F(A,B,C,D,E) = Σm(0,2,4,6,9,13,21,23,25,29,31) — Karnaugh map
exam standard5 variables drawn as two 4-variable planes
Answer
A′ · B′ · E′ + B · D′ · E + A · C · E
Why this example is worth doing
Five variables, drawn as two stacked 4-variable maps rather than one 4×8 strip. That choice is forced, not cosmetic: on a 3-bit Gray-coded axis six of the twenty-seven subcubes are non-contiguous, so a single wide map would draw groups that are not legal cubes and reject groups that are. With two planes, adjacency means the same cell position in the other plane, and the tool renders a cross-plane group as linked rectangles in both. Six variables extend the same idea to four planes.
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′ · E′ |
| 2 | B · D′ · E |
| 3 | A · C · E |
| # | Cover |
|---|---|
| 1 | A′ · B′ · E′ + B · D′ · E + A · C · E |
3 term(s), 9 literal(s); 3 essential prime implicant(s).
Truth table
| # | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 1 | 0 | 1 |
| 3 | 0 | 0 | 0 | 1 | 1 | 0 |
| 4 | 0 | 0 | 1 | 0 | 0 | 1 |
| 5 | 0 | 0 | 1 | 0 | 1 | 0 |
| 6 | 0 | 0 | 1 | 1 | 0 | 1 |
| 7 | 0 | 0 | 1 | 1 | 1 | 0 |
| 8 | 0 | 1 | 0 | 0 | 0 | 0 |
| 9 | 0 | 1 | 0 | 0 | 1 | 1 |
| 10 | 0 | 1 | 0 | 1 | 0 | 0 |
| 11 | 0 | 1 | 0 | 1 | 1 | 0 |
| 12 | 0 | 1 | 1 | 0 | 0 | 0 |
| 13 | 0 | 1 | 1 | 0 | 1 | 1 |
| 14 | 0 | 1 | 1 | 1 | 0 | 0 |
| 15 | 0 | 1 | 1 | 1 | 1 | 0 |
| 16 | 1 | 0 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 1 | 0 |
| 18 | 1 | 0 | 0 | 1 | 0 | 0 |
| 19 | 1 | 0 | 0 | 1 | 1 | 0 |
| 20 | 1 | 0 | 1 | 0 | 0 | 0 |
| 21 | 1 | 0 | 1 | 0 | 1 | 1 |
| 22 | 1 | 0 | 1 | 1 | 0 | 0 |
| 23 | 1 | 0 | 1 | 1 | 1 | 1 |
| 24 | 1 | 1 | 0 | 0 | 0 | 0 |
| 25 | 1 | 1 | 0 | 0 | 1 | 1 |
| 26 | 1 | 1 | 0 | 1 | 0 | 0 |
| 27 | 1 | 1 | 0 | 1 | 1 | 0 |
| 28 | 1 | 1 | 1 | 0 | 0 | 0 |
| 29 | 1 | 1 | 1 | 0 | 1 | 1 |
| 30 | 1 | 1 | 1 | 1 | 0 | 0 |
| 31 | 1 | 1 | 1 | 1 | 1 | 1 |