Figures $3\mathrm{.}2,3\mathrm{.}3,$ and $3\mathrm{.}4$ show $3$ different examples performing mod $3.$ The

first is decimal $27(5$b$11011)$ and results in a remainder of $0.$ The second is

decimal $34(6$b$100010)$ and results in a remainder of $1.$ The last is decimal

$17(6$b$010001)$ and results in a remainder of $2.$

$($a$)$ Using the following state assignment $...$

S$0=2$

b$00$

S$1=2$

b$01$

S$2=2$

b$10$

$...$ create the state transition table assuming D$-$type flip flops.

$($b$)$ Create simplified equations for the next state logic.