Extending from the idea of minterms and maxterms, we define some useful ways to express a logic function based on the rows of a truth table: the sum-of-product and product-of-sum forms.
Sum-of-products
Sum-of-products (SOP) refers to any sum of product terms. The canonical SOP form (also standard form) is a unique representation of a function as a sum of midterms.
Any SOP form logic function can be done with NAND, making a NAND equivalent circuit, since it’s a universal logic gate.
Product-of-sums
Product-of-sums (POS) refers to any product of sum terms. The canonical POS form is where each OR is a maxterm. It’s a little hard to convince yourself that this is valid, but work through a dummy example and it’ll line up. Any POS form function can be implemented with NOR.
