$($a$)$ Draw the FSM for a counter with $8$ states xmod$8,$ and the transitions are $x2$xmod$8$ or $x3$xmod$8$ based on some input. The output is $x+1$ at each state.

$($b$)$ Encode the states of the FSM by bits. List your encoding in a table or show the encoding on your diagram.

$($c$)$ Write the truth table for the next state function. Your truth table should have one row for every combination of possible input values and state.

$($d$)$ Write the truth table for the output function. Recall that the output is $1-$bit

$($e$)$ Using D$-$Flipflops to represent the states implement the FSM$.$

Implement the FSM in problem $2$ in circuitverse