Rushdi, Ali Muhammad Ali
(2019)
*A Comparison of Map-Based Methods for Handling
Type-2 and Type-3 Problems of Digital Circuit Design.*
In:
Advances in Applied Science and Technology Vol. 3.
B P International, pp. 80-100.
ISBN 978-93-89246-54-4

## Abstract

With the advent of digital computers, several prominent problems of digital circuit design emerged. A

particular elementary class of these problems, (called Type-2 problems) can be divided into two

subclasses depending on whether an honest translator is possible or a sneaky translator is warranted.

The case of an honest translator is simply an inverse problem of logic, in which knowledge of the

vectorial function Z(X) is utilised to produce its inverse vectorial function X(Z). Though an old method

of solving type-2 problems was known almost half a century ago, two modern map-based methods

are now possible, namely the method of Boolean-equation solving and the method of input-domain

constraining. The paper aims to expose and illustrate these two novel methods, with stress on

comparing them together and demonstrating their superiority to (as well as an agreement with) the old

conventional method. This purpose is achieved by way of three typical classical examples for which

conventional solutions are somewhat tedious and cumbersome, while modern solutions are simple

and insightful. Throughout these examples, the Karnaugh map is effectively utilised, either in its

conventional version or in its variable-entered version. The Boolean-equation-solving method seems

to involve certain unwarranted steps that might be possibly skipped. However, its map-based variant

is an effective method for handling a related class of digital-design problems called Type-3 problems.

An example of a Type-3 problem is given to show how this method resolves and circumvents a certain

discrepancy that conventional techniques fell short of handling completely. The present study

exposed, illustrated, and compared the two methods of Boolean-equation solving and input-domain

constraining, which are novel methods for handling Type-2 problems of digital circuit design. Three

typical classical examples are presented, for which known conventional methods of solution are

somewhat tedious and cumbersome, while the map-based methods of solution presented herein are

simple and insightful. Throughout these examples, the Karnaugh map is effectively utilised, either in

its conventional version or in its variable-entered version. When used with Type-2 problems, the

Boolean-equation-solving method seems to involve certain unwarranted steps that might be possibly

skipped. However, its map-based variant is an effective method for handling a related class of digitaldesign

problems called Type-3 problems. An example of a Type-3 problem is given to show how this

method resolves and circumvents a certain discrepancy that conventional techniques fell short of

handling completely.

Item Type: | Book Section |
---|---|

Subjects: | Oalibrary Press > Multidisciplinary |

Depositing User: | Managing Editor |

Date Deposited: | 20 Nov 2023 04:42 |

Last Modified: | 20 Nov 2023 04:42 |

URI: | http://asian.go4publish.com/id/eprint/3309 |