A truth table is a table that shows the outputs of a logical function for all possible combinations of inputs. It is a useful tool for visualizing the behavior of a digital circuit and for simplifying logical expressions.
To construct a truth table, first write down all of the possible input combinations. Then, for each input combination, determine the output of the logical function. The output can be either 0 or 1.
For example, the truth table for a two-input AND gate is as follows:
| A | B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The truth table shows that the output of the AND gate is 1 only when both inputs are 1. Otherwise, the output is 0.
Truth tables can be used to design and simplify digital circuits. By visualizing the behavior of a logical function, designers can identify redundant logic and simplify the circuit. This can lead to smaller, faster, and more efficient circuits.