In this problem's solution, how is the first DFA obtained?

[s3a]

Homework Statement

PDF with problem statement and its solution:
https://www.docdroid.net/BkVhr32/4.pdf

Homework Equations

State Diagrams for DFAs

The Attempt at a Solution

My question is what's the logic behind the first DFA's implementation?

I understand that the second DFA just has the arrows' direction reversed, but how does one come up with the first one? I know how DFAs work and have made other ones before; my problem is specifically this binary divisible by 101 stuff.

If someone could help me understand the logic, I would GREATLY appreciate it!

 

[QuantumQuest]

My question is what's the logic behind the first DFA's implementation?

The first DFA is designed to accept bit strings for which $int(w)$ is divisible by 5. You can work with the decimal representations and think about the cases where a positive integer is divisible by 5 or not. What is the form of these numbers? Then start to design a DFA with these forms of numbers. Think about the input and the patterns that binary inputs imply for the decimal representation.