Simplifying the Boolean Equation Based on Simulation System using Karnaugh Mapping Tool in Digital Circuit Design

In computerized integrated circuits, the fundamental principle intends to avoid the multifaceted nature of the circuitry by making it as brief as attainable and minimize the expenditure. Techniques like Quine- McCluskey (QM) and Karnaugh Map (K-Map) are often used approaches of simplifying Boolean functions. This study presents a recreation framework of simplification of the Boolean capacities by the utilize of the K- Map definition for beginner-level learners. It uses the algebraic expression of the Boolean function to decrease the number of terms, generates a circuit, and does not use any redundant sets. In this way, it gets to be competent to deal with lots of parameters and minimize the computational cost. The result of the assessment is performed in this paper by contrasting it with the C- Minimizer algorithm. In computation time terms, the result appears that our comprehensive K mapping tool outflanks in current procedures, and the relative error accomplishes a lower rate of percentage (2%), which fulfills the satisfactory level. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 76-84

Boolean Algebra

This chapter addresses Boolean algebra, which is based on Boolean logic. In the social sciences, Boolean algebra comes under different labels. It is often used in set-theoretic and qualitative comparative analysis to assess complex causation that leads to particular outcomes involving different combinations of conditions. The basic features of Boolean algebra are the use of binary data, combinatorial logic, and Boolean minimization to reduce the expressions of causal complexity. By calculating the intersection between the final Boolean equation and the hypotheses formulated in Boolean terms, three subsets of causal combinations emerge: hypothesized and empirically confirmed; hypothesized, but not detected within the empirical evidence; and causal configurations found empirically, but not hypothesized. This approach is both holistic and analytic because it examines cases as a whole and in parts.

Systems of Inclusions with Unknowns in Multioperations

We consider systems of inclusions with unknowns and coefficients in multioperations of finite rank. An algorithm for solving such systems by the method of reduction to Boolean equations using superposition representation of multioperations by Boolean space matrices is given. Two methods for solving Boolean equations with many unknowns are described for completeness. The presentation is demonstrated by examples: the representation of the superposition of multioperations by Boolean space matrices; solving a Boolean equation by analytical and numerical methods; and finding solutions to an inclusion with one unknown. The resulting algorithm can be applied to the development of logical inference systems for multioperator logics.

Systems of k Boolean inequations and a Boolean equation

In this paper elementary generalized systems of Boolean equations are investigated. The formula for solving systems of k Boolean inequations and a Boolean equation is presented. This systems have many applications in computer science for solving logical problems. Presented formulas can accelerate application of elementary generalized systems of Boolean equations.

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

Partial-order reduction (POR) is a well-established technique to combat the problem of state-space explosion. We propose POR techniques that are sound for parity games, a well-established formalism for solving a variety of decision problems. As a consequence, we obtain the first POR method that is sound for model checking for the full modal $$\mu $$-calculus. Our technique is applied to, and implemented for the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments indicate that substantial reductions can be achieved.

Frailty in the Elderly and Interventions Supported by Information and Communication Technologies

Fragility affects the ability to recover from stress conditions as the use of information and communication technologies in health care grows. The objective of this chapter is to identify evidence on interventions using ICT technology to prevent or delay frailty. A systematic review of the literature was used. Search was performed in April 2019 through B-on and EBSCO host, in databases Academic Search Complet, with Full Test in MEDLINE, CINAHL Plus®, and MedicLatina. Boolean equation ((Telemedicine) OR (mobile health) OR (computer reality) OR (virtual reality)) AND (Frail Elderly) AND (randomized controlled trial), from 2013 to 2017. Articles followed PRISMA flowchart. Results show that 2946 articles were selected, and 17 met the criteria. The used ICT were virtual-augmented reality, multidisciplinary home-telehealth and telemonitoring, nurse home visits, Wii Fit, and other interactive video games. The chapter conclude that the implementation of ICT to manage self-care at home requires an interdisciplinary, collaborative, and user-centered approach to improve the viability, acceptability, and usability of innovations.