Truth tables are used to show the logical outputs of logic gates. When combined together, logic gates are called logic circuits.

Describing logic gates uses a similar process to describing an equation in maths. In fact, the same rules of using brackets are applied.

When resolving your logic circuits, resolve the brackets on the left first, then the middle gate, then the brackets on the right.

For example, the logic circuit shown to the left would be written as the following logic equation:

D = A AND (B OR NOT C)

Notice that the logic equation appears to be reading the diagram from the right, then from the top to the bottom. The value of D is dependent on what the values of A, B, and C are, and we can show all possible values by creating a truth table.

The first step is to create a column for all the inputs and one for the output, and enough rows to hold all possible values. The number of rows is calculated at 2^(number of inputs):A |
B |
C |
D |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

? | ? | ? | ? |

A |
B |
C |
D |

0 | ? | ? | ? |

1 | ? | ? | ? |

1 | ? | ? | ? |

0 | ? | ? | ? |

0 | ? | ? | ? |

1 | ? | ? | ? |

1 | ? | ? | ? |

0 | ? | ? | ? |

A |
B |
C |
D |

0 | 0 | ? | ? |

1 | 0 | ? | ? |

1 | 1 | ? | ? |

0 | 1 | ? | ? |

0 | 1 | ? | ? |

1 | 1 | ? | ? |

1 | 0 | ? | ? |

0 | 0 | ? | ? |

A |
B |
C |
D |

0 | 0 | 0 | ? |

1 | 0 | 0 | ? |

1 | 1 | 0 | ? |

0 | 1 | 0 | ? |

0 | 1 | 1 | ? |

1 | 1 | 1 | ? |

1 | 0 | 1 | ? |

0 | 0 | 1 | ? |

A |
B |
C |
D |

0 | 0 | 0 | 0 |

1 | 0 | 0 | ? |

1 | 1 | 0 | ? |

0 | 1 | 0 | ? |

0 | 1 | 1 | ? |

1 | 1 | 1 | ? |

1 | 0 | 1 | ? |

0 | 0 | 1 | ? |

A |
B |
C |
D |

0 | 0 | 0 | 0 |

1 | 0 | 0 | 1 |

1 | 1 | 0 | 1 |

0 | 1 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 1 | 1 | 1 |

1 | 0 | 1 | 0 |

0 | 0 | 1 | 0 |

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