On a separate sheet of paper, 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 1, 2 or 3, the binary output should be one less than the input. When the binary input is 4,5, or 6, the binary output should be one greater than the input. Ignore inputs 0 and 7. Show only the truth table.