An arithmetic and logic unit $($ALU$)$ performs integer and logic operations.

Implement the logic of a simple ALU that performs only $1-$bit addition and $1-$bit logical bitwise AND, where Op$=0$ is addition and Op$=1$ is bitwise AND.

Assume the operands are

and

$,$ and the output is

$.$

Also, there is a carry bit designated as

$.$

Do not draw a circuit, your answer should be in the form of logic equations, that is$,$

and