Do the chart on a paper please

$($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$[[,$Next State,Output $($Z$1$ Z$2)],[\backslash$table$[[$Present$],[$State$]],x1x2=,00,01,10,11,x1x2=,00,01,10,11],[$S$0,S3,S2,S1,S0,00,10,11,01,,],[$S$1,S0,S1,S2,S3,10,10,11,11,,],[$S$2,S3,S0,S1,S1,00,10,11,01,,],[$S$3,S2,S2,S1,S0,00,00,01,01,,]$