Truth Table Generator
Generate a truth table for any Boolean or logic expression with up to 6 variables: a column for each part, tautology or contradiction, equivalence of two statements, the converse and contrapositive, and the minimal sum of products.
About the Truth Table Generator
A truth table lists every combination of true (1) and false (0) for the variables and the expression's value in each, with a column for every part of the expression, the way textbooks build it up.
Give a second expression to test equivalence: two statements are equivalent when their columns match in every row (p → q and ¬q → ¬p, for instance, which is why the contrapositive proves the same thing; the converse q → p does not). For digital electronics, the minterms give the canonical sum of products, and the Quine–McCluskey method reduces it to a minimal one, the same answer a Karnaugh map gives.
The formula
Rows = 2ⁿ for n variables; NOT > AND > XOR > OR > → > ↔
Operators you can type
| Operator | Write as |
|---|---|
| NOT | not, !, ~, ¬, or A' |
| AND | and, &, *, ∧ |
| OR | or, |, +, ∨ |
| XOR | xor, ^, ⊕ |
| Implies | ->, → |
| If and only if | <->, ↔ |
| NAND / NOR | nand, nor |
Worked example
Example: True in = 1 of 4 rows
- Input: Boolean expression: A and not B.
- Formula: Rows = 2ⁿ for n variables; NOT > AND > XOR > OR > → > ↔
- Result: True in = 1 of 4 rows
- Classification: a contingency
- Minterms Σm: Σm(2)
- Maxterms ΠM: ΠM(0, 1, 3)
Questions people ask
Are A → B and not A or B the same?
Yes: enter one as the expression and the other under “Compare with”, and the calculator confirms they're equivalent.
Can I use 1 and 0?
Yes, as constants.
Is the minimal form unique?
Not always: some functions have several minimal sums of products of the same size. Any of them is correct.