Home
Online minimization of boolean functions

# Online minimization of boolean functions

## bin ( 3 ) 11011011

Truth table
a | b | c | Output |

0 |
0 |
0 |
1 |

0 |
0 |
1 |
1 |

0 |
1 |
0 |
0 |

0 |
1 |
1 |
1 |

1 |
0 |
0 |
1 |

1 |
0 |
1 |
0 |

1 |
1 |
0 |
1 |

1 |
1 |
1 |
1 |

DNF (with ~) = ~a~b~c + ~a~bc + ~abc + a~b~c + ab~c + abc

DNF (with overline) = abc + abc + abc + abc + abc + abc

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

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

Some minimal forms exist.

Minimal Form (with ~) =

bc + a~c + ~a~b

ab + ~ac + ~b~c

Minimal Form (with overline) =

bc + ac + ab

ab + ac + bc

Karnaugh map
| c |
c |

ab |
1 |
1 |

ab |
0 |
1 |

ab |
1 |
1 |

ab |
1 |
0 |