-bit adder. (Hint: design a 1-bit full adder first, then connect them together) 0 4-bit Parallel Adder 0 A3 B3 A2 B2 A1 B1 Ao Bo 5. Please design the following multiple outputs by sharing gates among them to reduce the cost. fila,b,c,d)-m(23,5,7,8,9,10,1113,15) f(a, b,c,d)-2m(2,3,5,6,7,10,111415) f(a,b,c,d)-(6,7,8,91314.15)