F(A,B,C) = Σm(0,1,2,4) — SOP and POS
coreF and F′ as index sets
Answer
Σm(0,1,2,4) = ΠM(3,5,6,7)
Why this example is worth doing
Four minterms chosen so that the complement is also four minterms, which makes the index arithmetic easy to check: the ON-set of F′ is the complement of the ON-set of F within 0..2^n−1, and the maxterm list of F is the minterm list of F′. Three statements of one fact. The page lays them out as a single table with a column per representation, and this is the example the converter bar uses to demonstrate carrying an index list across to the K-map and the truth table.
Try your own input in the SOP & POS canonical forms. Expand to canonical minterms and maxterms, and convert between the two.
How the answer is reached
Canonical sum of products
A′ · B′ · C′ + A′ · B′ · C + A′ · B · C′ + A · B′ · C′
Canonical product of sums
(A + B′ + C′) · (A′ + B + C′) · (A′ + B′ + C) · (A′ + B′ + C′)
Truth table
| # | A | B | C | F |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 | 0 |
| 4 | 1 | 0 | 0 | 1 |
| 5 | 1 | 0 | 1 | 0 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 0 |