A truth table is a tabular representation that lists all possible combinations of input values for a logic circuit or function and the corresponding output values that result from applying a specific logic operation. It provides a concise and systematic way to illustrate how a logic circuit or function behaves under different input conditions.
In a truth table:
- Each row corresponds to a unique combination of input values.
- Each column represents an input or an output variable.
- The entries in the output column(s) indicate the resulting output values for each input combination.
Truth tables are commonly used in digital logic design, mathematics, computer science, and other fields where logical operations are applied. They are especially useful for analyzing and understanding the behavior of logic gates, circuits, and functions, as well as for verifying the correctness of logical expressions.
For example, consider a simple AND gate with two inputs, A and B. The truth table for this AND gate would list all possible combinations of A and B (0 or 1), and the corresponding output value of the AND operation:
| A | B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The truth table clearly shows that the AND gate produces an output of 1 (true) only when both inputs are 1; otherwise, the output is 0 (false).
Truth tables are essential tools for logical analysis, circuit design, and understanding the behavior of logic systems. They serve as a foundation for more complex logical operations and can be used to guide the construction and verification of digital circuits.