Truth Tables
Often the logical functionality of a gate or a series of gates is illustrated by a truth table. With a truth table all possible combinations of input states are considered and the output value for each of these input states is listed in a table. Examples of truth tables can be found in the descriptions of basic logic gates and other logic gates.
The "don't care" condition
It can easily be seen that for a logic gate with n inputs then the corresponding truth table requires 2n rows or entries. For devices with 4 or more inputs, representing each input state in this way can be a lengthy procedure. To simplify this representation of a logic function the concept of the "dont care" condition is introduced.
Consider, for example the truth table for a three-input OR gate, it looks like
 |  |
| ++ |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
This table can be simplified by writing
| |
| ++ |
| 0 | 0 | 0 | 0 |
| 1 | x | x | 1 |
| x | 1 | x | 1 |
| x | x | 1 | 1 |
where x can equal 0 or 1.
