Prove that the following two circuits are both implementations of the full-adder circuit defined by the...

 

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Prove that the following two circuits are both implementations of the full-adder circuit defined by the truth table in Figure 3.3(a). Yi CI Circuit A C; +1 C X Y $ C+1 2. (50 points) Consider a 1-bit full subtractor circuit which performs 1-bit subtraction with borrow- in. This circuit has three inputs x, y, and wi (which is the borrow-in). It computes x - Y - W and store the result in r; and the borrow-out in wi+1. Please draw the truth tables and write the canonical SOP expressions for the functions r; and w+1 based on x, yi and w. Prove that the following two circuits are both implementations of the full-adder circuit defined by the truth table in Figure 3.3(a). Yi CI Circuit A C; +1 C X Y $ C+1 2. (50 points) Consider a 1-bit full subtractor circuit which performs 1-bit subtraction with borrow- in. This circuit has three inputs x, y, and wi (which is the borrow-in). It computes x - Y - W and store the result in r; and the borrow-out in wi+1. Please draw the truth tables and write the canonical SOP expressions for the functions r; and w+1 based on x, yi and w.