(1) Draw a half-adder using only NAND gates. (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 = 011 outputs 110; 4 = 100 outputs 001.) Show your truth table, all computations for simplification, and the final circuit (3) Draw the combinational circuit that directly implements the following Boolean expression: F(x, y, z) = x + xy + yz (4) Find the truth table that describes the following circuit: poby (5) How many inputs does a decoder have if it has 64 outputs