$1.$ Deterministic Construction $[9$ points$]$

Consider the language A over the alphabet $\backslash$Sigma $=\{0,1\}$:

A $=\{$w : w has $1$ as one of the last three digits$\}$

$($a$)$ Generate the state diagram for a DFA which decides A$.$

Make sure to clearly indicate your start state and final state$($s$).$

$($b$)$ Give the $5-$tuple which represents your DFA from $1($a$).$

You may use a table to represent the transition function $\backslash$delta $.$