Homework $9(45$ pts$)$

Design a sequential circuit with two flip$-$flops A and $B,$ and one input $x.$ When $x=0,$ the state of the circuit remains the same. When $x=1,$ the circuit goes through the state transitions from $00$ to $01,$ to $11,$ to $10,$ back to $00,$ and repeats.

$($a$)$ Use $D$ flip$-$flops in the design.

$($b$)$ Use $JK$ flip$-$flops in the design.

$($c$)$ Use $T$ flip$-$flops in the design.

Note: You must show the complete state table, k$-$maps and final circuit diagram, for each part. No credits will be given if all the required work is not shown.