42eXplore
Thematic pathfinders and reference tools for classrooms

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

LogicSymbolType here
Negation¬p!A
Conjunctionp ∧ qA&B
Disjunctionp ∨ qA+B
Exclusive orp ⊕ qA^B
Implicationp → q!A+B
Biconditionalp ↔ q!(A^B)

Implication and the biconditional have no direct symbol here, so rewrite them: pq is equivalent to ¬pq, and pq 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.