a$.$ Fill the following state table. $(10$pts$)$

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

$\backslash$hline $\backslash$multicolumn$\{3\}\{|$c$|\}\{$ Current state $\}$ & $\backslash$multicolumn$\{3\}\{$c$|\}\{$ Next state $\}\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{2\}\}\backslash )$ & $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{1\}\}\backslash )$ & $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{0\}\}\backslash )$ & $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{2\}\}\backslash )$ & $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{1\}\}\backslash )$ & $\backslash (\backslash$mathbf$\{$A$\}\_\{\backslash$mathbf$\{0\}\}\backslash )\backslash \backslash$

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

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

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

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

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

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

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

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

$\backslash$hline

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

b$.$ Considering that the propagation time of flip$-$flops are $\backslash ($ t$\_\{$p$,$ F F$\}=10\backslash$mathrm$\{$ps$\}\backslash ),$ complete the following timing diagram after the positive clock edge. $(10$pts$)$