a$.$ Design an $8$ bit processor which has the following specifications: $4$ registers: $R0$&$R1$

$($Inputs$),$ R$2$ & R$3($Outputs$).$ It is capable of performing ADD, SUB, MUL. Processor has got $2-$bit

control inputs, one of the operations is performed based on the control input. $($Note: use the

required Combinational circuits $-$ Gates, Mux, Encoder, Decoder etc$).$

b$.$ Take any Boolean expression $(F)$ of $3$ variables and prove that $F+F^{\text{'}}=1$ and $F^{\text{'}}{F}^{\text{'}}=0$