Design a sequential circuit of a binary up$-$down counter with two JK flip$-$flops A and $B$ and two inputs $E$ and $x.$ If $E=0,$ the circuit remains in the same state regardless of the value of $x.$ 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. $(2$ points$).$

$\backslash$table$[[$Requirement$,$Answer$],[$State Table,$]]$