How to make a minimal DFA

Question

Draw a minimal DFA which accepts a language L over {a,b}

01 [ ((10) *  + 111) * + 0 ] * 1

Answer 1

Minimum number of states =$5$

Comments

Plz describe it in detail.and how to understand this part [ ((10) *  + 111) * + 0 ] * .

Could you unroll this for more clarity ?

Answer 2

We can make minimal DFA step by step by unrolling regular expression.

Given r= 01 [ ((10) *  + 111) * + 0 ] * 1

Step 1

Step 2

Step 3

Step 4

Complete the system by making dead state