Regular Expressions & DFAs

$1(a)$

$[4$ Marks$]$

Given a binary alphabet $\{0,1\},$ write a regular expression that recognises all words

that have an odd number of $\text{'}1\text{'}$s and ends with a $\text{'}1\text{'}.$

$1(b)$

$[6$ Marks$]$

Use the subset construction method to derive a deterministic finite state automaton

that recognises the language from part $($a$).$