Problem 1) Model each of the following functions using three different techniques (1- Using discrete logic gates with optimization, 2- Using a Decoder, 3- Using a Multiplexer). While designing, specify the PIs and EPIs. You should also design the decoders and multiplexers used in these models:
a. F(A,B,C) = Σm(0, 2, 4, 7) + Σd(5, 6)
b. G(x,y,z) = Î M(1, 2, 4) + Î d(0, 3, 5)
c. W(A,B,C,D) = Σm(0, 2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15)
Problem 2) Evaluate the cost of all the models designed in Problem 1 and order them based on the cost.