Was (wer) ist sum of products - definition

CONCEPT IN BOOLEAN ALGEBRA

Maxterm; Minterm; Normal form (Boolean algebra); Product of sums; Sum of products; Minterms; Maxterms; Product-Of-Sums; Sum-Of-Products; Minimal POS; Minimal SOP; Sum of Products; Product of Sums; Canonical form (Boolean algebra); Canonical conjunctive normal form; Minterm canonical form; Maxterm canonical form; Canonical disjunctive normal form; Boolean normal form; Min-term; Max-term; Sum-of-products; Product-of-sums

sum of products

1. <mathematics, logic> Any mathematical expression in which an addition operator is applied to two or more subexpressions each of which is an application of a multiplication operator. The most common case would be scalar addition and multiplication, e.g. ab + cd but the term is used for other kinds of operators with similar properties, such as AND and OR in Boolean algebra, e.g. (a AND b) OR (c AND d) 2. <types> algebraic data type. (2008-02-04)

sums

ADDITION OF A SEQUENCE OF NUMBERS

Sigma notation; Sums; Summation Number; Sum Of; Summation identities; Summation sign; Capital-sigma notation; Sumation; Capital sigma notation; Sum identities; ⅀; Summation (mathematics); Sum (mathematics); ⎲; ⎳; Mathematical sum; Algebraic sum; Sum symbol; Summation operator; Big sigma notation; Draft:Summation Formula List; Finite sum; Finite summation; Sum character; Summation symbol

n. to do sums

Summation

ADDITION OF A SEQUENCE OF NUMBERS

·vt The act of summing, or forming a sum, or total amount; also, an Aggregate.

Wikipedia

Canonical normal form

In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form and its dual canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller).

Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan's laws.

Two dual canonical forms of any Boolean function are a "sum of minterms" and a "product of maxterms." The term "Sum of Products" (SoP or SOP) is widely used for the canonical form that is a disjunction (OR) of minterms. Its De Morgan dual is a "Product of Sums" (PoS or POS) for the canonical form that is a conjunction (AND) of maxterms. These forms can be useful for the simplification of these functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.

https://en.wikipedia.org/wiki/Canonical normal form