# Boolean Algebra

## Summary of primitive logic functions

In boolean algebra the values of variables are true *(1)* or false *(0)*.

### BUF

*y = a (1)*

a | y |
---|---|

0 | 0 |

1 | 1 |

### AND

*y = a & b (2)*

a | b | y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

### OR

*y = a | b (3)*

a | b | y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

### XOR

*y = a ⊻ b (4)*

a | b | y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

### NOT

*y = a (5)*

a | y |
---|---|

0 | 1 |

1 | 0 |

### NAND

*y = a & b (6)*

a | b | y |
---|---|---|

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

### NOR

*y = a | b (7)*

a | b | y |
---|---|---|

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

### NOR

*y = a ⊻ b (8)*

a | b | y |
---|---|---|

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |