# Logic Gates

Controlling electricity gives us the ability to make yes and no decisions or

**true**

and **false**

. By combining two signals, we can give a single **true**

or **false**

answer, depending on the **logic**

. The flow of electricity is controlled using **gates**

(no, not named after Bill Gates - like a gate).Standard Logic Gate Symbols

NOT

AND

NAND

OR

NOR

XOR

XNOR

All Truth Tables

The simplest gate, this item

**or reverses the signal.**`inverts`

$Q= \overline A$

Input (A) | Output (Q) |

0 | 1 |

1 | 0 |

Only outputs true if both inputs are true.

$Q = A \cdot B \text{ or } A \times B$

A | B | Output (Q) |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

Any gate with a dot is an

`inverted`

gate. $Q = \overline{A \cdot B} \text{ or } \overline{A \times B}$

This is the NOT AND gate: A | B | Output (Q) |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

One or the other or both!

$Q = A+B$

A | B | Output (Q) |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

Very simply NOT OR.

$Q = \overline{A+B}$

A | B | Output (Q) |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

Exclusive OR meaning only one is true, not both.

$Q = A \bigoplus B$

A | B | Output (Q) |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Exclusively NOT OR. If both inputs are the same, output true.

$Q = \overline{A \bigoplus B}$

A | B | Output (Q) |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

The two "universal" gates are

**NOR**

and **NAND**

- it is said that you can create all the other logic gates with a combination of just these two.There are tons of videos available about logic gates. If I had to pick a favourite, my current is this one, although she talks incredibly fast and you might need to slow it down or rewind.

Last modified 5yr ago