Product of Sums
In digital electronics, POS is acronym for Product of Sum. It is a method of representing and simplifying Boolean expressions. The POS form is the complement of the SOP (Sum of Products) form.
Example:
For example, consider a Boolean function F(A, B, C, D) defined as:
F(A, B, C, D) = (A OR B OR C’) AND (A OR B’ OR C) AND (A OR C OR D’)
In POS form, this function can be represented as:
POS(A, B, C, D) = (A + B + C’) * (A + B’ + C)*(A + C + D’)
Prime Implicants and Explicit Implicants
Implicants play a crucial role in Boolean logic, as they form the building blocks for both SOP and POS expressions. An implicant can be thought of as a product term in SOP or a sum term in POS representing a Boolean function. Essentially, implicants encapsulate the various input combinations (minterm or maxterm) for which the Boolean function evaluates to true.