Design a combinational circuit with 3 inputs, x, y, and z, and three outputs, A, B, and C. when the binary input is 3, 4, 5, 6, or 7, the binary output is one less than the input. When the binary input is 0,1, or 2, the binary output is two greater than the input.

a. Provide a truth table of the combinational circuit.

b. Use Karnaugh maps to simplify each output.

c. Draw the logic diagram to implement this circuit.