What is a truth table?

A truth table is a mathematical table that shows the output of a boolean logic expression for every possible combination of input values. Each variable can be either true (1) or false (0). With n variables, there are 2^n rows: 2 variables = 4 rows, 3 variables = 8 rows, 4 variables = 16 rows. Truth tables are used in digital logic design, computer science, and propositional logic to verify expressions and design circuits.

What are the basic logic gates and their truth tables?

AND: output is 1 only when BOTH inputs are 1. OR: output is 1 when AT LEAST ONE input is 1. NOT: inverts the input (0 becomes 1, 1 becomes 0). XOR (exclusive OR): output is 1 when inputs DIFFER. NAND: NOT AND — output is 0 only when both inputs are 1. NOR: NOT OR — output is 1 only when both inputs are 0. XNOR: NOT XOR — output is 1 when inputs are EQUAL.

What is De Morgan's Law in boolean algebra?

De Morgan's Laws are two fundamental theorems in boolean algebra: (1) NOT(A AND B) = (NOT A) OR (NOT B), and (2) NOT(A OR B) = (NOT A) AND (NOT B). These laws are used to simplify logic circuits and convert NAND/NOR gates to equivalent AND/OR/NOT combinations. In digital logic: NAND gates alone can implement any boolean function, as can NOR gates alone — both are functionally complete.

What is a tautology vs a contradiction in logic?

A tautology is a boolean expression that is always true (1) regardless of input values. Example: A OR (NOT A) is always true. A contradiction (unsatisfiable formula) is always false (0) regardless of input values. Example: A AND (NOT A) is always false. This truth table generator automatically detects tautologies (all result rows = 1) and contradictions (all result rows = 0).

How do I write a boolean expression for the truth table generator?

Use single letters (A, B, C, ...) for variables. Supported operators: AND (write AND or &&), OR (write OR or ||), NOT (write NOT or !), XOR (write XOR or ^), NAND (write NAND), NOR (write NOR), XNOR (write XNOR). Use parentheses for grouping: (A AND B) OR C. Examples: 'NOT A OR B' is a conditional, '(A XOR B) AND C' is a 3-variable expression. Variables are case-insensitive.

What is the Majority function in boolean logic?

The Majority function with 3 inputs returns 1 when at least 2 of 3 inputs are 1: (A AND B) OR (B AND C) OR (A AND C). It is used in fault-tolerant systems and voting circuits. With 3 inputs, it is true for 4 out of 8 combinations (when 2 or more are true). This is different from the OR function (true when 1 or more are true) and the AND function (true only when all 3 are true).

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Truth Table Generator

A truth table shows all possible input combinations and the corresponding output for a boolean expression. With n variables: 2^n rows (2 vars = 4 rows, 3 = 8, 4 = 16, 5 = 32). AND truth table: 0,0→0; 0,1→0; 1,0→0; 1,1→1. OR: 0,0→0; 0,1→1; 1,0→1; 1,1→1. XOR: 0,0→0; 0,1→1; 1,0→1; 1,1→0. NAND is NOT AND; NOR is NOT OR. A tautology is always true; a contradiction is always false.

Generate truth tables for any boolean logic expression. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR operators and up to 5 variables (32 rows). Detects tautologies and contradictions. Copy results as tab-separated data.

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Expression

Operators: AND (&&), OR (||), NOT (!), XOR (^), NAND, NOR, XNOR. Use parentheses for grouping.

Presets

How to Use

1
Enter a boolean expression
Type your logic expression using variables A-Z and operators: AND, OR, NOT, XOR, NAND, NOR, XNOR. Example: A AND B OR NOT C. Use parentheses for grouping.
2
View the truth table
The truth table generates instantly with all 2^n combinations. True rows are highlighted green. The result column shows 0 (false) or 1 (true) for each row.
3
Check for special cases
If all rows are 1, the expression is a tautology (always true). If all rows are 0, it is a contradiction (always false). The row counts show how many times the expression is true.
4
Copy the table
Click Copy to get the truth table as tab-separated values. Paste directly into Excel or Google Sheets for further analysis.

Frequently Asked Questions

What is a truth table?: A truth table is a mathematical table that shows the output of a boolean logic expression for every possible combination of input values. Each variable can be either true (1) or false (0). With n variables, there are 2^n rows: 2 variables = 4 rows, 3 variables = 8 rows, 4 variables = 16 rows. Truth tables are used in digital logic design, computer science, and propositional logic to verify expressions and design circuits.
What are the basic logic gates and their truth tables?: AND: output is 1 only when BOTH inputs are 1. OR: output is 1 when AT LEAST ONE input is 1. NOT: inverts the input (0 becomes 1, 1 becomes 0). XOR (exclusive OR): output is 1 when inputs DIFFER. NAND: NOT AND — output is 0 only when both inputs are 1. NOR: NOT OR — output is 1 only when both inputs are 0. XNOR: NOT XOR — output is 1 when inputs are EQUAL.
What is De Morgan's Law in boolean algebra?: De Morgan's Laws are two fundamental theorems in boolean algebra: (1) NOT(A AND B) = (NOT A) OR (NOT B), and (2) NOT(A OR B) = (NOT A) AND (NOT B). These laws are used to simplify logic circuits and convert NAND/NOR gates to equivalent AND/OR/NOT combinations. In digital logic: NAND gates alone can implement any boolean function, as can NOR gates alone — both are functionally complete.
What is a tautology vs a contradiction in logic?: A tautology is a boolean expression that is always true (1) regardless of input values. Example: A OR (NOT A) is always true. A contradiction (unsatisfiable formula) is always false (0) regardless of input values. Example: A AND (NOT A) is always false. This truth table generator automatically detects tautologies (all result rows = 1) and contradictions (all result rows = 0).
How do I write a boolean expression for the truth table generator?: Use single letters (A, B, C, ...) for variables. Supported operators: AND (write AND or &&), OR (write OR or ||), NOT (write NOT or !), XOR (write XOR or ^), NAND (write NAND), NOR (write NOR), XNOR (write XNOR). Use parentheses for grouping: (A AND B) OR C. Examples: 'NOT A OR B' is a conditional, '(A XOR B) AND C' is a 3-variable expression. Variables are case-insensitive.
What is the Majority function in boolean logic?: The Majority function with 3 inputs returns 1 when at least 2 of 3 inputs are 1: (A AND B) OR (B AND C) OR (A AND C). It is used in fault-tolerant systems and voting circuits. With 3 inputs, it is true for 4 out of 8 combinations (when 2 or more are true). This is different from the OR function (true when 1 or more are true) and the AND function (true only when all 3 are true).

Basic Logic Gates Truth Table

A	B	AND	OR	NAND	NOR	XOR	XNOR
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Boolean Operator Syntax Reference

Operator	Word Form	Symbol	Example	Meaning
AND	AND	&& or &	A AND B	Both inputs must be true
OR	OR	\|\| or \|	A OR B	At least one input true
NOT	NOT	!	NOT A	Invert the input
XOR	XOR	^	A XOR B	Inputs must differ
NAND	NAND	—	A NAND B	NOT AND — false only when both true
NOR	NOR	—	A NOR B	NOT OR — true only when both false
XNOR	XNOR	—	A XNOR B	Inputs must be equal