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Online minimization of boolean functions

# Online minimization of boolean functions

## Input equation = ab(~(a+~c))+b(ac+~ab)+(a+b)(~a+cd)

Truth table
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 |
1 |

0 |
1 |
0 |
1 |
1 |

0 |
1 |
1 |
0 |
1 |

0 |
1 |
1 |
1 |
1 |

1 |
0 |
0 |
0 |
0 |

1 |
0 |
0 |
1 |
0 |

1 |
0 |
1 |
0 |
0 |

1 |
0 |
1 |
1 |
1 |

1 |
1 |
0 |
0 |
0 |

1 |
1 |
0 |
1 |
0 |

1 |
1 |
1 |
0 |
1 |

1 |
1 |
1 |
1 |
1 |

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

DNF (with overline) = 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) (~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) (a + b + c + d)

Minimal Form (with ~) = acd + ~ab + bc

Minimal Form (with overline) = acd + ab + bc

Karnaugh map
| cd |
cd |
cd |
cd |

ab |
0 |
0 |
0 |
0 |

ab |
1 |
1 |
1 |
1 |

ab |
0 |
0 |
1 |
1 |

ab |
0 |
0 |
1 |
0 |