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

$($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.

$($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.

$($HDL$$see Problem $5\mathrm{.}38)$