Karnaugh Map Practice Problems
A fresh randomly generated K-map every time, marked as you go. Group the cells yourself and find out whether your answer is minimal, not merely correct.
No groups yet.
Cover every 1 using 2 groups and 4 literals.
Click cells to select them, then confirm. Take the largest legal group you can each time: groups may wrap around the edges of the map.
How to use it
- Pick a difficulty. Easy is 3 variables; medium and hard are 4 variables and add don't-cares.
- Click cells to select a group, then press Confirm group. Repeat until every 1 is covered.
- Your answer is checked against the true minimal solution, so it tells you when a correct answer could still be smaller.
- Press New random problem for another one, or Give up to see the worked answer.
Common questions
How do you know if a Karnaugh map answer is minimal?+
An answer is minimal when no other grouping covers the same 1s with fewer product terms, and no other grouping with that many terms uses fewer literals. This tool computes the true minimum with the Quine-McCluskey algorithm and compares your grouping against it, so a correct-but-oversized answer is marked as such.
What order should I pick Karnaugh map groups in?+
Start with any 1 that can only be covered one way, since the group covering it is forced. Take the largest legal group each time, and stop as soon as every 1 is covered. A group whose 1s are all already covered by other groups is redundant and should be dropped.
Are these Karnaugh map problems random?+
Every problem is generated from a random seed rather than drawn from a fixed set, so the supply does not run out. Generated maps are filtered to remove degenerate cases: problems that simplify to a constant, or where circling each 1 separately is already optimal, are discarded because they teach nothing.
How many variables do the practice problems use?+
Easy problems use 3 variables on a 2 by 4 map. Medium and hard use 4 variables on a 4 by 4 map, and include don't-care cells. Hard problems have more product terms and more don't-cares, so there is more scope for a correct answer to be non-minimal.