$2.$ For the state machine described by the following state table, with input $\backslash ($ s $\backslash ),$ output $\backslash ($ f $\backslash ),$ and JKFFs for the state elements, answer the following questions:

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

$\backslash$hline $\backslash$multicolumn$\{2\}\{|$c$|\}\{$ Present state $\}$ & Input & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$ Next state $\}$ & Output & $\backslash$multicolumn$\{3\}\{|$c$|\}\{\backslash$begin$\{$tabular$\}\{$c$\}$

JFFF Input functions $\backslash \backslash$

$($for state transition$)$

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

$\backslash$hline Q$1$ & Q$0$ & s & Q$1*\backslash (^\{*\}\backslash )$ & QO$*\backslash (^\{*\}\backslash )$ & f & J$1$ & K$1$ & J$0$ & K$0\backslash \backslash$

$\backslash$hline $0$ & $0$ & $0$ & $1$ & $0$ & $0$ & & & & $\backslash \backslash$

$\backslash$hline $0$ & $0$ & $1$ & $0$ & $1$ & $0$ & & & & $\backslash \backslash$

$\backslash$hline $0$ & $1$ & $0$ & $1$ & $1$ & $1$ & & & & $\backslash \backslash$

$\backslash$hline $0$ & $1$ & $1$ & $0$ & $0$ & $1$ & & & & $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $0$ & $1$ & $0$ & $0$ & & & & $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $1$ & $1$ & $1$ & $1$ & & & & $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $0$ & $0$ & $0$ & $1$ & & & & $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $1$ & $0$ & $1$ & $1$ & & & & $\backslash \backslash$

$\backslash$hline

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

a$.$ Fill in the state table given above. Make sure to use don't care $($denote it as X $)$ if possible. $[10$pts$]$ c$.$ Draw its state transition diagram. $[15$pts$]$

d$.$ Find JKFF input functions in mSOP form. $[20$pts$]$

e$.$ Draw logic diagram of the given state machine. $[15$pts$]$