Q$5.($Total $12$ points$)$ For the following state table

$\backslash$table$[[\backslash$table$[[$Present$],[$State$]],$Next State,Output$],[$x$=0,$x$=1,$x$=0,$x$=1],[$a$,$d$,$b$,1,0],[$b$,$d$,$a$,0,1],[$c$,$f$,$c$,0,1],[$d$,$g$,$a$,1,0],[$e$,$h$,$a$,0,1],[$f$,$d$,$b$,1,0],[$g$,$a$,$c$,0,1],[$h$,$g$,$a$,1,0]]$

$($a$)(5$ points$)$ Draw the corresponding state diagram of the table above.

$($b$)(5$ points$)$ Tabulate the reduced state table.

$($c$)(2$ points$)$ Draw the state diagram corresponding to the reduced state table.