**MA Mingyu (Derek)** | 14110562D | Nov 12, 2017

derek.ma | derek.ma@connect.polyu.hk

Characteristic table:

\(S\) | \(R\) | \(Q(t)\) | \(Q(t+\Delta)\) |
---|---|---|---|

0 | 0 | 0 | disallowed |

0 | 0 | 1 | disallowed |

0 | 1 | 0 | 1 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 0 |

1 | 1 | 1 | 1 |

K-map:

row:\(SR\); col:\(Q(t)\) | 00 | 01 | 11 | 10 |
---|---|---|---|---|

0 |
X | 1 | 0 | 0 |

1 |
X | 1 | 1 | 0 |

Next-state equation:

\(Q(t+\Delta) = \overline{S(t)} + R(t)Q(t)\)

The relationship between this latch and the one using NOR gates is exact opposite.

\(S\) here is actually \(\overline{S}\), and \(R\) here is actually \(\overline{R}\) compared to the one using NOR gates.

Characteristic table for this latch:

\(E\) | \(D\) | \(Q\) | \(Q_{next}\) | \(\overline{Q_{next}}\) |
---|---|---|---|---|

0 | X | 0 | 0 | 1 |

0 | X | 1 | 1 | 0 |

1 | 0 | X | 0 | 1 |

1 | 1 | X | 1 | 0 |

where X means "don't care the value of this variable".

Another possible characteristic table is:

\(E\) | \(D\) | \(Q\) | \(Q_{next}\) | \(\overline{Q_{next}}\) |
---|---|---|---|---|

0 | 0 | X | \(Q\) | \(\overline{Q}\) |

0 | 1 | X | \(Q\) | \(\overline{Q}\) |

1 | 0 | X | 0 | 1 |

1 | 1 | X | 1 | 0 |