Truth-table generator
Type any Boolean expression. We accept AND OR NOT XOR NAND NOR in any case, plus standard symbols (&& || ! ⊕ · + ¬) and English (and or not). Variables are single uppercase letters A–H. Parentheses for grouping.
A AND B
A OR (B AND NOT C)
(A AND B) OR (NOT A AND C)
(A OR B) AND (A OR NOT B)
A XOR B XOR C
De Morgan check
tautology
contradiction
Truth table
Canonical normal forms
SOP — Sum of Products (DNF)
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POS — Product of Sums (CNF)
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SOP is the OR of all rows where the expression is true (each row written as an AND of its variables). POS is the AND of all rows where it's false (each row written as an OR of negated variables). Either form is enough to rebuild any Boolean function — and SOP maps directly onto a circuit of ANDs feeding an OR (used in PLAs and FPGAs).
Step-by-step evaluator
Type your expression and choose values for each variable. The evaluator walks left-to-right by operator precedence: NOT first, then AND, then XOR, then OR. Each sub-expression is reduced to T or F.
Trace
Enter an expression and toggle the variable values.
Identity & equivalence laws
These are the algebra of Boolean expressions — verified by every truth table. They let you simplify circuits and prove two expressions are equivalent.
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