$1.$ Deterministic Construction $[9$ points$]$Consider the language A over the alphabet $=\{0,1\}$: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 $.$