Design a circuit with three inputs (x,y and z) representing the bits in a binary num

ber, and three outputs (a,b and c) also representing bits in a binary num

ber. (Assume unsigned binary representation.) When the input is decimal 0, 1, 2, or 3, expressed in binary, the output should be one more than the input. When the input is 4, 5, 6, or 7, the output should be one less than the input. Show your truth table, the Boolean function for the above circuit, and the final circuit (using only OR gates, AND gates, and NOT gates) we need a circuit that correctly implements the functionality (and not necessarily themost efficient circuit).