Finite State Machine

$3.($a$)$ Draw the state diagram for a FSM with states xmod$4,$ and the transitions are $x2$xmod$4$ or $x3$xmod$4$ based on some binary input I, the outputs are xmod$3$ and $x+1$mod$3$ respectively.

$($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. $($Note that you need at least two bits to represent output$)$

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

$($f$)$ Repeat the previous parts using the following state encoding $11000,20100,30010,00001$