Formal derivation of a particular input of a single AND (OR) gate in terms of its output and other inputs
Other Title(s)
الاشتقاق الرياضي الرصين لأحد مدخلات بوابة تقاطع (اتحاد) بدلالة مخرجها و بقية مدخلاتها
Joint Authors
al-Qawasimi, Muhammad Ahmad
Rushdi, Ali Muhammad Ali
Source
Journal of King Abdulaziz University : Engineering Sciences
Issue
Vol. 26, Issue 2 (31 Dec. 2015), pp.51-64, 14 p.
Publisher
King Abdulaziz University Scientific Publishing Center
Publication Date
2015-12-31
Country of Publication
Saudi Arabia
No. of Pages
14
Main Subjects
Engineering & Technology Sciences (Multidisciplinary)
Abstract EN
This note studies two dual problems that arise frequently in the probabilistic and testability analysis of combinational digital circuits and the a posteriori analysis of fault trees.
These problems pertain to expressing a particular input of a single AND or (OR) gate in terms of its output and other inputs.
We formally derive the required input, for each of the two dual cases, by finding the general parametric solution of an equivalent problem over a 'big' Boolean algebra.
The solutions obtained provide pedagogical insight and have direct interpretations in terms of substantially reduced truth tables.
As an offshoot, this note confirms, by way of concrete examples, that the a ‘big’ Boolean algebra is both useful and unavoidable for engineering applications, and that truth tables do not have to be explicitly of exponential sizes, but might be compressed, when possible, to few lines only.
American Psychological Association (APA)
Rushdi, Ali Muhammad Ali& al-Qawasimi, Muhammad Ahmad. 2015. Formal derivation of a particular input of a single AND (OR) gate in terms of its output and other inputs. Journal of King Abdulaziz University : Engineering Sciences،Vol. 26, no. 2, pp.51-64.
https://search.emarefa.net/detail/BIM-717962
Modern Language Association (MLA)
Rushdi, Ali Muhammad Ali& al-Qawasimi, Muhammad Ahmad. Formal derivation of a particular input of a single AND (OR) gate in terms of its output and other inputs. Journal of King Abdulaziz University : Engineering Sciences Vol. 26, no. 2 (2015), pp.51-64.
https://search.emarefa.net/detail/BIM-717962
American Medical Association (AMA)
Rushdi, Ali Muhammad Ali& al-Qawasimi, Muhammad Ahmad. Formal derivation of a particular input of a single AND (OR) gate in terms of its output and other inputs. Journal of King Abdulaziz University : Engineering Sciences. 2015. Vol. 26, no. 2, pp.51-64.
https://search.emarefa.net/detail/BIM-717962
Data Type
Journal Articles
Language
English
Notes
Includes appendices : p. 62-63
Record ID
BIM-717962