A 'half adder' adds two one$-$bit binary numbers $($A and B$).$ The output is the sum of the two

bits $($S$)$ and the carry $($C$).$ Read Example $1\mathrm{.}1($page $10)$ first.

$($a$)$ Determine the truth table for a 'half adder'. Use $\text{'}A\text{'}$ and $\text{'}B\text{'}$ for inputs and $\text{'}S\text{'}$ and $\text{'}C\text{'}$ as

Sum and Carry outputs, respectively.

$($b$)$ From the truth table, determine the Boolean functions for Sum $($S$)$ and Carry $($C$).$