4. [25 points] Prove that NOR gate is universal, by showing how AND, OR, and NOT gates can be built by wiring a bunch of NOR gates. Draw the wire diagram for each case. 1. [25 points] Given the following truth table, where X, Y, and Z are input and Wis output, write the canonical expression and generate gate-level logical circuit (draw the wire diagram). X Y Z W 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 2. [25 points] Simply the following Boolean expressions as much as you can. a) Y=BC+-A-B-C +B-C b) Y=-(A+-AB+-A-B) +-(A+-B)