$2)$ A synchronous sequential finite state machine with one input X and one output Z is to be

designed. The output Z becomes logic$-$l if a $3-$bit binary number formed by three

consecutive bits on X is divisible by $3($most significant bit comes first$).$ Otherwise, the

output Z is equal to logic$-0.$ The circuit returns to its initial State if the output Z becomes

logic$-$l$.$ You should $$e D flip$-$flops $($Y$$D$).$ Example input$-$output sequence:

x: $001101110011000001$

z: $000100100001001000$