1. (50 points) Design the simplest circuit that has four inputs, a, b, c, and d, which produces an output value of 1 whenever three or more of the input variables have the value 1; otherwise, the output has to be 0. You can only use AND gates and OR gates with any number of inputs and NOT gates. Let the cost of a logic circuit be the total number of gates plus the total number of inputs to all gates in the circuit. What is the cost of your circuit? 2. (50 points) Derive a minimum cost realization of the four variable function that is equal to 1 if exactly two or exactly three of its variables are equal to 1; otherwise it is equal to 0. You can only use NOR gates with any number of inputs and NOT gates. Let the cost of a logic circuit be the total number of gates plus the total number of inputs to all gates in the circuit. What is the cost of your circuit?