implementation of full adder using half adder
A full adder essentially consists of two half adders and an additional OR gate.
Each half adder computes a partial sum (P) and a partial carry (Cp), which are then combined to produce the final Sum (S) and Cout (carry-out).
The first half adder takes two inputs, x and y. It produces two outputs: a partial sum (P1) and a partial carry (Cp1).
P1 is computed using an XOR gate: P1 = x ⊕ y
Cp1 is computed using an AND gate: Cp1 = x .y
The second half adder takes the partial sum (P1) from the first half adder and the third input, z. It produces two outputs: another partial sum (P2) and a partial carry (Cp2).
P2 is computed using an XOR gate: P2 = P1 ⊕ z
Cp2 is computed using an AND gate: Cp2 = P1 . z
The final Sum (S) is the result of the second half adder, and the Cout (carry-out) is produced by combining the partial carries from both half adders using an OR gate: