# Boolean Algebra

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 |

### XNOR

*y = a ⊻ b (8)*

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

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Binary to Decimal, Hexadecimal and ASCII Converter

Convert between binary, decimal and hexadecimal numbers.

### Binary, Octal and Hexadecimal Numbers

Decimal, binary, octal and hexadecimal numbers.

### Data Types

Signed vs. unsigned datatypes.

### Fractions

Law of fractions

### Prefixes for Binary Multiplies

IEC International Standard names and symbols