Boolean Truth Table Calculator – Logic Gates
Generate truth tables for AND, OR, NOT, NAND, NOR, XOR, and XNOR logic gates.
About This Calculator
Generate truth tables for AND, OR, NOT, NAND, NOR, XOR, and XNOR logic gates. Use the calculator above for instant results.
Worked Examples
- Full truth table: 00→0, 01→0, 10→0, 11→1
Answer: 1 AND 1 = 1
- XOR is 1 when inputs differ: 01→1, 10→1, others→0
Answer: 1 XOR 0 = 1
- NAND = NOT AND. Only 11→0, all others→1
Answer: 1 NAND 1 = 0
Who Uses This Calculator?
Logic gate truth tables for coursework.
Verify logic circuit behavior.
Interactive logic gate demonstrations.
Digital electronics lab reference.
Common Mistakes to Avoid
❌ NAND and NOR are universal gates
Any logic circuit can be built from only NAND gates (or only NOR gates). They are called universal gates.
❌ XOR vs XNOR
XOR is 1 when inputs differ (exclusive or). XNOR is 1 when inputs are equal (its complement).
Frequently Asked Questions
Universal gates?
NAND and NOR are universal — any boolean function can be implemented using only one gate type. Cheaper to manufacture one gate type in bulk.
De Morgan's theorem?
NOT(A AND B) = (NOT A) OR (NOT B). NOT(A OR B) = (NOT A) AND (NOT B). Essential for logic simplification.
Boolean algebra uses?
Digital circuit design, CPU logic units, database query optimization (AND/OR/NOT conditions), conditional programming logic.