Boolean Expression Evaluator
Variables:
A B C D (case-insensitive, up to 4 variables)Operators:
AND OR NOT NAND NOR XOR XNOR · & · | · ^ · ! · ~Grouping:
( ) — e.g. A AND (B OR NOT C)
Results
Truth Table
Canonical Forms
📐 Boolean Algebra Laws
Null: A AND 0 = 0 · A OR 1 = 1
Idempotent: A AND A = A · A OR A = A
Complement: A AND NOT A = 0 · A OR NOT A = 1
De Morgan: NOT(A AND B) = NOT A OR NOT B · NOT(A OR B) = NOT A AND NOT B
❓ FAQ
What is a minterm?
A minterm is a product term (AND of all variables) that evaluates to 1 for exactly one row of the truth table. The Sum of Minterms (SOM) is also called the canonical Sum of Products (SOP) form — it's the OR of all minterms where the output is 1. Every Boolean function has a unique SOM representation.
What is a maxterm?
A maxterm is a sum term (OR of all variables) that evaluates to 0 for exactly one row of the truth table. The Product of Maxterms (POM) is the canonical Product of Sums (POS) form — it's the AND of all maxterms where the output is 0.
How do I simplify a Boolean expression?
Use Boolean algebra laws (De Morgan's, distributive, absorption) or Karnaugh Maps (K-maps) for systematic minimization. For 2 variables use a 2×2 K-map; for 3 variables use a 2×4 K-map; for 4 variables use a 4×4 K-map. Group adjacent 1s in powers of 2 to find simplified AND terms.