Design a sequential circuit has two D flip$-$flops A and B$,$ two inputs E and x$.$ If E$=0,$ the circuit remains in the same state regardless of the value of the x$.$ When E$=1$ and x$=1,$ the circuit goes through the state transitions from $00$ to $01$ to $10$ to $11$ back to $00,$ and repeats. When E$=1$ and x$=0,$ the circuit goes through the state transitions from $00$ to $11$ to $10$ to $01$ back to $00,$ and repeats. Fill in the Truth table, the Karnaugh maps with their Boolean expressions, and complete the circuit. $($Circuit made in Digital works, max $4$ inputs per logic gate.$)$