Boolean Algebra Simplifier (Karnaugh Map)

Boolean Algebra Simplifier (Karnaugh Map) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: select, text
Output type: text
Sample coverage: 4
API ready: Yes

Overview

The Boolean Algebra Simplifier minimizes switching expressions and minterm sets using the Quine–McCluskey tabular method. It computes prime implicants, determines essential prime implicants for an exact minimal Sum of Products (SOP), displays a Gray-coded Karnaugh map, and verifies the simplified output across all variable assignments.

When to use

Minimizing combinatorial logic equations up to 4 variables for digital circuit designs.
Checking manual Karnaugh map groupings against an automated Quine–McCluskey prime implicant table.
Converting minterm index lists into simplified sum-of-products formulas with verification across all truth assignments.

How it works

1Choose between expression mode (using boolean variables A through D) or minterms mode (entering decimal indices).
2The tool parses operators including OR (+), AND (· or juxtaposition), NOT (' or !), and XOR (^), or evaluates the selected minterm list against the chosen variable count.
3Quine–McCluskey computes prime implicants and extracts an exact minimal SOP cover alongside canonical Σm notation.
4Results output a formatted Gray-coded Karnaugh map table and run an automated evaluation across all 2^N truth assignments to verify equivalence.

Use cases

Engineering students verifying homework solutions for digital logic design and switching algebra.
Hardware developers minimizing gate counts and literal counts in combinational logic blocks.
Software engineers optimizing multi-condition branching logic and Boolean flags into reduced expressions.

Examples

1. Simplifying an Algebraic Expression with Absorption

Computer Engineering Student

Background

Working on a logic synthesis assignment where boolean terms need reduction to their minimum literal count.

Problem

Verify that AB + A'B simplifies to the single variable B.

How to use

Set Input Mode to Expression, enter 'AB + A'B' into the Boolean expression field, and select 2 variables.

inputMode: expression, expression: AB + A'B, varCount: 2

Outcome

Calculates canonical form Σm(1, 3), yields minimal SOP 'F = B' with 1 literal, and displays the 2x2 Gray-coded Karnaugh map alongside complete verification.

2. Minimizing a 3-Variable Minterm Truth Table

Hardware Logic Designer

Background

Designing an address decoder with specified active-high decimal minterm outputs.

Problem

Find the minimal sum-of-products implementation for minterms 0, 1, 2, 4, 5, and 6 across variables A, B, and C.

How to use

Set Input Mode to Minterms (Σm), select 3 variables, and enter '0,1,2,4,5,6' into the minterm list field.

FAQ

Which Boolean operators are supported in expression mode?

You can use + for OR, · or variable juxtaposition for AND, ' or ! for NOT, ^ for XOR, and standard parentheses for grouping.

How many variables can this tool handle?

The tool supports functions with 2, 3, or 4 distinct variables (A, B, C, and D).

What is the difference between expression and minterms input modes?

Expression mode accepts symbolic switching algebra equations, while minterms mode takes a comma-separated list of decimal ON-set indices (Σm).

How does the tool verify the simplification?

It tests both the original function and the minimized SOP across every possible binary truth assignment (4, 8, or 16 states) to ensure exact equivalence.

Does the Karnaugh map follow standard Gray code ordering?

Yes, row and column labels use Gray code sequences (00, 01, 11, 10) so adjacent cells differ by exactly one bit.

inputMode: minterms, mintermList: 0,1,2,4,5,6, varCount: 3

Run this tool

Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Simplifying an Algebraic Expression with Absorption

2. Minimizing a 3-Variable Minterm Truth Table

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

Web Image Processing Rust Samples

Dilution Ratio Converter (1:X ↔ 1/X ↔ %)

Extended Euclidean Algorithm (ax + by = gcd(a, b))

Modular Inverse Calculator (Extended Euclidean Algorithm)

Modular Arithmetic Calculator (Add / Subtract / Multiply / Inverse / Power)