16. Two full-adder implementations are presented in Figure la & lb. Cin Sum Cin DFD Sum...

 

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16. Two full-adder implementations are presented in Figure la & lb. Cin Sum Cin DFD Sum Cout Cout (a) 13-in XOR, 32-in AND, and 1 3-in OR. (b) 2 2-in XOR, 22-in AND, and 1 2-in OR. Figure 1: Two different implementations of a full-adder (a) (3 Points) Prove that these two implementations are functionally equivalent using Boolean theorems. (Hint: Consensus) (b) (1 Point) Which one of the two full-adder implementation above would you choose for your design? Justify your choice. (c) (1 Points) For the implementation you chose, convert the full-adder to a full-subtracter. assuming negative numbers are represented in 2's complement. 16. Two full-adder implementations are presented in Figure la & lb. Cin Sum Cin DFD Sum Cout Cout (a) 13-in XOR, 32-in AND, and 1 3-in OR. (b) 2 2-in XOR, 22-in AND, and 1 2-in OR. Figure 1: Two different implementations of a full-adder (a) (3 Points) Prove that these two implementations are functionally equivalent using Boolean theorems. (Hint: Consensus) (b) (1 Point) Which one of the two full-adder implementation above would you choose for your design? Justify your choice. (c) (1 Points) For the implementation you chose, convert the full-adder to a full-subtracter. assuming negative numbers are represented in 2's complement.