Q.Write the truth table and timing diagram of a full adder.

A full adder adds three bits A, B and carry-in $C_{in}$, giving $\text{Sum} = A \oplus B \oplus C_{in}$ and $\text{Carry}_{out} = AB + BC_{in} + AC_{in}$. The eight-row truth table and output waveforms follow from these equations. …

[!TLDR]

Full adder: $\text{Sum} = A \oplus B \oplus C_{in}$ (1 for an odd number of input 1s) and $C_{out} = AB + BC_{in} + AC_{in}$ (1 when two or more inputs are 1).

The full adder adds three input bits — the two operand bits A and B and the carry-in $C_{in}$ — producing a SUM bit and a CARRY-OUT bit. The SUM is the exclusive-OR of all three inputs, so it is HIGH whenever an odd number of inputs is 1. The CARRY-OUT is HIGH whenever a majority (two or three) of the inputs is 1. …