# Karnaugh Maps

###### Introduction to Digital Logic - CPE2210 - 2 February 2018

What is the simplified function for F(w, x, y, z) = Σ(0, 2, 4, 6, 12, 14)?

yz | ||||||

00 | 01 | 11 | 10 | |||

wx | 00 | 0 | 1 | 3 | 2 | |

01 | 4 | 5 | 7 | 6 | ||

11 | 12 | 13 | 15 | 14 | ||

10 | 8 | 9 | 11 | 10 |

yz | ||||||

00 | 01 | 11 | 10 | |||

wx | 00 | 1a | 0 | 0 | 1a | |

01 | 1ab | 0 | 0 | 1ab | ||

11 | 1b | 0 | 0 | 1b | ||

10 | 0 | 0 | 0 | 0 |

The simplified function consists of groups a and b, which comprise: w’z’ + xz’

### Don’t Care Conditions

Denoted by a hyphen

x | y | z | f |

0 | 0 | 0 | 1 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | - |

0 | 1 | 1 | 0 |

1 | 0 | 0 | 1 |

1 | 0 | 1 | - |

1 | 1 | 0 | 0 |

1 | 1 | 1 | 0 |

minterm canonical formula

f(x, y, z) = Σ(0,4) +

dc(2, 5)

maxterm canonical formula

f(x, y, z) = Π(1, 3, 6, 7) +

dc(2, 5)

This chart depicts a k-map with Don’t Cares, and since they are there, you can fill them with whatever you want.

In this case, filling it with 1s which will simplify our equation to **y’**