Boolean Algebra Calculator
Boolean Algebra Calculator works out Simplified (sum of products) and Simplified (product of sums) from Boolean expression, Variable order (optional) and Variables have multi-letter names. The default figures on this page give simplified (sum of products) of A + B; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Variables in order: A, B (2 variables, 4 rows).
- Rows where the expression is 1 (minterms): 1, 2, 3.
- Canonical sum of products: A'B + AB' + AB
- Quine-McCluskey prime implicants: B, A
- Minimum cover: A + B (2 term(s), 2 literal(s)).
- Complement minimised and De Morgan applied gives the product of sums: (A + B)
Mintermstable
Maxtermstable
Variablestable
Prime implicantstable
Truth tabletable
| A | B | F |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Boolean Algebra Calculator calculates
Simplifies a boolean expression to its minimum sum-of-products and product-of-sums form, with the truth table, minterms, maxterms and prime implicants.
How to use this Boolean Algebra Calculator
Enter Boolean expression, Variable order (optional) and Variables have multi-letter names. Simplified (sum of products) updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Simplified (sum of products), Simplified (product of sums) and Canonical sum of products.
The method follows M. Morris Mano and Michael D. Ciletti, Digital Design, Chapter 2 (Boolean Algebra and Logic Gates) and Chapter 3 (Gate-Level Minimization) and E. V. Huntington, "Sets of independent postulates for the algebra of logic", Transactions of the AMS 5 (1904), 288-309.
Absorption: A + A'B example
With Boolean expression: A + A'B, the calculator returns Simplified (sum of products): A + B, Minterms: see result table, Simplified (product of sums): (A + B). This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Simplified (sum of products), Simplified (product of sums) and Canonical sum of products. The inputs you can vary are Boolean expression, Variable order (optional) and Variables have multi-letter names.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to calculate Boolean algebra?
Simplifies a boolean expression to its minimum sum-of-products and product-of-sums form, with the truth table, minterms, maxterms and prime implicants. Open “How this is worked out” beside the result to see each step for your own figures.
Can a TI-84 solve algebra?
Simplifies a boolean expression to its minimum sum-of-products and product-of-sums form, with the truth table, minterms, maxterms and prime implicants. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give A + B.
What are the 12 rules of Boolean algebra?
On the figures this page opens with, the simplified (sum of products) is A + B. No single number fits everyone: it follows Boolean expression, Variable order (optional) and Variables have multi-letter names, so enter your own above and the answer updates as you type.
How difficult is Boolean algebra?
It needs Boolean expression, Variable order (optional) and Variables have multi-letter names. Nothing else is required, and the figures stay in your browser.
What information do I need for the Boolean Algebra Calculator?
You need Boolean expression, Variable order (optional) and Variables have multi-letter names. The page opens with default figures that give simplified (sum of products) of A + B, so you can see the scale before entering your own.
What does this Boolean Algebra Calculator show?
It shows Simplified (sum of products), Simplified (product of sums), Canonical sum of products, Canonical product of sums, Minterms, Maxterms, Variables and Prime implicants, with the working and any warnings for your entries.