Karnaugh Map Practice Problems With Full Solutions

Six problems, beginner to advanced, each solved and verified against the actual solver engine — not answers written from memory. Work each one out yourself first, then check against the solution underneath.

Problem 1 (2 variables) — warm-up

F(A,B) = Σm(0,2)

F = B′

Both required minterms have B=0; A is irrelevant to the result.

Problem 2 (3 variables)

F(A,B,C) = Σm(1,2,3,5,7)

F = C + A′B

Two essential groups: C covers four cells where C=1 (1,3,5,7), and A′B picks up the remaining minterm 2.

Problem 3 (3 variables)

F(A,B,C) = Σm(0,1,2,5,6,7)

F = A′B′ + BC′ + AC

Three overlapping groups — check your work against Overlapping Groups in K-Maps if this one doesn't match on the first try; overlap here is expected, not a sign of an error.

Problem 4 (4 variables)

F(A,B,C,D) = Σm(1,3,5,7,9,11,13,15)

F = D

Every required minterm is odd — a single literal is the entire answer. If your worked answer has more than one term, check for a missed wraparound or an oversized set of smaller groups instead of the one largest one — see Common Karnaugh Map Mistakes.

Problem 5 (4 variables) — practice with wraparound

F(A,B,C,D) = Σm(0,2,5,7,8,10,13,15)

F = B′D′ + BD

Both groups rely on left-right wraparound within their respective rows — a good check on whether wraparound adjacency is second nature yet. See K-Map Wraparound diagrams if this one comes out with more terms than shown here.

Problem 6 (4 variables) — with don't-cares

F(A,B,C,D) = Σm(1,3,5,7,9), don't-cares at 11, 13, 15.

Without don't-cares: F = A′D + B′C′D
With don't-cares: F = D

Same five required minterms, but the don't-cares let the whole thing collapse to a single literal — solve it both ways to see the difference directly, exactly the effect covered in Handling Don't-Care Conditions in K-Maps.

Unlimited additional practice

For more problems at any variable count, use the 🎲 Random example button on the solver — it generates a fresh, non-degenerate problem on demand, with the full solution, prime implicant analysis, and circuit diagram computed live so you can check your own work immediately after solving it by hand.

Try it on the solver

Work through the examples above directly — enter the same minterms or expression into the live tool.

Open the K-Map Solver