A sequential circuit with a D flip$-$flop A and a T flip$-$flop B$,$ two inputs, x and y; and one output z

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

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

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

z $=$ A$\text{'}+$ B

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

$($b$\}$ List the state table for the sequential circuit.

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