How many variables can a truth table have?

The truth table generator supports up to four variables, producing tables with up to 16 rows (2^4). This covers the vast majority of practical Boolean logic analysis and digital design exercises. Expressions with more variables would require 32 or more rows, which becomes impractical to display and is better handled with Karnaugh maps or software tools.

What is the difference between XOR and OR?

OR returns true when at least one input is true, including when both are true. XOR (exclusive OR) returns true only when exactly one input is true — it returns false when both inputs are true or both are false. XOR is used in applications like parity checking, error detection, and cryptographic operations where you need to detect whether exactly one of two conditions holds.

How are NAND and NOR gates universal?

NAND and NOR are called universal gates because any Boolean function — including AND, OR, NOT, XOR, and any combination — can be implemented using only NAND gates or only NOR gates. This is important for chip manufacturing because it means an entire processor can be built from a single gate type, simplifying fabrication. You can verify equivalences by comparing truth tables of the original expression and its NAND-only or NOR-only version.

Can I use this for digital logic homework?

Yes — the Boolean calculator is designed for exactly this use case. You can enter expressions from textbook problems and generate truth tables to verify your work. It supports standard Boolean notation and is particularly useful for checking whether two different expressions are logically equivalent by comparing their truth tables side by side.

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Boolean Logic Calculator

Evaluate boolean logic expressions: AND, OR, XOR, NOT, NAND, NOR, XNOR.

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Operations

AND

FALSE

TRUE

XOR

TRUE

NAND

TRUE

NOR

FALSE

XNOR

FALSE

Boolean Expression Evaluator

Use TRUE/FALSE/0/1 with AND, OR, XOR, NOT, parentheses

How to Use

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Enter boolean expressions

Type your logical expression using AND (∧), OR (∨), NOT (¬), XOR (⊕), and parentheses for grouping. Use 0/1 or true/false as input values.

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Evaluate the expression

Click Evaluate to compute the boolean result. A truth table is generated showing all possible input combinations and their outputs.

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Copy result or table

Copy the result value or the full truth table. Essential for digital logic design, programming conditionals, and formal logic study.

What is Boolean Logic Calculator?

The boolean calculator evaluates logical expressions using AND, OR, NOT, XOR, NAND, and NOR operators, and generates complete truth tables for expressions with up to four variables. Enter any Boolean expression and see its evaluated result and full truth table instantly. It is the most practical Boolean logic calculator for digital design and discrete mathematics coursework.

Why use Boolean Logic Calculator?

Truth table generation for multi-variable expressions is tedious by hand and error-prone — this tool eliminates that work entirely and lets you focus on interpreting results rather than filling in rows. It supports all standard logic gates, making it useful both for pure Boolean algebra and for digital circuit analysis. Students preparing for logic design exams can test expressions rapidly and build intuition about gate behavior.

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How it works

Electrical engineering students use this tool to verify Karnaugh map simplifications by comparing truth tables before and after reduction. Software developers working on conditional logic in code use it to confirm that complex if-else combinations behave as intended. Cybersecurity students studying access control policies use Boolean expressions to model permission logic.

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Pro Tip

Use the NAND-only or NOR-only equivalents of your expression (NAND and NOR are universal gates) and verify with the truth table that the simplified form matches the original — this is a common exam technique worth practicing.

Frequently Asked Questions

The calculator supports the six fundamental logical operators: AND, OR, NOT, XOR (exclusive OR), NAND (not AND), and NOR (not OR). These cover all standard Boolean algebra and digital logic gate types. You can combine multiple operators in a single expression to model complex logic circuits or conditional rules.

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