F(A,B) = Σm(1,2) — Karnaugh map
core2-variable map; no groups possible
Answer
A′ · B + A · B′
Why this example is worth doing
The smallest map the tool draws, and the case where nothing groups: two isolated 1s on a diagonal. The answer is the canonical sum, and that is the correct answer rather than a failure. It is worth having explicitly because two-variable K-maps are a real exam question and most solvers start at three. The function is A ⊕ B, so it is also the shortest possible illustration of why XOR is invisible to sum-of-products minimisation — a theme the 3-variable and 4-variable XOR examples develop.
Try your own input in the Karnaugh map solver. Group a 2- to 6-variable map yourself and have every group marked right or wrong.
How the answer is reached
Quine–McCluskey
| # | Term |
|---|---|
| 1 | A′ · B |
| 2 | A · B′ |
| # | Cover |
|---|---|
| 1 | A′ · B + A · B′ |
Warning:
2 term(s), 4 literal(s); 2 essential prime implicant(s).
Truth table
| # | A | B | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 0 |