$3)(40$ points$)$ Design a pattern detector Mealy state machine that detects if the last $3$ inputs are $"001".$ Show the state diagram and the state table.

Example output:

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

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

Clock $\backslash \backslash$

Cycle

$\backslash$end$\{$tabular$\}$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9\backslash \backslash$

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

Input $\backslash \backslash$

X

$\backslash$end$\{$tabular$\}$ & $0$ & $0$ & $0$ & $1$ & $0$ & $0$ & $1$ & $1$ & $0\backslash \backslash$

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

Output $\backslash \backslash$

F

$\backslash$end$\{$tabular$\}$ & $0$ & $0$ & $0$ & $1$ & $0$ & $0$ & $1$ & $0$ & $0\backslash \backslash$

$\backslash$hline

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