You are to design a 1-bit full adder stage. The inputs are the 2 bits A and B to be added and the carry in, called Cin. The outputs are the sum (S) and the carry out (Cout).

a) Show the truth table of your circuit. Make sure you show all inputs and outputs.

b) Write the equations for S and Cout in canonical form

c) Write the minimized equations for S and Cout. Use any method you wish but make sure you show your work.

d) Use a 3-to-8 active high decoder and OR gate to implement the S and Cout functions

e) Using two 4-to-1 multiplexers, build 2 circuits that implement S and Cout. Make sure you specify the order of your input lines (Most Significant (MSB) and Least Significant (LSB) lines).