$5\mathrm{.}16$ Design a sequential circuit with two $D$ flip$-$flops A and $B,$ and one input $x_{i}n.$

$($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 $5\mathrm{.}38.)$