Logical Design of n-bit Comparators: Pedagogical Insight from Eight-Variable Karnaugh Maps
Ali Muhammad Ali Rushdi, Sultan Sameer Zagzoog
Journal of Advances in Mathematics and Computer Science · pp. 1–20 · Published 22 May 2019
10.9734/jamcs/2019/v32i330146Abstract
An -bit comparator is a celebrated combinational circuit that compares two -bit inputs and and produces three orthonormal outputs: G (indicating that is strictly greater than ), E (indicating that and are equal or equivalent), and L (indicating that is strictly less than ). The symbols ‘G’, ‘E’, and ‘L’ are deliberately chosen to convey the notions of ‘Greater than,’ ‘Equal to,’ and ‘Less than,’ respectively. This paper analyzes an -bit comparator in the general case of arbitrary and visualizes the analysis for on a regular and modular version of the 8-variable Karnaugh-map. The cases 3, 2, and 1 appear as special cases on 6-variable, 4-variable, and 2-variable submaps of the original map. The analysis is a tutorial exposition of many important concepts in switching theory including those of implicants, prime implicants, essential prime implicants, minimal sum, complete sum and disjoint sum of products (or probability-ready expressions).
Cited by 5
A. Rushdi, Raid Mohammad Salih Badawi · Journal of Engineering Research and Reports · 2021
A. Rushdi, Raid Mohammad Salih Badawi · Asian Journal of Education and Social Studies · 2021
A. Rushdi, Raid Mohammad Salih Badawi · 2021
Abdulaziz I. Al-Darrab, Ali Muhammad Ali Rushdi · 2021 National Computing Colleges Conference (NCCC) · 2021
Yan Zhang, Wenyi Liu, Mirza Ali Shaheer · 2021 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC) · 2021
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