Q.Realize the full adder using two half adders and a OR gate.

A full adder can be built from two half adders and one OR gate: the first half adder adds A and B, the second adds that partial sum to the carry-in $C_{in}$, and the OR gate combines the two carries. …

[!TLDR]

Two half adders in series produce the full-adder sum $A\oplus B\oplus C_{in}$; an OR gate combines their two carries into $C_{out}$.

A full adder's SUM output $(A \oplus B \oplus C_{in})$ is a double exclusive-OR, which is exactly what two cascaded half adders (each an XOR/AND pair) can generate. The design proceeds in three stages:

1. First half adder — inputs A and B: it gives the partial sum $S_1 = A \oplus B$ and the first carry $C_1 = AB$.
2. Second half adder — inputs $S_1$ and $C_{in}$: it gives the final SUM $= S_1 \oplus C_{in} = A \oplus B \oplus C_{in}$ and a second carry $C_2 = S_1 C_{in} = (A \oplus B)C_{in}$.
3. OR gate — inputs $C_1$ and $C_2$: it gives the carry-out $C_{out} = C_1 + C_2$. …