In Design a $2-$bit ALU with accumulator

The designed circuit should performs $2$ operations only.

Two Feedback registers must be used to store the output bits, and load the second input bits.

$2-$Bit ALU with accumulator

$2$ Bit ALU has :

Two $2-$bit inputs $x(x1,x0)$ & $Y(Y1,Y0)$

One selection bit $"$S$"$ used to select the operation

One $2-$bit output F $($ F$1,$ F$0)$

One $1-$bit output "Cout $||$ Bout"

Two feedback registers D$0$ and D

Operation $1$ Subtraction F$=$X$-$Y

Operation $2$ Add $2\text{'}$d complement of Y to X