1. Given the combinational logic diagram below, with inputs x, y, and z and output F: Drs a) Construct the truth table for this logic diagram a) Find the most simplified Boolean function to implement that logic (Show all computations for simplification. You can use identities or K-map, your choice! 2. Design a circuit with three inputs (x, y, and z) representing the bits in a binary number, and three outputs (a, b, and c) also representing bits in a binary number. When the input is 0, 1, 6, or 7, the binary output will be the complement of the input. When the binary input is 2, 3, 4, or 5, the output is the input shifted left with rotate. (For example, 3 = 0112 outputs 110; 4 = 1002 outputs 001): a) Construct the truth table for this design b) Find the most simplified Boolean function (Show all computations for simplification. You can use identities or K-map, your choice) c) Show the final digital circuit to implement your simplified Boolean function from step b)