Deterministic Construction $[9$ points$]$

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

$A=\{w$:$w$ has $1as$ 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 $.$