# Disjointed sum of products by a novel technique of orthogonalizing ORing

Disjointed sum of products by a novel technique of orthogonalizing ORing AbstractThis work presents a novel combining method called ‘orthogonalizing ORing ◯∨\$\bigcirc\!\!\!\!\!\!\vee \$’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

# Disjointed sum of products by a novel technique of orthogonalizing ORing

, Volume 16 (1): 15 – Apr 26, 2018
15 pages

/lp/degruyter/disjointed-sum-of-products-by-a-novel-technique-of-orthogonalizing-ic3f8fsHZI
Publisher
de Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0038
Publisher site
See Article on Publisher Site

### Abstract

AbstractThis work presents a novel combining method called ‘orthogonalizing ORing ◯∨\$\bigcirc\!\!\!\!\!\!\vee \$’ which enables the building of the union of two conjunctions whereby the result consists of disjointed conjunctions. The advantage of this novel technique is that the results are already presented in an orthogonal form which has a significant advantage for further calculations as the Boolean Differential Calculus. By orthogonalizing ORing two calculation steps - building the disjunction and the subsequent orthogonalization of two conjunctions - are performed in one step. Postulates, axioms and rules for this linking technique are also defined which have to be considered getting correct results. Additionally, a novel equation, based on orthogonalizing ORing, is set up for orthogonalization of every Boolean function of disjunctive form. Thus, disjointed Sum of Products can be easily calculated in a mathematical way by this equation.

### Journal

Open Mathematicsde Gruyter

Published: Apr 26, 2018

Keywords: Disjoint Sum of Products; Orthogonalization; Disjunctive Form; Conjunction; K-map; 03B99; 03G05; 03G25; 94C10