About Truth Table Generator
Generate truth tables for any boolean expression. AND, OR, NOT, XOR, IMPLIES, IFF — auto-detects variables, shows step-by-step columns. Free, no sign-up.
How to use
- Type a boolean expression in the input. Variables are single uppercase letters (A, B, C, …). Operators can be typed as words (AND, OR, NOT) or symbols (&, |, !).
- Click the operator chips to insert at the cursor — handy for symbols like → or ⊕ that aren't on the keyboard.
- The table updates live. Each row is one combination of variable values; columns include each sub-expression so you can trace the calculation step by step.
- The final column (highlighted) is your full expression's result. The summary chips at the top tell you whether it's a tautology (always true), contradiction (always false), or somewhere in between.
- Maximum 8 variables (256 rows). Beyond that the table becomes too unwieldy — split your expression into smaller pieces.
Frequently asked questions
What's the operator precedence?
From highest (binds tightest) to lowest: NOT > AND > OR > XOR > IMPLIES > IFF. So A OR B AND C parses as A OR (B AND C). Always use parentheses if you want a different grouping — they make the expression unambiguous.
Can I use lowercase variables?
Yes — they get auto-uppercased. a and b works the same as A AND B. The column headers always show uppercase.
How does IMPLIES work? It's confusing.
A IMPLIES B is true except when A is true and B is false. Think of it as 'if A is true, then B must be true.' If A is false, the whole statement is vacuously true (the premise didn't hold). Equivalent to (NOT A) OR B.
What's the difference between IFF and AND?
A IFF B means 'A and B have the same truth value' — true when both are true OR both are false. A AND B requires both to be true. So IFF is true 2 of 4 rows; AND is true 1 of 4.
Can I use this for digital logic / circuit design?
Yes. Boolean expressions in this tool map directly to digital logic gates: AND = ∧ gate, OR = ∨ gate, NOT = inverter, XOR = exclusive-or gate. The truth table is the gate's complete behavior. For circuit minimization (finding the smallest equivalent expression), use a Karnaugh map or Quine-McCluskey method — those aren't part of this tool but the truth table is the input they need.
Why max 8 variables?
2⁸ = 256 rows. Beyond that the table becomes unreadable and slow. If your expression has more than 8 variables, you can either factor it into independent sub-problems or use a SAT solver — that's specialized software designed for very large boolean problems.
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