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a | b | c | d | Output |
---|---|---|---|---|

0 | 0 | 0 | 0 | 0 |

0 | 0 | 0 | 1 | 0 |

0 | 0 | 1 | 0 | 0 |

0 | 0 | 1 | 1 | 0 |

0 | 1 | 0 | 0 | 0 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 |

0 | 1 | 1 | 1 | 1 |

1 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 1 | 1 |

1 | 0 | 1 | 0 | 1 |

1 | 0 | 1 | 1 | 1 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 0 | 1 | 1 |

1 | 1 | 1 | 0 | 1 |

1 | 1 | 1 | 1 | 0 |

DNF (with ~) = ~ab~cd + ~abc~d + ~abcd + a~b~cd + a~bc~d + a~bcd + ab~cd + abc~d

DNF (with overline) = abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd

CNF (with ~) = (a + b + c + d) (a + b + c + ~d) (a + b + ~c + d) (a + b + ~c + ~d) (a + ~b + c + d) (~a + b + c + d) (~a + ~b + c + d) (~a + ~b + ~c + ~d)

CNF (with overline) = (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b + c + d)

Some minimal forms exist.

Minimal Form (with ~) =

a~bc + a~cd + bc~d + ~abd

ac~d + a~bd + ~abc + b~cd

Minimal Form (with overline) =

abc + acd + bcd + abd

acd + abd + abc + bcd

cd | cd | cd | cd | |
---|---|---|---|---|

ab | 0 | 0 | 0 | 0 |

ab | 0 | 1 | 1 | 1 |

ab | 0 | 1 | 0 | 1 |

ab | 0 | 1 | 1 | 1 |