Karnaugh Map Solver Calculator

Minimise 2–6 variable functions from minterms and don’t-cares, with a colour-grouped K-map.

What it does

A Karnaugh map groups the 1s of a function to find its simplest form. Enter the minterms (and any don’t-cares) and get the minimal SOP and POS with colour-coded groups.

Where it's used

Minimising logic for gates or FPGAs and digital-design coursework.

How to use it

Choose the number of variables.
Type the minterms where the output is 1, separated by commas.
Optional: add don’t-care terms.
Read the minimal expression and look at the grouped map.

The formula explained

Minterm: row number (in binary A B C…) whose output is 1
Don’t-care (X): can be treated as 0 or 1 to make bigger groups
Gray order: rows/columns ordered 00, 01, 11, 10 so neighbours differ by one bit

Worked example

Inputs:

Variables: 3 (A–C)
Minterms (1s): 1, 3, 5, 6, 7

The calculator gives:

Minimal SOP: F = C + AB
Minimal POS: F = (A + C)(B + C)

Tips and common mistakes

Groups must be rectangles of 1, 2, 4 or 8 cells, and may wrap around the edges.
Bigger groups give simpler terms.
Variable A is the most significant bit.

Questions people ask

What are don’t-care terms?

Input combinations that never happen or whose output doesn’t matter — for example codes 10 to 15 in a BCD circuit. The solver may treat them as 1 or 0, whichever gives bigger groups and a simpler answer.

Why are the rows ordered 00, 01, 11, 10?

That is Gray-code order: neighbouring cells differ in only one variable, so a group of adjacent 1s always drops a variable. It is also why groups may wrap around the edges.

How can I check the result?

Put each minterm back into the answer. For F = C + AB, minterm 6 (A = 1, B = 1, C = 0) gives AB = 1, and minterms 1, 3, 5 and 7 all have C = 1 — every 1 is covered and nothing else is.

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