Design and implement an FSM to control an elevator for a building with $\backslash (\backslash$mathbf$\{3\}\backslash )$ floors. Simulate the FSM to verify its functionality.

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

$\backslash$hline Input$/$Output & $\backslash$begin$\{$tabular$\}\{$l$\}$

Signal $\backslash \backslash$

Name

$\backslash$end$\{$tabular$\}$ & Meaning & $\backslash$begin$\{$tabular$\}\{$l$\}$

$\backslash$# of $\backslash \backslash$

bits

$\backslash$end$\{$tabular$\}$ & Note $\backslash \backslash$

$\backslash$hline $\backslash$multirow$\{4\}\{*\}\{$Input$\}$ & reset$\_$i & Resets the machine & $1$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

$-$ Connected to a button $\backslash \backslash$

$-$ Asynchronous

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

$\backslash$hline & clock$\_$i & Clock signal & $1$ & $50$ MHz $\backslash \backslash$

$\backslash$hline & up$\_$btn$\_$i & Request to move up & $1$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

$-$ Connected to a button $\backslash \backslash$

$-$ One button on each floor

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

$\backslash$hline & down$\_$btn$\_$i & Request to move down & $1$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

$-$ Connected to a button $\backslash \backslash$

$-$ One button on each floor

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

$\backslash$hline $\backslash$multirow$[$b$]\{2\}\{*\}\{$Output$\}$ & cur$\_$floor$\_$o & Indicates the floor where the elevator is & $4$ & Connected to a $4-$input $7$ segment LED $\backslash \backslash$

$\backslash$hline & direction$\_$o & Direction Indicator: Up or down & $1$ & Connected to $2$ LEDs $\backslash \backslash$

$\backslash$hline

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

Note: The Direction Indicator should be on for $2$ seconds before the Floor Indicator changes its value.