Design a four$-$input $($A$,$ B$,$ C$,$ D$)$ and one$-$output $($Z$)$ combinational circuit, where the

inputs AB represents a $2-$bit binary number and the inputs CD represent another $2-$bit number. The output Z is

$1$ if AB and CD are equal; otherwise, Z$=0.$ Show your work to get credit.

a$.(4$ pts$)$ Construct a truth table for the circuit.

b$.(11$ pts$)$ Find all prime implicants and essential prime implicants using K$-$map. Write a simplified

sum$-$of$-$products expression.

Prime Implicants $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Essential Prime Implicants $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Output Z $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$