## Answers

**3)**

**A Mealy FSM to detect the sequence " 1100110" with Overlap is implemented below.**

**Since the length of the sequence is equal to 7 then total number of states required is also equal to 7**

**The states are assigned with Alphabets**

**SINCE THERE ARE 7 STATES NUMBER OF BITS TO REPRESENT THE STATE IS EQUAL TO 3**

**STATE ASSIGNMENT TABLE:**

STATES | BINARY VALUE |

A | 000 |

B | 001 |

C | 010 |

D | 011 |

E | 100 |

F | 101 |

G | 110 |

**STATE TRANSITION DIAGRAM :**

**STATE TRANSITION TABLE:**

**From the below state transition table we can clearly see that the output becomes 1 when there is a transition from G to C.**

**It implies that the required sequence has been detected and due to the overlap of the sequence the next transition state is C. but not A. **

TOTAL NUMBER OF STATES =**7**

**AND WE KNOW THAT**

So, N= 3.

Hence 3 number of flipflops are required.

**4)**

**A M****oore FSM****to detect the sequence " 1100110" with Overlap is implemented below.**

**Since the length of the sequence is equal to 7 then total number of states required is equal to 8**

**The states are assigned with Alphabets**

**SINCE THERE ARE 8 STATES NUMBER OF BITS TO REPRESENT THE STATE IS EQUAL TO 3**

**STATE ASSIGNMENT TABLE:**

STATES | BINARY VALUE |

A | 000 |

B | 001 |

C | 010 |

D | 011 |

E | 100 |

F | 101 |

G | 110 |

H | 111 |

**STATE TRANSITION DIAGRAM**

**STATE TRANSITION MATRIX:**

**From the below state transition table we can clearly see that the output becomes 1 when the Circuit enters the H state.**

**It implies that the required sequence has been detected and due to the overlap of the sequence the next transition state is E if input is 0 and B if input is 1 but not A. **

TOTAL NUMBER OF STATES =**8**

**AND WE KNOW THAT**

So, N= 3.

**Hence 3 number of flipflops are required.**