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Truth Table Generator

Name: Truth Table Generator
Author: AskMathAI

Generate truth tables for boolean expressions step-by-step. Get instant truth tables with detailed evaluations for AND, OR, NOT, XOR, implication, and equivalence operations.

Truth Table Generator

Enter a boolean expression to generate a complete truth table

Boolean Expression

Supported operators:

& (AND)

| (OR)

! (NOT)

^ (XOR)

→ (Implication)

↔ (Equivalence)

Master Boolean Logic with Our Advanced Truth Table Generator

Our truth table generator is designed to help students, engineers, and professionals analyze boolean expressions efficiently. Whether you're working on logic homework, designing digital circuits, or studying computer science, this tool provides comprehensive truth table generation capabilities that enhance your understanding of boolean logic.

The boolean logic calculator supports all fundamental logical operations: AND ( $\land$ ), OR ( $\lor$ ), NOT ( $\lnot$ ), XOR ( $\oplus$ ), implication ( $\rightarrow$ ), and equivalence ( $\leftrightarrow$ ). Our truth table maker is particularly useful for digital electronics design, logic circuit analysis, and computer architecture where understanding boolean relationships is crucial.

Perfect for university students in computer science and electrical engineering courses,professionals working with digital systems, and researchers in formal logic. The truth table generator provides not just truth tables, but detailed step-by-step evaluations that help you understand the underlying logic and verify your boolean expressions.

Supported Logical Operations

Operation	Symbol	Description	Truth Table
AND (Conjunction)	&	True only when both inputs are true	A & B: 00→0, 01→0, 10→0, 11→1
OR (Disjunction)	\|	True when at least one input is true	A \| B: 00→0, 01→1, 10→1, 11→1
NOT (Negation)	!	Inverts the input value	!A: 0→1, 1→0
XOR (Exclusive OR)	^	True when exactly one input is true	A ^ B: 00→0, 01→1, 10→1, 11→0
Implication	->	False only when A is true and B is false	A -> B: 00→1, 01→1, 10→0, 11→1
Equivalence	<->	True when both inputs have the same value	A <-> B: 00→1, 01→0, 10→0, 11→1

Common Mistakes to Avoid

Operator Precedence

Remember operator precedence: NOT (!) has highest priority, then AND (&), then OR (|). Use parentheses to clarify: $(A \& B) | C$ vs $A \& (B | C)$ .

Implication vs Equivalence

$A \rightarrow B$ (implication) is different from $A \leftrightarrow B$ (equivalence). Implication is false only when $A$ is true and $B$ is false.

Variable Names

Use single letters for variables (A, B, C, etc.). Avoid special characters except for operators. Maximum 8 variables allowed for performance.

How to Generate Truth Tables

A truth table shows all possible combinations of input values and their corresponding output values for a boolean expression. It's essential for understanding logic circuits and boolean algebra.

For $n$ variables, there are $2^n$ rows in the truth table.

Each row represents one possible combination of input values, and the result column shows the output of the boolean expression for that combination.

Evaluation Steps

Extract Variables

Identify all unique variables in the expression

Generate Combinations

Create all possible input combinations (2^n rows)

Substitute Values

Replace variables with their values in each row

Evaluate Expression

Apply logical operators following precedence rules

Record Results

Store the final output for each input combination

Applications

Digital Electronics

Logic circuit design, gate optimization

Computer Science

Algorithm design, program logic

Formal Logic

Mathematical proofs, logical reasoning

Examples

Simple AND Gate

Expression:

A & B

Description:

Basic conjunction operation

Digital logic, circuit design

Complex Expression

Expression:

(A & B) | (!A & C)

Description:

Combination of AND, OR, and NOT operations

Boolean algebra, logic optimization

Implication Logic

Expression:

A -> B

Description:

If A then B (implication)

Mathematical logic, proofs

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Frequently Asked Questions

What is a truth table?

A truth table is a mathematical table used in logic to determine the functional values of logical expressions for each combination of input values. It shows all possible input combinations and their corresponding outputs.

How many rows does a truth table have?

For n variables, a truth table has 2^n rows. For example, 2 variables = 4 rows, 3 variables = 8 rows, 4 variables = 16 rows, and so on.

What is the difference between AND and OR?

AND (conjunction) is true only when both inputs are true. OR (disjunction) is true when at least one input is true. In boolean algebra: A AND B = A & B, A OR B = A | B.

What is implication in logic?

Implication (A → B) means "if A then B". It is false only when A is true and B is false. In all other cases, it is true. This is different from equivalence (A ↔ B) which is true only when A and B have the same value.

How do I use parentheses in boolean expressions?

Parentheses control the order of operations. NOT has highest priority, then AND, then OR. Use parentheses to group operations: (A & B) | C means "A AND B, OR C", while A & (B | C) means "A AND (B OR C)".

What is XOR (exclusive OR)?

XOR is true when exactly one input is true, but not both. It is false when both inputs are false or both inputs are true. XOR is commonly used in digital electronics and cryptography.

Truth Table Generator