Karnaugh Map Calculator
Minimise a boolean function of up to 4 variables using the Quine-McCluskey method.
About Karnaugh Map Calculator
The Karnaugh map (K-map) is a visual method for boolean function minimisation. This calculator uses the equivalent Quine-McCluskey algorithm: it systematically finds all prime implicants, then selects a minimal covering set to produce the simplest sum-of-products expression.
Formula
Minimised SOP = sum of essential and selected prime implicants covering all minterms
- SOP
- Sum of Products
- minterms
- Input indices where f=1
Worked example
With the default values below, Karnaugh Map Calculator returns Minimised SOP of B'C + BC' + AC. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number of Variables (2–4)accepts 2–4
- 3
- Minterms (comma separated indices)
- 1, 2, 5, 6, 7
Results
- Minimised SOP
- B'C + BC' + AC
- Prime Implicants
- B'C, BC', AC, AB
- Number of Terms
- 3
Step by step
- 1Values used
- 2Formula applied
- 3Minimised SOP= B'C + BC' + AC
- 4Prime Implicants= B'C, BC', AC, AB
- 5Number of Terms= 3
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is a minterm?
A minterm is a product term where every variable appears exactly once (complemented or not). Minterm index i corresponds to the binary encoding of variable values.
Why limit to 4 variables?
K-maps are traditionally drawn for 2–4 variables. Beyond 4, the Quine-McCluskey algorithm still works but the visual map becomes impractical.