This question is concerned with the optimization of logic functions using combinational circuit components. Use the cost definition of logic circuits presented in the course. Suppose that the input variables are not available in their complemented form. Derive a minimum-cost realization of the four-variable function that is equal to 1 if any three or all four of its variables are equal to 1 (called the majority function). Use Karnaugh maps to minimize the function and implement the circuit using NAND gates only, with a maximum fan-in of 4. Provide the final cost of the circuit.

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