a) Suppose we are given a 4:1 multiplexer but we wanted to use it as a 2:1 multiplexer. Show how that conversion could be made. (4 points) b) Show how you can implement a 4.1 multiplexer using any number of 2.1 multiplexers. (4 points) c) Implement the 2-input function F = A'B' + AB using a 2:1 multiplexer and any additional gates. Now implement the same function using a 4.1 multiplexer and any additional gates if necessary. (8 points) d) Given the 3-input function F = A'B'C + ABC + A'BC + AB'C, design the circuit for Fusing a 3:8 decoder using 1-HOT logic and any gates necessary. Then show how the same function could be implemented using a 0- COLD logic 3:8 decoder. (8 points) e) Given the function having 3 inputs X,Y.Z and single output F having the equation F = (X xor Z) + Y. i) Obtain the truth table for the function F. (2 points) ii) Design the circuit for Fusing a 3:8 decoder using 1-HOT logic and a SINGLE 2-input NOR gate. (HINT: A 3:8 1-HOT decoder and a single gate can implement F') (4 points)