On ‘Big’ Boolean-Equation Solving and Its Utility in Combinatorial Digital Design | Chapter 03 | Advances in Applied Science and Technology Vol. 2
This chapter considers the problem of
solving a system of Boolean equations over a finite (atomic) Boolean algebra
other than the
two-valued one. A
prominent “misnomer” in
mathematical and engineering circles
is the term
‘Boolean algebra’. This
term is widely
used to refer
to switching algebra, which is
just one particular case of a ‘Boolean algebra’ that has 0 generators, 1 atom
and two elements belonging to B={0,1}.The chapter outlines classical and novel
direct methods for deriving the general parametric solution of such a system
and for listing all its particular solutions. A detailed example over Bis used to illustrate these two methods as well
as a third method that starts by
deriving the subsumptive
solution first. The
example demonstrates how
the consistency condition forces a
collapse of the
underlying Boolean algebra
to a subalgebra, and
also how to list
a huge number of particular
solutions in a very compact space. Subsequently, the chapter proposes some
potential applications for
the techniques of
Boolean-equation solving. These
techniques are very promising as useful extensions of
classical techniques based on two-valued Boolean algebra.
Author(s) Details
Ali Muhammad Ali Rushdi
Department of Electrical and
Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589,
Saudi Arabia.
Sultan Sameer Zagzoog
Department of Electrical and
Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589,
Saudi Arabia.
Comments
Post a Comment