Truth Table Generator

Truth tables for logic expressions with AND, OR, NOT, XOR and implication, plus minterms and maxterms.

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Logic expression

Use words or symbols: NOT (! ¬ ~), AND (& ∧ ·), OR (| ∨ +), XOR (^ ⊕), NAND, NOR, implies (-> →) and if and only if (<-> ↔). Variables are letters or words, up to six. Order of operations: NOT first, then AND, XOR, OR, →, and ↔ last; NAND ranks with AND and NOR with OR. Brackets go first.

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Values

Variables

Truth table

ContingencyTrue in some rows and false in others. True in 7 of 8 rows.

Truth table for A ∧ B → ¬C
#Row number	A	B	C	A ∧ B	¬C	A ∧ B → ¬C
0	0	0	0	0	1	1
1	0	0	1	0	0	1
2	0	1	0	0	1	1
3	0	1	1	0	0	1
4	1	0	0	0	1	1
5	1	0	1	0	0	1
6	1	1	0	1	1	1
7	1	1	1	1	0	0

Minterms, maxterms and canonical forms

Notation

Minterms (rows that are true): Σm(0, 1, 2, 3, 4, 5, 6)
Maxterms (rows that are false): ΠM(7)
Canonical sum of products (SOP): (¬A ∧ ¬B ∧ ¬C) ∨ (¬A ∧ ¬B ∧ C) ∨ (¬A ∧ B ∧ ¬C) ∨ (¬A ∧ B ∧ C) ∨ (A ∧ ¬B ∧ ¬C) ∨ (A ∧ ¬B ∧ C) ∨ (A ∧ B ∧ ¬C)
One AND-term for each true row, joined with OR.
Canonical product of sums (POS): ¬A ∨ ¬B ∨ ¬C
One OR-term for each false row, joined with AND.

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