Exercise Nr$.3(10$ points$)$ Design an FSM that takes two inputs, A and $B,$ and generates one output, $Z.$ The output in cycle $n,Z_n,$ is either the the previous input value $A_{n-1}$ or the Boolean AND of the corresponding input $A_n$ and the previous input $A_{n-1},$ depending on the other input, $B_n$ :

$Z_n=\{\begin{array}{ccc}{A}_{n-1}& if& B_n=0\\ A_{n-1}{A}_n& if& B_n=1\end{array}$

a$.$ Is this FSM a Moore or a Mealy machine?

b$.$ Design the FSM$.$ Show your state transition diagram, encoded state transition table, next state and output equations, and schematic.