Click cells to set them to 1 or a don't-care. The map is solved as you type, showing the minimal sum-of-products expression with every group outlined, including the ones that wrap around the edges.
F = 0
The map is empty, so the function is constant 0. Click cells to set them to 1.
It finds every prime implicant of the function using the Quine-McCluskey method, keeps the ones that are essential (the only group covering some 1), then searches for the cheapest combination that covers whatever is left. The result is a genuinely minimal sum of products, not just a correct one.
A don't-care, written X, is an input combination the function will never receive, so its output does not matter. You may include it in a group when doing so makes the group larger, or leave it out. Using them well often removes a whole term from the answer.
Because the rows and columns are labelled in Gray code, where neighbouring labels differ in exactly one bit. The first and last columns also differ in one bit, so they are adjacent too. That makes the map a torus rather than a flat rectangle, which is why the four corner cells of a 4-variable map form a single valid group.
Any power of two: 1, 2, 4, 8 or 16 cells, arranged as a rectangle that may wrap around the edges. Each doubling of the group size removes one literal from the term, so the largest legal group is always the one you want.
Yes. Many functions have several groupings that are all equally minimal, with the same number of terms and literals. Any of them is a correct answer, which is why this tool reports when alternatives exist rather than treating one arrangement as the only right one.