Show your work to receive full credit. 1. F=(A+C+D)(A+B+D)(A+C+D)(B+C+D)(5.5 points +1 extra credit point) a. Create the truth table for this equation [1 point] b. Implement this function using a 16:1 multiplexer [1.5 points] c. Implement this function using an 8:1 multiplexer and any additional gates needed [1.5 points] d. Implement this function using a 4:1 multiplexer and any additional gates needed [1.5 points] e. Demonstrate the internal logic of a 2:1 multiplexer using gates. Explain how you know the circuit works. (Video submission is on Canvas) 2. Consider the Full Adder logic expressions S=(AB)CIN and COUT=AB+ (AB)CIN, where A,B, and CIN are the data inputs and carry-in input respectively while S and Cout are the sum and carry-out output respectively. (2.5 points) a. Fill in the truth table [1 nointl b. Implement the logic expressions S and Cout using 2:1 multiplexers with C1N as the selector bit. [1.5 points] 3. Using Boolean algebra, show that the 2 Half Adder implementation of the Full Adder is correct. The HA equations are s=XY and c=XY. (2 points)