F(A,B,C,D) = Σm(0,1,4,5,8,9,12,13) — Karnaugh map
coreone 8-cell group; answer is a single literal
Answer
C′
Why this example is worth doing
Eight 1s forming two full columns of the 4-variable map, which combine into one octet and reduce to the single literal C̄. The lesson is how to read a group's product term: a variable appears only if it holds the same value across every cell of the group, and here only C does. Students routinely under-group this, circling two quads and writing a two-term answer that is correct but not minimal. The tool marks that cover valid, complete and non-minimal, which is three separate judgements.
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 | C′ |
| # | Cover |
|---|---|
| 1 | C′ |
Warning:
1 term(s), 1 literal(s); 1 essential prime implicant(s).
Truth table
| # | A | B | C | D | F |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 2 | 0 | 0 | 1 | 0 | 0 |
| 3 | 0 | 0 | 1 | 1 | 0 |
| 4 | 0 | 1 | 0 | 0 | 1 |
| 5 | 0 | 1 | 0 | 1 | 1 |
| 6 | 0 | 1 | 1 | 0 | 0 |
| 7 | 0 | 1 | 1 | 1 | 0 |
| 8 | 1 | 0 | 0 | 0 | 1 |
| 9 | 1 | 0 | 0 | 1 | 1 |
| 10 | 1 | 0 | 1 | 0 | 0 |
| 11 | 1 | 0 | 1 | 1 | 0 |
| 12 | 1 | 1 | 0 | 0 | 1 |
| 13 | 1 | 1 | 0 | 1 | 1 |
| 14 | 1 | 1 | 1 | 0 | 0 |
| 15 | 1 | 1 | 1 | 1 | 0 |