A register cell A is to implement the following register transfers:

AND: A $$ A $$ B

OR: A $$ A $$ B

NOT: A $$ A

We assume that $(1)$ Only one of AND, OR$,$ and NOT is equal to $1$; $(2)$ For all of AND,

OR$,$ and NOT equal to $0,$ the content of A remains unchanged. Now design this register

cell directly for D flip$-$flops using a sequential circuit design approach.