A Comparison of Map-Based Methods for Handling Type-2 and Type-3 Problems of Digital Circuit Design | Chapter 07 | Advances in Applied Science and Technology Vol. 3
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 toinvolve 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
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.
Author(s) Details
Ali Muhammad Ali Rushdi
Department of Electrical and
Computer Engineering, King Abdulaziz University, P.O.Box80204, Jeddah 21589,
Saudi Arabia.
View Volume: https://doi.org/10.9734/bpi/aast/v3
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