Karnaugh Mapping Calculator
Karnaugh mapping calculator works out Minimal sum of products and Minimal product of sums from Describe the function by, Variables and Minterms (cells that are 1). The default figures on this page give minimal sum of products of B'C' + B'D' + A'C'D; 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
- Map over A, B, C, D: 4 rows (AB) by 4 columns (CD), Gray-coded so neighbours differ in one variable.
- 1-cells: 0, 1, 2, 5, 8, 9, 10.
- Prime implicants (all maximal groups): B'C', B'D', A'C'D
- Essential prime implicants (each is the only group covering some 1): B'C', B'D', A'C'D
- Minimum cover: F = B'C' + B'D' + A'C'D (3 term(s), 7 literal(s)).
- Minimising the 0-cells and applying De Morgan gives F = (A' + B')(B' + D)(C' + D').
Prime implicantstable
Essential prime implicantstable
Groups in the chosen covertable
| term | cells | size |
|---|---|---|
| B'C' | 0, 1, 8, 9 | 4 |
| B'D' | 0, 2, 8, 10 | 4 |
| A'C'D | 1, 5 | 2 |
Karnaugh maptable
| 10 | 11 | AB | 00 | 01 |
|---|---|---|---|---|
| 1 | 0 | 00 | 1 | 1 |
| 0 | 0 | 01 | 0 | 1 |
| 0 | 0 | 11 | 0 | 0 |
| 1 | 0 | 10 | 1 | 1 |
Row labels (Gray code)table
Column labels (Gray code)table
Minterms usedtable
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the karnaugh mapping calculator calculates
Builds the Gray-coded Karnaugh map for 2 to 6 variables and minimises the function to its simplest sum-of-products and product-of-sums form, listing prime and essential prime implicants.
How to use this karnaugh mapping calculator
Enter Describe the function by, Variables, Minterms (cells that are 1) and Don't-care cells. Minimal 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 Minimal sum of products, Minimal product of sums and Terms (AND gates).
The method follows M. Karnaugh, "The Map Method for Synthesis of Combinational Logic Circuits", Transactions of the AIEE 72 (1953), 593-599 and M. Morris Mano and Michael D. Ciletti, Digital Design, Chapter 3: Gate-Level Minimization.
Mano-style 4-variable map: F(A,B,C,D) = Sum m(0,1,2,5,8,9,10) example
With Describe the function by: minterms, Variables: A, B, C, D, Minterms (cells that are 1): 0,1,2,5,8,9,10, the calculator returns Minimal sum of products: B'C' + B'D' + A'C'D, Terms (AND gates): 3, Literals (gate inputs): 7. 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 Minimal sum of products, Minimal product of sums and Terms (AND gates). The inputs you can vary are Describe the function by, Variables, Minterms (cells that are 1), Don't-care cells, Truth-table output column and Boolean expression.
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 Karnaugh map?
Builds the Gray-coded Karnaugh map for 2 to 6 variables and minimises the function to its simplest sum-of-products and product-of-sums form, listing prime and essential prime implicants. Open “How this is worked out” beside the result to see each step for your own figures.
Is there a Karnaugh map solver available?
Builds the Gray-coded Karnaugh map for 2 to 6 variables and minimises the function to its simplest sum-of-products and product-of-sums form, listing prime and essential prime implicants. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give B'C' + B'D' + A'C'D.
What information do I need for the karnaugh mapping calculator?
You need Describe the function by, Variables, Minterms (cells that are 1), Don't-care cells, Truth-table output column and Boolean expression. The page opens with default figures that give minimal sum of products of B'C' + B'D' + A'C'D, so you can see the scale before entering your own.
What does this karnaugh mapping calculator show?
It shows Minimal sum of products, Minimal product of sums, Terms (AND gates), Literals (gate inputs), Prime implicants, Essential prime implicants, Groups in the chosen cover and Karnaugh map, with the working and any warnings for your entries.
Can I check how the karnaugh mapping calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.