Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling
digital information and circuitry that is an alternative to Boolean algebra. While the Boolean
algebraic model has been wildly successful and is responsible for many advances in modern
information technology the approach described in this book offers new insight and different
ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0
1} allows digital circuits to be characterized with transfer functions in the form of a linear
transformation matrix. The use of transfer functions is ubiquitous in many areas of engineering
and their rich background in linear systems theory and signal processing is easily applied to
digital switching circuits with this model. The common tasks of circuit simulation and
justification are specific examples of the application of the linear algebraic model and are
described in detail. The advantages offered by the new model as compared to traditional methods
are emphasized throughout the book. Furthermore the new approach is easily generalized to
other types of information processing circuits such as those based upon multiple-valued or
quantum logic thus providing a unifying mathematical framework common to each of these
areas.Modeling Digital Switching Circuits with Linear Algebra provides a blend of theoretical
concepts and practical issues involved in implementing the method for circuit design tasks.
Data structures are described and are shown to not require any more resources for representing
the underlying matrices and vectors than those currently used in modern electronic design
automation (EDA) tools based on the Boolean model. Algorithms are described that perform
simulation justification and other common EDA tasks in an efficient manner that are
competitive with conventional design tools. The linear algebraic model can be used to implement
common EDA tasks directly upon a structural netlist thus avoiding the intermediate step of
transforming a circuit description into a representation of a set of switching functions as is
commonly the case when conventional Boolean techniques are used. Implementation results are
provided that empirically demonstrate the practicality of the linear algebraic model.
