Designing a State Machine for Overlapping Pattern of 1001

Q1: How can we design a state machine to recognize the overlapping pattern of 1001?

Overview of State Machine Design

In order to design a state machine that can recognize the overlapping pattern of 1001, we need to create a series of states and transitions based on the input sequence. Each state will represent a specific condition or sequence of inputs, and the transitions between states will depend on the input received. By following the transitions, we can track the progress of pattern recognition.

Step-by-Step State Machine Design

1. Initial State: Start with an initial state, labeled as State 0.

2. First Digit Input: When the first digit of the pattern, which is '1', is inputted, transition to State 1.

3. Processing Input: If another '1' is inputted in State 1, transition to State 2.

4. Handling '0' Input: If a '0' is inputted, transition back to State 0.

5. Recognizing Pattern: If a '1' is inputted after a '0' in State 2, transition to State 3.

6. Transitioning Back: If a '1' is inputted after a '1' in State 3, transition back to State 2.

7. Completing the Pattern: If a '0' is inputted after a '1' in State 3, transition back to State 0.

8. Repeat: Repeat steps 2-7 for the remaining digits in the pattern.

Summary of State Machine

The designed state machine for the overlapping pattern of 1001 includes four states: State 0, State 1, State 2, and State 3. Each state has specific transition rules based on the input received, allowing the machine to recognize and track the pattern effectively.

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