$(20$ points$)$ The $4-$bit binary abcd number will be incremented$/$subtracted depending on the selector $S).$ When $S=0,$ the value of the number will increase by $2,$ while when $S=1,$ the value of the number will decrease by $2.$ For example, if the number abcd is decimal $9,$ it will appear as decimal $11$ when $S=0$ and decimal $7$ when $S=1.$ Design the required circuit in a hierarchical structure using one$-$bit full adders.