Boolean Expression Simplifier
Simplify Boolean logic expressions to minimal sum-of-products form online.
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What is Boolean Expression Simplifier?
The Boolean Expression Simplifier reduces complex Boolean logic down to its minimal sum-of-products form. It parses any expression built from AND, OR, NOT, XOR, NAND, and NOR operators, constructs the full truth table, and applies the Quine-McCluskey algorithm to find the smallest equivalent expression. A built-in truth table lets you verify that the simplified result behaves exactly like the original.
Key Benefits
- Produces the minimal sum-of-products expression automatically
- Supports AND, OR, NOT, XOR, NAND, NOR, parentheses, and up to 6 variables
- Quine-McCluskey tabulation works for any number of variables
- Built-in truth table for instant verification
- 100% in-browser - no data leaves your device
Common Use Cases
- •Minimize Boolean algebra for homework and exam practice
- •Simplify logic before building digital circuits and PLA designs
- •Optimize expressions for FPGAs, CPLDs, and HDL implementation
- •Verify hand-written K-map or algebra simplifications
How to Use the Boolean Expression Simplifier
- Enter your expression: Type a Boolean expression using variables A-Z and the operators AND, OR, NOT, XOR, NAND, NOR. Use parentheses to group terms, for example (A OR B) AND NOT C. Complement literals written with a prime mark are also accepted.
- Click Simplify: Press the Simplify button or hit Enter. The tool parses your expression, builds its full truth table, and runs the Quine-McCluskey algorithm to find the minimal sum-of-products expression.
- Verify with the truth table: Toggle Show truth table to compare the output of your original expression against the simplified one across every combination of inputs - they must match.
- Copy the result: Click Copy to place the simplified expression on your clipboard, ready to paste into a schematic, HDL, breadboard, or documentation.
Key Features
- Reduces any expression to minimal sum-of-products form
- Supports AND, OR, NOT, XOR, NAND, and NOR operators
- Handles parentheses, complement literals, and up to 6 variables
- Built-in truth table to verify the result
- One-click copy of the simplified expression
Frequently Asked Questions
What is sum-of-products (SOP) form?
Sum-of-products is a standard way to write a Boolean function as the OR (sum) of AND terms (products), for example AB + BC. Every Boolean function can be expressed this way, and SOP is the usual starting point for building digital logic from a truth table. The simplifier outputs your expression in minimal SOP form.
Which operators and symbols are supported?
The tool accepts AND, OR, NOT, XOR, NAND, and NOR keywords, plus the symbols AND, OR, NOT, XOR, and the prime mark for complement literals. It also accepts parentheses, and variables from A to Z (up to 6 distinct variables).
How does the simplification algorithm work?
The tool builds the full truth table of your expression, then runs the Quine-McCluskey algorithm to find all prime implicants and selects the minimum set that covers every true output. This is the same tabulation method used for Karnaugh maps, but it works for any number of variables without manual grouping.
Is my expression sent anywhere?
No. Everything runs locally in your browser using JavaScript. Your expression is never transmitted to any server, so you can safely simplify proprietary or sensitive logic offline.