$1.$ Design a $2-$bit counter with one control signal input that works as follows:

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

$\backslash$hline Control Input $($CI$)$ A & Operation $\backslash \backslash$

$\backslash$hline $0$ & Constant value $2(01$ in binary$)\backslash \backslash$

$\backslash$hline $1$ & Counting sequence $\backslash \backslash$

& $\backslash (1,0,3,2,1,0,3,2\backslash$ldots $\backslash )\backslash \backslash$

$\backslash$hline

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

a$.$ Assume that you use two TFFs as state holding elements. Complete the following state transition table: $[10$pts$]$

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

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

TFF input functions $\backslash \backslash$

$($for state transition$)$

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

$\backslash$hline A & Q$1$ & Q$0$ & Q$1*$ & Q$0*$ & T$1$ & TO $\backslash \backslash$

$\backslash$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$\}$