The $4-$bit abcd number will be incremented$/$subtracted depending on the selector. 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 $9,$ it will appear as $11$ when S$=0$ and $7$ when S$=1.$ Design the required circuit in a hierarchical structure using one$-$bit full adders.