$65\mathrm{.}2$ Construct an SM chart that is equivalent to the following state table. Test only one variable in each decision box.

Try to minimize the number of decision boxes. Show Mealy and Moore outputs on the SM chart.

Present

State

Next State Output $1$Z$1$Z$2$Z$32$

X$1$X$2500011011$ X$1$X$2500011011$

S$0$ S$1$ S$1$ S$1$ S$1000100110010$

S$1$ S$1$ S$1$ S$0$ S$0001001001001$

In addition, write a VHDL description of the state machine based on the SM chart.