*Kiddle Encyclopedia.*

**Boolean algebra** is algebra for binary (0 means false and 1 means true). It uses normal maths symbols, but it does not work in the same way. It is named after its creator George Boole.

## Contents

## NOT gate

NOT | |
---|---|

0 |
1 |

1 |
0 |

The NOT operator is written with a bar over numbers or letters like this:

It means the output is **not** the input.

## AND gate

AND | 0 | 1 |
---|---|---|

0 |
0 | 0 |

1 |
0 | 1 |

The AND operator is written as like this:

The output is true only if one **and** the other input is true.

## OR gate

OR | 0 | 1 |
---|---|---|

0 |
0 | 1 |

1 |
1 | 1 |

The OR operator is written as like this:

One **or** the other input can be true for the output to be true.

## XOR gate

XOR | 0 | 1 |
---|---|---|

0 |
0 | 1 |

1 |
1 | 0 |

XOR basically means "exclusive or", meaning one input or the other must be true, but not both.

The XOR operator is written as like this:

To make it more simple, one **or** the other input must be true, but **not** both.

## Identities

Different gates can be put together in different orders:

- is the same as an AND then a NOT. This is called a NAND gate.

It is **not** the same as a NOT then an AND like this:

which is called *XOR identity table*

XOR | 1 | 0 | Any |
---|---|---|---|

1 | TRUE | 0 | 0 |

0 | 0 | 0 | |

Any | 0 |

, if .

or if ~~=TRUE, TRUE~~.,

## DeMorgan's laws

Augustus De Morgan found out that it is possible to change a sign to a sign and make or break a bar. See the 2 examples below:

"Make/break the bar and change the sign."