Truth Table Generator
Full truth table for any expression up to six variables.
Press Generate table.
Examples: (A+B)&!C · A^B (XOR) · !A+B (implication)
How to read the table
Each row is one assignment of truth values to the variables. With n variables there are 2n rows, counted in binary from all-zeros at the top, so the row index doubles as the minterm number.
Logical connectives in this notation
| Logic | Symbol | Type here |
|---|---|---|
| Negation | ¬p | !A |
| Conjunction | p ∧ q | A&B |
| Disjunction | p ∨ q | A+B |
| Exclusive or | p ⊕ q | A^B |
| Implication | p → q | !A+B |
| Biconditional | p ↔ q | !(A^B) |
Implication and the biconditional have no direct symbol here, so rewrite them: p → q is equivalent to ¬p ∨ q, and p ↔ q is the negation of exclusive or. A row where the output is 1 everywhere makes the expression a tautology; all zeros makes it a contradiction.
Related: boolean algebra calculator for SOP and POS forms.