The half$-$adder does not take the carry bit from its previous stage into account. This carry bit from its previous stage is

called carry$-$in bit. A combinational logic circuit that adds two data bits, $x$ and $y,$ and a carry$-$in bit, $C_{in},$ is called a full$-$

adder. The Boolean functions describing the full$-$adder are:

$S_{FA}=(xo+y)o+C_{in},C_{FA}=xy+C_{in}(xo+y)$

Build a full$-$adder and draw its truth table to verify its function.

Fig. $1.$ XOR.