1. (40 points) Given a 3-input function F(A,B,C) =m(1,4,5,6,7). Assume that AND gates and OR gates of any number of inputs and NOT gates can be used. 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. Show your steps in the following questions.

(a) (20 points) Implement F using one 4-to-1 MUX and a minimal number of basic gates.Assume the MUX is implemented as in Fig. 4.2. What is the total cost of your implementation(including the gates inside the MUX)?In this question, you should minimize the cost of yourimplementation by determining the best inputs to be used as the select inputs to the MUX.

(b) (20 points) Implement F using one 8-to-1 MUX and a minimal number of basic gates.Assume the MUX is implemented using the idea in Fig. 4.1 and Fig. 4.2 but extend to a 8-to-1MUX. What is the total cost of your implementation (including the gates inside the MUX)?