Design a circuit with output f and inputs x 1 , x 0 , y 1 ,

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Design a circuit with output f and inputs x1, x0, y1, and y0. Let X = x1xand Y = y1yrepresent two 2-digit binary numbers. 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.

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