A sequential circuit has two D Flip$-$Flops $($A and B$),$ two inputs $(x$ and $y),$ and one output $(z).$ The

circuit is specified by the following next$-$state and output equations:

$A(t+1)=x^{\text{'}}y+xA$

$B(t+1)=x^{\text{'}}B+xA$

$z=B$

a$)$ List the state table for the sequential circuit.

b$)$ Draw the corresponding state diagram.