Derivation of All Particular Solutions of a ‘Big’ Boolean Equation with Applications in Digital Design
Ali Muhammad Rushdi, Sultan Sameer Zagzoog
Current Journal of Applied Science and Technology · pp. 1–16 · Published 18 May 2018
10.9734/CJAST/2018/41481Abstract
This paper considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one. The paper outlines classical and novel direct methods for deriving the general parametric solution of such a system and for listing all its particular solutions. A detailed example over B256 is used to illustrate these two methods as well as a third method that starts by deriving the subsumptive solution first. The example demonstrates how the consistency condition forces a collapse of the underlying Boolean algebra to a subalgebra, and also how to list a huge number of particular solutions in a very compact space. Subsequently, the paper proposes some potential applications for the techniques of Boolean-equation solving. These techniques are very promising as useful extensions of classical techniques based on two-valued Boolean algebra.
Cited by 6
A. Rushdi, Raid Mohammad Salih Badawi · 2021
A. Balamesh, A. Rushdi · International Journal of Computer Mathematics Computer Systems Theory · 2019
A. Rushdi, Fares Ahmad Muhammad Ghaleb · Journal of Engineering Research and Reports · 2019
A. Rushdi, S. S. Zagzoog, A. Balamesh · Journal of Advances in Mathematics and Computer Science · 2018
A. Rushdi, W. Ahmad · Current Journal of Applied Science and Technology · 2018
A. Rushdi · 2018
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