A sequential circuit has two flip$-$flops $($A and B$),$ two inputs $($x and y$)$ and an output $($z$).$ The flip$-$flop

input functions and the circuit output function are as follows:

JA $=$ xB $+$ y$$B$,$ KA $=$ xy$$B$,$ JB $=$ xA$,$ KB $=$ xy$+$ A and z $=$ xyA $+$ x$$y$$B

Obtain the logic diagram, state table and the state diagram.