Design circuit with output f and inputs x1, x0, y1, and y0, Let X = x1x0 be a number, where the for possible values of X, namely, 00,01, 10, and 11, represent the four number 0, 1,2, and 3, respectively. (We discuss representation of number in Chapter 5.) Similarly, let Y = y1y0 represent another number with the same four possible values. The output f should be 1 if the numbers represented by X and Y are equal. Otherwise. f should be 0.

(a) Show the truth table for f.

(b) Synthesize the simplest possible product-of-sums expression for f.