# Truth Table Generator

Complete truth table (≤ 6 variables, 64 rows) with alphabetical variable order, per-row function values, and canonical Σm/ΠM forms.

> Canonical page: https://elysiatools.com/en/tools/truth-table-generator

- **Category:** Math & Numbers

- **Keywords:** truth table, boolean expression, logic gates, minterms, maxterms, canonical form, digital logic, logic circuits, discrete math, parity function

## Overview

Generate complete truth tables for Boolean expressions with up to 6 variables (A–F) and up to 64 evaluation rows. The tool supports standard switching-algebra notation, orders inputs alphabetically, computes function values per row, and derives canonical sum-of-minterms (Σm) and product-of-maxterms (ΠM) representations.

## Inputs

- **Boolean expression (A–F, up to 6 variables)** (text): Classic switching-algebra notation: + OR, ^ XOR, · or juxtaposition AND, ' or ! NOT, parentheses. At most 6 distinct variables.

## When to use

- Analyzing digital logic functions such as multiplexers, parity checkers, and basic switching circuits.
- Deriving minterm (Σm) and maxterm (ΠM) lists for Karnaugh map minimization and algebraic simplification.
- Verifying homework problems and logic proofs in discrete mathematics or computer architecture courses.

## How it works

- Enter a Boolean expression using variables A through F and supported operators like + (OR), ^ (XOR), !/~/' (NOT), and · or juxtaposition (AND).
- The tool parses the expression, identifies all distinct variables, and builds an ordered binary assignment table for up to 64 input combinations.
- It computes output F for every combination and displays the full truth table alongside canonical Σm and ΠM notations.

## Use cases

- Digital circuit analysis: Verifying selector logic for 2-to-1 multiplexers and standard switching gates.
- Parity calculation: Determining odd-parity and error-checking behavior with chained XOR expressions.
- Canonical formulation: Extracting exact minterm lists before entering values into Karnaugh maps or logic synthesizers.

## Frequently asked questions

### Which operators are supported in Boolean expressions?

The generator accepts + for OR, ^ for XOR, ! or ~ or ' for NOT, and ·, *, &, or direct variable juxtaposition for AND.

### How many variables can I include in a single expression?

You can use up to 6 unique variables (A through F), generating a truth table of up to 64 rows.

### How are variables ordered in the truth table?

All detected variables are sorted and evaluated in alphabetical order (e.g., A, B, C).

### What are canonical Σm and ΠM representations?

Σm represents the ON-set (row indices where F = 1), while ΠM represents the OFF-set (row indices where F = 0).

### Does juxtaposition like AB automatically represent logical AND?

Yes, placing variables side by side such as AB or A'C evaluates as a logical AND operation.

## Related tools

- [Header Remover](https://elysiatools.com/en/tools/header-remover): Remove headers from CSV data to create clean header-less files. Perfect for database imports, data processing pipelines, API integrations, and systems that require header-less CSV format. Features: - Remove first row (header) from CSV data - Remove multiple header rows - Skip empty lines before removing headers - Preserve data integrity - Support various CSV separators - Preview before removal - Data validation options - Batch processing capabilities Common Use Cases: - Prepare data for database imports - Clean up API response data - Remove metadata from exported files - Create header-less data for machine learning - Prepare data for systems that don't use headers - Extract pure data values from structured files
- [Markdown TOC Generator](https://elysiatools.com/en/tools/markdown-toc-generator): Generate a table of contents from Markdown headings with GitHub-style anchor links
- [Slug Generator](https://elysiatools.com/en/tools/slug-generator): Generate clean URL slugs from any text, with built-in Chinese-to-Pinyin conversion. Collapse separators, lowercase, and optional max-length word-aware truncation.
- [Barcode Batch Generator](https://elysiatools.com/en/tools/barcode-batch-generator): Batch generate Code 128, EAN-13, UPC-A, ITF-14, QR Code, and Data Matrix outputs from CSV or multiline text
- [Boolean Algebra Simplifier (Karnaugh Map)](https://elysiatools.com/en/tools/boolean-algebra-simplifier): Minimal SOP via Quine–McCluskey with essential prime implicants, exact minimum cover, Gray-coded Karnaugh map, and full-assignment verification.
- [Dilution Ratio Converter (1:X ↔ 1/X ↔ %)](https://elysiatools.com/en/tools/dilution-ratio-converter): Convert dilution notations 1:X ↔ 1/X ↔ percent, with dilution factor, parts, and mixing volumes.
- [Email Signature HTML Builder](https://elysiatools.com/en/tools/email-signature-html-builder): Generate a clean, copy-paste HTML email signature that renders correctly in Gmail, Outlook, and Apple Mail — with avatar/logo, social icons (auto-detected from your links), accent color, light/dark/auto theme, and a table-based email-safe layout using inline styles. Copy the raw HTML and paste straight into your mail client.
- [Extended Euclidean Algorithm (ax + by = gcd(a, b))](https://elysiatools.com/en/tools/extended-euclidean-algorithm): Bézout coefficients for any-sign integers with the full division-step table, lcm, and optional linear Diophantine solving (particular + general solution).

## Samples

- [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion
- [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion
- [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion
- [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion