[M] A number code in which consecutive numbers are represented by binary patterns that differ only in one bit position is called a Gray code. A truth table for a 3-bit Gray code to binary code converter is shown in Figure PA.2a. (a) Implement the three functions f1, f2, and f3 using only NAND gates (draw the logic circuit). (b) A lower-cost network for performing this code conversion can be derived by noting the following relationships between the input and output variables. f1 = a f2 = f1 b f3 = f2 c Using these relationships, specify the contents of a combinational network N that can be repeated, as shown in Figure PA.2b, to implement the conversion. Compare the total number of NAND gates required to implement the conversion in this form to the number required in part (a).

(a) Three-bit Gray code to binary code conversion (b) Code conversion network Figure PA.2 Gray code conversion example for Problem A.14