Sum of products, or SOP, ORs together AND terms. Product of sums, or POS, ANDs together OR terms. Neither must be canonical: a simplified term can omit variables. Choose a form that makes the specification and intended gate structure easier to understand.
Worked example
F = AB + AC is SOP. Factoring A gives A(B + C), a POS expression containing the one-literal sum A and the sum B + C. Check A = 1, B = 0, C = 1: both versions evaluate to one.
What to watch for
The words sum and product mean OR and AND here. A change of form must preserve all truth-table outputs, not just one example row.
Try it yourself
Is (A + B)(C + D) SOP or POS?
Answer: It is POS: two OR terms are combined by AND. Expanding it gives the SOP AC + AD + BC + BD.
How to study this topic
Read one operation at a time and use parentheses generously. Check a simplification with every truth-table row, not just a convenient example. A useful simpler expression must preserve the complete specified function.
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