$($b$)$ Design an arithmetic circuit with one selection variable $S$ and two $2-$bit data inputs A and B $.$ The circuit generates the following four arithmetic operations in conjunctior with the input carry $C_{in}$ :

Question $4$:

$\backslash$table$[[$S$,C_{in},$Output,Microoperation$],[0,0,A+B,$Add$],[0,1,A+B+1,$Add with carry$],[1,0,A\frac{+}{b}ar(B),$Subtract with borrow$],[1,1,A-B,$Subtract$],[,,,],[,,,],[,,,2^{10}=2^{11}$