$5\mathrm{.}6)$ 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:

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

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

$z=B$

a$)$ Draw the logic diagram of the circuit.

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

c$)$ Draw the corresponding state diagram.