F = Ā·B + A·B̄ — SOP and POS
coreXOR in canonical form
Answer
Σm(1,2) = ΠM(0,3)
Why this example is worth doing
XOR written out as a canonical sum, Σm(1,2), and its POS partner ΠM(0,3). The page's point is that the canonical forms are unique — every function has exactly one canonical SOP and one canonical POS — whereas minimal forms need not be. That uniqueness is what makes canonical forms the right thing to compare when you want to prove two expressions equal, and it is why the equivalence checker on this site normalises to canonical form rather than trying to rewrite one expression into the other.
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 + A · B′
Canonical product of sums
(A + B) · (A′ + B′)
Truth table
| # | A | B | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 0 |