Problem A Multi-Function Gate consists of a combinational circuit in which the function performed changes according to its control signal(s). The diagram below illustrates a Multi-Function Gate consisting of 3 inputs, 2 control signals, and a single output. Multi-Function GateF Design a Multi-Function Gate such that the function performed with inputs A, B, C changes according to control signals X, Y as the table states below. X Y Function 01NAND 11 NOR 0 AND Prelab 1. Derive a truth table and K-map such that all possible outcomes from the problem stated above are included. Obtain the simplified Boolean expression in both SOP and POS forms for the derived K-map. 2. 3. Draw the circuit diagram for both SOP and POS expressions. 4. Find the lowest cost circuit