Consider an adder which adds two $2-$bit unsigned binary numbers $A_1{A}_0$ and $B_1{B}_0$ and outputs

a $2-$bit sum $S_1{S}_0.$ Since the output is a $2-$bit binary, for some of the cases overflow may occur.

If the adder has a one$-$bit output $C$ where it is $1$ if overflow happened and $0$ otherwise,

$($a$)$

Fill the adders's truth table and express the simplified function in sum$-$of$-$

products form using K$-$map.

$($b$)$

Draw the logic circuit of the adder.

Table $3$: Simple Adder Truth Table