$($a$)$ Construct an $SM$ chart equivalent to the following state table. Test only one variable in each decision box. Minimize the number of decision boxes.

$($b$)$ Write a VHDL description of the state machine based on the SM chart.

$($c$)$ Verfy the operation of the state machine.

$\backslash$table$[[\backslash$table$[[$Present$],[$State$]],$Next State,Output $($Z$1$ Z$2)],[12=,00,01,10,,12=,00,01,10,11],[$So$,S3,,2,$S$1,$so$,,00,10,11,01],[$S$1,$So$,,1,$S$2,$S$3,,10,10,11,],[S2,$S$3,,0,$S$1,$S$1,,00,10,11,01],[$S$3,$S$2,,2,$S$1,$So$,,00,00,01,01-1$