Q.Realize the full adder using two X-OR, two AND gates and an OR gate.

A full adder is realised with two X-OR gates (for the sum), two AND gates and one OR gate (for the carry). …

[!TLDR]

Two X-OR gates give the sum and two AND gates plus an OR gate give the carry of a full adder.

Realization with two X-OR, two AND and one OR gate:

• X-OR gate 1 (inputs $A, B$): output $P = A\oplus B$.
• X-OR gate 2 (inputs $P, C_{in}$): output $Sum = (A\oplus B)\oplus C_{in} = A\oplus B\oplus C_{in}$.
• AND gate 1 (inputs $P, C_{in}$): output $= (A\oplus B)\,C_{in}$.
• AND gate 2 (inputs $A, B$): output $= A\cdot B$.
• OR gate (inputs of AND1 and AND2): output $C_{out} = AB + (A\oplus B)C_{in}$. …