Implicant

As a prime implicant Primterm or a Boolean function is known such a disjunction of terms Konjunktionstermen, which can not be shortened, and therefore have minimum length. Primterme are so shortest of conjunction. Under the length of a term is in this case the number of conjunctions and disjunctions contained understood ( within one Konjunktionsterms this course, only conjunctions interesting). The finding of Primtermen is of high importance for the minimization of function expressions ( eg in the context of the design of switching networks). It can be done for operations with a low number of variables graphically by means of Karnaugh - Veitch - diagrams. For larger numbers variables, the method of Quine and McCluskey is suitable for this purpose. As a rule of thumb, Karnaugh Veitch -Diagram for 1-5 variables, Quine / McCluskey for 6 or more variables.

However Primterme guarantee in itself does not minimal disjunctive normal form, as they may be minimal, but superfluous though. Such Primterme that are not redundant for representing the function is referred to as Kernprimterme, core prime implicants Kernimplikanten, essential or essential prime implicants of the prime implicants.

• Mathematical Logic