What operators are supported?

AND (& or ·), OR (| or +), NOT (! or ~), and parentheses for grouping. You can also spell out AND, OR, NOT in uppercase. XOR (^) is also supported.

Which laws does the simplifier use?

Identity, null (domination), idempotent, complement, double negation, commutative, associative, distributive, absorption, and De Morgan's laws.

Are there limits on expression length?

Expressions up to ~50 characters work well. Very deeply nested or large expressions may not fully reduce in the fixed-step engine — use the truth table tab to verify correctness.

Does it verify the simplification is correct?

Yes. After simplification the tool evaluates both the original and simplified expression across all variable combinations to confirm they are logically equivalent.

What does the truth table show?

The truth table tab evaluates your original expression for every combination of true/false variable values, making it easy to spot any discrepancy.

Boolean Algebra Simplifier

Name: Boolean Algebra Simplifier
Availability: InStock
Author: Nham Vu

Enter a boolean expression to simplify it step-by-step using boolean algebra laws.

Boolean Expression

Expression

Operators: AND &, OR |, NOT !, XOR ^, parentheses

Quick examples

Operator syntax

AND : AND or & or · OR : OR or | or + NOT : NOT or ! or ~ XOR : XOR or ^

Enter an expression and click Simplify

Steps and truth table will appear here

Summary

Enter a boolean expression to simplify it step-by-step using boolean algebra laws.

How it works

Type a boolean expression using A, B, C (variables), AND, OR, NOT operators.
Use parentheses to group sub-expressions as needed.
Click "Simplify" to run the simplification engine.
Review each step — the applied law is shown next to every transformation.
The final simplified form is displayed at the bottom in highlighted output.

Use cases

Verify boolean expression simplifications for digital logic coursework.
Reduce logic gate counts before implementing circuits.
Check De Morgan transformations by hand against a reference.
Explore how absorption and idempotent laws collapse redundant terms.
Simplify Karnaugh map results for cross-validation.
Debug complex boolean conditions in code by seeing reduced form.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu