1. (16 point + 5 points bonus) Design a combinational circuit with three inputs, x, y, and z, and three outputs, A, B, and C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input. Find the following: a) Truth table (5 points) b) Logic circuit (5 points + 5 points bonus) (Bonus: if you submit a .circ file using Logisim for this part. Name it Q1b.circ.) c) Boolean function of A using minterms (2 points) d) Boolean function of B using maxterms (2 points) e) Boolean function of C using literals x,y,z and NAND gates (2 points) 2. (10 point + 5 points bonus) Design a four-bit combinational circuit 2's complementer. (The output generates the 2's complement of the input binary number.) Show that the circuit can be constructed with exclusive-OR gates. Can you predict what the output functions are for a five-bit 2's complementer? Find the following: a) Truth table (5 points) b) Logic circuit with exclusive-OR gates (5 points) c) The output functions for a five-bit 2's complementer (5 points bonus) About Question 2. Part b: Notice that since the Exclusive-or is not a universal gate, we cannot replace all logic gates by just exclusive-or gates. If we use exclusive-or gates , the final circuit in Q.2b will have fewer gates than SOP or POS forms including XOR and the other type of gates)