Utilization of Modular Eight-Variable Karnaugh Maps in Digital Design | Chapter 9 | Novel Research Aspects in Mathematical and Computer Science Vol. 8

 The 8-variable Karnaugh map, which is a map with an extraordinarily high variable-handling capability, is introduced in this chapter in both a regular and modular form. Additionally, in the broader scenario of arbitrary n, the chapter analyses an n-bit comparator and visualises this analysis for n = 4 on the aforementioned map. On the six-variable, four-variable, and two-variable submaps of the original map, the situations n = 3, 2, and 1 are respectively exceptional cases. A tutorial exposition of several key concepts in switching theory, including implicants, prime implicants, essential prime implicants, minimal sum, complete sum, disjoint sum of products (or probability-ready expressions), Boole-Shannon Expansion, and unate and threshold functions, are provided in the evaluation.

Author(s) Details:

Ali Muhammad Ali Rushdi,
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O. Box-80200, Jeddah-21589, Saudi Arabia.

Sultan Sameer Zagzoog,
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O. Box-80200, Jeddah-21589, Saudi Arabia.

Please see the link here: https://stm.bookpi.org/NRAMCS-V8/article/view/8363

Map Visualization of Cause-Effect Relations in Qualitative Comparative Analysis | Chapter 1 | Novel Perspectives of Engineering Research Vol. 3

 This chapter investigates cause-and-effect interactions modeled by partially-defined Boolean functions (PDBF) using a recent regular and modular version of the eight-variable Karnaugh map (known also as incompletely-specified switching functions). First, we show how to use a simple Karnaugh-map test to determine whether a certain variable must be included in a list of supporting variables for a function, or whether it should be excluded from such a set. This exclusion is achieved through certain don't-care assignments that ensure the equivalence of the Boolean quotient with respect to the variable and its complement, i.e., the exact matching of the half map representing the internal region of the variable and the remaining half map representing the external region of the variable, in which case either of these two half maps replaces the original full map as a representation of the function. This type of variable exclusion could be repeated with respect to other variables until a minimal set of supporting variables is found. The work deals with obtaining all of a PDBF's minimal sets of supporting variables without explicitly using integer-programming techniques. Standard map methods for extracting prime implicants allow the development of all irredundant disjunctive forms for each of the minimal sets obtained (IDFs). We avoid the effort of drawing prime-implicant loops on the initial eight-variable map by following this approach of first finding a minimal set of supporting variables, and we postpone this task until the map is (typically drastically) reduced in size. The approach described here has significant implications for the recently founded field of Qualitative Comparative Analysis (QCA). The mainstream QCA community is unlikely to appreciate these repercussions, as they plainly show that the too-often impressive outcomes reported by QCA adherents must be reviewed and investigated. More observations, in our opinion, are needed to limit down the possibilities and reduce the number of possible IDFs.

Author(S) Details

Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

Raid Salih Badawi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

View Book:- https://stm.bookpi.org/NPER-V3/article/view/4752

Map Visualization of Boolean Manipulations in Qualitative Comparative Analysis | Chapter 12 | Recent Advances in Mathematical Research and Computer Science Vol. 3

 As advanced studies on the communicariont facility from the standpoints of their beneficiaries and social infrastructure, some fundamental concepts and technology relating well-being systems are examined. In an ageing society, we primarily mention them in relation to the subjective demands of individual beneficiaries. Thus, in common tele-health scenarios, low-cost, simple equipment is discussed rather than surveillance of beneficiaries, with community-wide medicare providing security. However, a focus is placed on face-to-face communication and ease of use for beneficiaries, with options such as playing games for the less fortunate and dementia sufferers as examples. The same technology approach based on broadband is then stated to enable remote teleconferences and teleeducation for depopulated rural areas. Here, a simple technology is used in principle on the basis of its safety, reliability, and flexibility, reflecting previous technical achievements for the well-being of people, and the active use of the Internet environment for the wide provision of convenience and assistance in daily life on public benefits. In addition, various approaches for system management and software provisioning to start the computer from a distance are proposed. We give technical perspectives from our research on broad engineering concerns relevant to the development and practical use of basic Internet functionalities. As information and communication technology advances, appropriate systems for daily living, entertainment, guidance, health care, rehabilitation, nursing, and medicare are methodically designed. They allowed the recipients to not only seek neighbours for help in an emergency and obtain daily requirements, but also to conduct effective activities and communications in distant islands and/or depopulated areas where medical personnel may be scarce. In order to communicate bilaterally with beneficiaries, the suggested basic system's expanded functionalities are used for various systems, which are provided as concrete methods and apparatus to convey their relevant data. Important methods for everyday life assistance and rescue of a lonely living person with a life-threatening illness are realised in this study by combining an additional button-type computer with proposed communication techniques that do not require any complicated manipulation in an Internet environment.

Author(S) Details

Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

Raid Salih Badawi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

View Book:- https://stm.bookpi.org/RAMRCS-V3/article/view/4476

Utilization of Eight-Variable Karnaugh Maps in the Digital Design of n-bit Comparators | Chapter 5 | Theory and Practice of Mathematics and Computer Science Vol. 8

 An n-bit comparator is a common combinational circuit that compares two n-bit inputs, Y and Z, and generates three orthonormal outputs: G (indicating that Y is strictly greater than Z), E (indicating that Y and Z are equal or equivalent), and L (indicating that Y and Z are equal or equivalent) (indicating that Y is strictly less than Z). The symbols 'G,' 'Equal to,' and 'Less than,' respectively, are chosen to represent the concepts of 'Greater than,' 'Equal to,' and 'Less than.' The study for n=4 on a standard and modular version of the 8-variable Karnaugh-map is visualised in this paper for an n-bit comparator in the general case of arbitrary n. On 6-variable, 4-variable, and 2-variable submaps of the original map, the cases n= 3, 2 and 1 appear as special cases. Many important concepts in switching theory are covered in this review, including implicants, prime implicants, critical prime implicants, irredundant disjunctive forms, minimal sums, the complete sum, and disjoint sums of products (or probability-ready expressions).

Author(s) Details

Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

Sultan Sameer Zagzoog
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah 21589, Saudi Arabia.

View Book :- https://stm.bookpi.org/TPMCS-V8/issue/view/50