# Logic Gates

Logic Gates process **true** and **false** values.

## And

The "and" logic gate must have **both **inputs true to become true.

Try clicking on the left hand lines here (green is true and blue is false):

We can show that in a "truth table" (T is for true and F for false):

A | B | A and B | |
---|---|---|---|

F | F | F | |

F | T | F | |

T | F | F | |

T | T | T |

### Example: If we cut the grass **and** wash the car we get ice cream!

cut grass | wash car | ice cream | |
---|---|---|---|

F | F | F | |

F | T | F | |

T | F | F | |

T | T | T |

Only if we do both jobs do we get ice cream

## Or

The "or" logic gate can have **either **(or both) inputs true to become true:

In a truth table:

A | B | A or B | |
---|---|---|---|

F | F | F | |

F | T | T | |

T | F | T | |

T | T | T |

### Example: If we cut the grass **or** wash the car we get ice cream!

cut grass | wash car | ice cream | |
---|---|---|---|

F | F | F | |

F | T | T | |

T | F | T | |

T | T | T |

In this case we can do either job (or both) to get ice cream. Let's wash the car.

## Xor (eXclusive Or)

**Xor** is like **or** except it becomes false when **both **inputs are true:

Here we see **or** and **xor **side-by-side:

A | B | A or B | A xor B | |
---|---|---|---|---|

F | F | F | F | |

F | T | T | T | |

T | F | T | T | |

T | T | T | F |

**Xor **is like both your best friends fight. Life is fun with either one, but not both.

Think: "eXclusively yours" (no one else allowed).

## Not

We can also "not" or "invert":

- not true is false
- not false is true

As a "truth table":

A | not A | |
---|---|---|

F | T | |

T | F |

Important: it is the **circle** at the end that makes it "not":

So we can "not" the other logic gates like this:

## Nand

Nand is "and" with a "not", so it is true except when both inputs are true:

We can show that in a "truth table" (T is for true and F for false):

A | B | A and B | A nand B | |
---|---|---|---|---|

F | F | F |
T | |

F | T | F |
T | |

T | F | F |
T | |

T | T | T |
F |

## Nor

Nor is "or" and "not", so is false when **either (or both)** inputs are true:

In a truth table:

A | B | A or B | A nor B | |
---|---|---|---|---|

F | F | F |
T | |

F | T | T |
F | |

T | F | T |
F | |

T | T | T |
F |

## Xnor

**Xnor** is **xor** with a not:

As a truth table:

A | B | A xnor B | |
---|---|---|---|

F | F | T | |

F | T | F | |

T | F | F | |

T | T | T |

**Xnor **is true when both inputs **match **(both true or both false).

## All Together Now

Here they are together:

input |
output | |||||||||

A | B | and | nand | or | nor | xor | xnor | |||
---|---|---|---|---|---|---|---|---|---|---|

F | F | F | T | F | T | F | T | |||

F | T | F | T | T | F | T | F | |||

T | F | F | T | T | F | T | F | |||

T | T | T | F | T | F | F | T |

See them in action here (try clicking on the name, or the output line):

## In the Real World

This classic chip has 4 nand gates on it:

It's circuit diagram looks like this:

Example: you can connect pins 1 and 2 to different inputs, and will get an output from pin 3 except when both pins 1 and 2 are on.

(Note: power supply of 5 volts between "Vcc" and "GND")

There are many variations of these chips with different logic gates inside them. They operate really fast (millions of times a second), use very little power and cost very little. You can combine them to do amazing things.