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

0 | 0 | 0 | 0 | 1 |

0 | 0 | 0 | 1 | 0 |

0 | 0 | 1 | 0 | 1 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 0 | 1 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 0 |

0 | 1 | 1 | 1 | 1 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 1 | 1 |

1 | 0 | 1 | 0 | 1 |

1 | 0 | 1 | 1 | 0 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 0 | 1 | 1 |

1 | 1 | 1 | 0 | 1 |

1 | 1 | 1 | 1 | 1 |

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

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

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

Some minimal forms exist.

Minimal Form (with ~) =

~b~d + abc + a~cd + ~acd + ~ab~c

bd + ac~d + a~b~c + ~a~bc + ~a~c~d

Minimal Form (with overline) =

bd + abc + acd + acd + abc

bd + acd + abc + abc + acd

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

ab | 1 | 0 | 1 | 1 |

ab | 1 | 1 | 1 | 0 |

ab | 0 | 1 | 1 | 1 |

ab | 1 | 1 | 0 | 1 |