F(A,B,C,D,E,F) = Σm(0,2,8,10,16,18,24,26,32,34,40,42,48,50,56,58) — Quine–McCluskey
edge case1 prime implicants, 1 essential
Answer
D′ · F′
Why this example is worth doing
Sixteen minterms over six variables that collapse to a single two-literal product, because the pattern is regular: C and F are 0 in every one of them and nothing else is constrained. It is here to show the tabulation surviving a problem no one would attempt on a map — four planes of K-map, and a chart that would take a page to draw — while producing an answer that fits on one line. It is also the size at which the page starts reporting run time, and where the exact/heuristic threshold becomes worth explaining.
Try your own input in the Quine–McCluskey solver. Minimise past the K-map limit with the full tabular method and Petrick’s step.
How the answer is reached
Quine–McCluskey
| # | Term |
|---|---|
| 1 | D′ · F′ |
| # | Cover |
|---|---|
| 1 | D′ · F′ |
1 term(s), 2 literal(s); 1 essential prime implicant(s).
Truth table
| # | A | B | C | D | E | F | F |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
| 3 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 6 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
| 7 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| 8 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 10 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 11 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| 12 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
| 13 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 14 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
| 15 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
| 16 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
| 17 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 18 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 19 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
| 20 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| 21 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 22 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
| 23 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
| 24 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 25 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 26 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 27 | 0 | 1 | 1 | 0 | 1 | 1 | 0 |
| 28 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
| 29 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
| 30 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
| 31 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
First 32 of 64 rows.