Design a combinational circuit with three inputs x, y, and z, and three outputs, A, B, and C. When the binary input formed from xyz is 0, 1, 2, or 3, the binary output produced by ABC is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input. Produce truth tables, and simplified algebraic forms, followed by circuits for the simplified algebraic representations.