$7.$ Consider the following next state table

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$\{2\}\{*\}\{\backslash$begin$\{$tabular$\}\{$c$\}$

Present $\backslash \backslash$

state

$\backslash$end$\{$tabular$\}\}$ & $\backslash$multicolumn$\{2\}\{|$c$|\}\{$ Next state $\}$ & $\backslash$multirow$\{2\}\{*\}\{$ Output $\}\backslash \backslash$

$\backslash$cline $\{2-3\}$ & $\backslash (\backslash$mathrm$\{$X$\}=0\backslash )$ & $\backslash (\backslash$mathrm$\{$X$\}=1\backslash )$ & $0\backslash \backslash$

$\backslash$hline A & G & C & $0\backslash \backslash$

$\backslash$hline B & F & H & $0\backslash \backslash$

$\backslash$hline C & E & D & $1\backslash \backslash$

$\backslash$hline D & A & C & $0\backslash \backslash$

$\backslash$hline E & C & A & $1\backslash \backslash$

$\backslash$hline F & F & B & $1\backslash \backslash$

$\backslash$hline G & A & C & $0\backslash \backslash$

$\backslash$hline H & C & G & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Use the implication chart to reduce states.