A truth table is the complete, unambiguous description of a boolean function. It has one column per input, one column per output, and one row for every possible input combination.
Each input can be 0 or 1, and each extra input doubles the number of combinations, so n inputs give 2ⁿ rows: 4 rows for 2 inputs, 8 for 3, 16 for 4.
Rows are listed by counting in binary: 000, 001, 010, … 111. The first input column (A) is the most significant bit, so it changes slowest. A row is usually named by its input bits, so row 101 means A = 1, B = 0, C = 1, which is row 5 in decimal.
Why truth tables matter:
- They are the reference. Two expressions are equivalent exactly when their output columns match in every row.
- One row where they differ, a counterexample, is enough to prove two expressions are not equal.
- Later, every row where the output is 1 becomes a minterm and every row where it is 0 becomes a maxterm.
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |