F = A·B + C — SOP and POS
introexpand to canonical SOP and POS
Answer
Σm(1,3,5,6,7) = ΠM(0,2,4)
Why this example is worth doing
The basic expansion. A·B is missing C, so it splits into two minterms; C is missing both A and B, so it splits into four, and the union is five distinct minterms. The page shows the multiply-by-(X + X̄) step for each incomplete term, which is the mechanical procedure being examined, and stresses that duplicates collapse by idempotence rather than accumulating. The maxterm list is then simply the complementary index set — the observation that saves half the work on every question of this type.
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′ + A · B · C
Canonical product of sums
(A + B + C) · (A + B′ + C) · (A′ + B + C)
Truth table
| # | A | B | C | F |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 0 |
| 3 | 0 | 1 | 1 | 1 |
| 4 | 1 | 0 | 0 | 0 |
| 5 | 1 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 1 |
| 7 | 1 | 1 | 1 | 1 |