Q$3.(10$ points$)$ 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.