Prerequisite – Counters**Problem –** Design synchronous counter for sequence: 0 → 1 → 3 → 4 → 5 → 7 → 0, using T flip-flop.

**Explanation –** For given sequence, state transition diagram as following below:

State transition table logic:

Present State | Next State |
---|---|

0 | 1 |

1 | 3 |

3 | 4 |

4 | 5 |

5 | 7 |

7 | 0 |

State transition table for given sequence:

Present State | Next State | ||||
---|---|---|---|---|---|

Q_{3} | Q_{2} | Q_{1} | Q_{3}(t+1) | Q_{2}(t+1) | Q_{1}(t+1) |

0 | 0 | 0 | 0 | 0 | 1 |

0 | 0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 1 | 0 | 0 |

1 | 0 | 0 | 1 | 0 | 1 |

1 | 0 | 1 | 1 | 1 | 1 |

1 | 1 | 1 | 0 | 0 | 0 |

**T flip-flop –** If value of Q changes either from 0 to 1 or from 1 to 0 then input for T flip-flop is 1 else input value is 0.

Qt | Qt+1 | T |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Draw input table of all T flip-flops by using the excitation table of T flip-flop. As nature of T flip-flop is toggle in nature. Here, Q3 as Most significant bit and Q1 as least significant bit.

Input table of Flip-Flops | |||
---|---|---|---|

T_{3} | T_{2} | T_{1} | |

0 | 0 | 1 | |

0 | 1 | 0 | |

1 | 1 | 1 | |

0 | 0 | 1 | |

0 | 1 | 0 | |

1 | 1 | 1 |

Find value of T_{3}, T_{2}, T_{1} in terms of Q_{3}, Q_{2}, Q_{1} using K-Map (Karnaugh Map):

Therefore,

T_{3}= Q_{2}

Therefore,

T_{2}= Q_{1}

Therefore,

T_{1}= Q_{2}’

Now, you can design required circuit using expressions of K-maps: