how did you conclude that A=C=1 places should be replaced with don't care?

0 votes

A logic circuit implements the following Boolean function:

F = A’C + AC’D’

it is found that the circuit input combination A=C=1 can never occur. Find a simpler expression for F using the proper don't-care conditions.

F = A’C + AC’D’

it is found that the circuit input combination A=C=1 can never occur. Find a simpler expression for F using the proper don't-care conditions.

1 vote

Best answer

Given function = A'C + AC'D'

for the given function min terms are: 𝝨m (2,3,6,7,8,12)

given A = C = 1 will never occur. use dont cares in these combinations.

A |
B | C |
D | F |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 0 | 1 | 0 |

0 | 0 | 1 | 0 | 1 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 0 | 0 |

0 | 1 | 0 | 1 | 0 |

0 | 1 | 1 | 0 | 1 |

0 | 1 | 1 | 1 | 1 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 1 | 1 |

1 | 0 | 1 | 0 | X |

1 | 0 | 1 | 1 | X |

1 | 1 | 0 | 0 | 1 |

1 | 1 | 0 | 1 | 0 |

1 | 1 | 1 | 0 | X |

1 | 1 | 1 | 1 | X |

by forming k map and simplifying the boolean expression

simplified expression will be **AD' + C**