Question $5$:

Design a three$-$bit counter$-$like circuit controlled by the input $w.$ If $w=1,$ then the counter adds $2$ to its contents, wrapping around if the count reaches $8$ or $9($i$.$e$.,$ if the present state is $8$ or $9,$ then the next state becomes $0$ or $1,$ respectively$).$ If $w=0,$ then the counter subtracts $1$ from its contents, acting as a normal down$-$counter.