please include your work for both question 1, 2 and 3p

1. Complete the truth table for the circuit below. It has four inputs (w, x, y, z) and two outputs (C, S). (16 points) DEcoDES ADDe 3 0 0 0 0 2(a) Write a Boolean expression in sum of product form for the following truth table. (10 points) 0 0 0 0 0 0 0 0 0 0 0 2(b) Implement a logic circuit diagram, using AND and OR gates, for the function represented in the truth table in 2(a). (10 points) 2(c) Implement a logic circuit diagram, using only NAND gates, for the function represented in the truth table in 2(a). (10 points) 3. Simplify the following Boolean expressions using Boolean algebra properties. 9+9 points) (A + C)(AD + AD') + AC + C A BC A'BC+ABC [Note that "D" is complemented in ADI