A sequential circuit with two $D$ flip$-$flops A and $B,$ two inputs, $x$ and $y,$ and one output z is specified by the following next$-$state and output equations

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

$B(t+1)=x\text{'}A+xB$

$z=A$

$($a$)$ Draw the iogic diagram of the circuit.

$($b$)$ List the state table for the sequential circuit.

$($c$)$ Draw the corresponding state diagram.