Design a sequential circuit with two D flip$-$flops A and B$,$ and one input x$\_$in$.$

$1.($a$)*$ When x$\_$in$=0,$ the state of the circuit remains the same.

When x$\_$in$=1,$ the circuit goes through the state transitions from $00$ to $01,$ to $11,$ to $10,$ back to $00,$ and repeats.

$2.($b$)$ When x$\_$in$=0,$ the state of the circuit remains the same.

When x$\_$in$=1,$ the circuit goes through the state transitions from

$00$ to $11,$ to $01,$ to $10,$ back to $00,$ and repeats.