Karnaugh Map Simplifier

What Karnaugh Map Simplifier does

This tool takes a list of minterm indices (the rows of a truth table where the output is 1) and finds a simplified sum-of-products Boolean expression. It groups adjacent cells in a Karnaugh map, including wrapped-around edges, to eliminate variables that change within a group.

Worked example

Here, the minterms 1,3,5,7 correspond to all rows where C=1, so the expression simplifies to just C.

Calculation method

The tool enumerates all valid implicant cubes (power-of-two groups of adjacent minterms) that cover only the supplied minterms. It then selects a cover with the fewest terms, and among those, the fewest literals. Variables are named A, B, C, D from most significant to least significant bit.

Input and output details

• Enter minterm indices as integers from 0 to 15, separated by commas or spaces. Duplicates are removed.
• The tool infers the smallest number of variables (1 to 4) needed to represent the largest index.
• Output shows the inferred variable count, the canonical minterm list, and the simplified expression.
• If you supply all minterms for the inferred width, the result is constant 1.

Limits and review checks

• This tool supports up to 4 variables and does not accept don't-care conditions.
• It produces only a sum-of-products form, not product-of-sums or hazard-free designs.
• There is no visual Karnaugh map; the simplification is computed algorithmically.
• Always verify the result with your own truth table or an independent method.

Frequently asked questions

Why is my input rejected?

Check that you entered only integers between 0 and 15, separated by commas or spaces. The tool does not accept variable names, expressions, or don't-care symbols.

Can I use this result in a high-stakes decision?

Use the tool for learning and independent checks. Verify legal, financial, safety or security decisions with an authoritative method and qualified reviewer.

How does the tool handle duplicate minterms?

Duplicate minterms are automatically removed. The tool works with the unique set of minterms you provide.