Truth Table
A table listing a logic function's output for every possible combination of its inputs.
Definition
A truth table enumerates all input combinations of a Boolean function and gives the output for each. For n inputs it has 2^n rows, fully specifying the function's behavior.
Because a truth table doubles in size with each added input, it is a practical specification tool only for small functions; larger designs are described behaviorally and synthesized automatically. Even so, the truth table remains the conceptual definition of correctness a synthesized circuit must meet.
Truth tables underpin equivalence checking, a verification technique that confirms two circuits compute the same function. For small functions this can be exhaustive; for large ones, tools use compact symbolic representations such as binary decision diagrams to reason about the same information without enumerating every row. Either way, the truth table remains the definition of correctness that a synthesized or optimized circuit must provably preserve.
| A | B | A XOR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Uses
- Defining a desired logic function unambiguously.
- Verifying that a circuit matches its specification.
- Deriving a minimal expression, often via a Karnaugh map.
Why it matters
Truth tables are the ground truth for combinational logic: two circuits are equivalent exactly when their truth tables match. They are the starting point for design and the reference for verification, though they grow exponentially with input count.
Fusion connection
Safety-critical interlock logic in a fusion facility can be specified and checked against an exhaustive truth table when the input count is small enough to enumerate.