Modeling digital switching circuits with linear algebra / Mitchell A. Thornton.

Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (pages 135-139) and index.

1. Introduction --

2. Information as a vector -- 2.1 Switching theory -- 2.2 Linear algebra -- 2.2.1 Vector space mappings -- 2.2.2 Bra-ket notation and the outer product -- 2.3 Modeling information in the Hilbert space --

3. Switching network transfer functions -- 3.1 Switching network models -- 3.2 Switching network transfer matrix derivation -- 3.3 Transfer matrices of common switching circuits -- 3.3.1 Fanout structure transfer matrix -- 3.3.2 Fanout structure transfer matrix -- 3.3.3 Crossover structure transfer matrix -- 3.3.4 Other basic switching elements -- 3.4 Logic network transfer matrices --

4. Simulation and justification -- 4.1 Network output response -- 4.2 Transfer matrix properties -- 4.3 The pseudo-inverse of a transfer matrix and network justification -- 4.4 The justification matrix --

5. MVL switching networks -- 5.1 MV information representation in the vector space -- 5.2 Extensions to binary switching networks -- 5.3 General ternary switching networks -- 5.4 MVSN justification --

6. Binary switching network spectra -- 6.1 Spectral methods within the vector space model -- 6.2 The spectral domain of a switching network -- 6.3 Fourier basis functions -- 6.4 Walsh transform -- 6.4.1 Walsh transform of scalar-valued switching functions -- 6.4.2 Walsh transform for vector-valued switching functions -- 6.4.3 Walsh spectral response matrices -- 6.4.4 Computing Walsh spectral coefficients from a netlist -- 6.5 The Reed-Muller transform -- 6.5.1 RM transform of scalar-valued switching functions -- 6.5.2 RM transform for vector-valued switching functionS -- 6.5.3 Reed-Muller spectral response matrices -- 6.5.4 Calculation of the RM spectra through netlist traversals -- 6.6 Other spectral response matrices -- 6.6.1 The arithmetic spectral transform --

7. Multi-valued switching network spectra -- 7.1 MV spectra -- 7.2 Chrestenson transform -- 7.2.1 Chrestenson transform of scalar-valued switching functions -- 7.2.2 Chrestenson transform of vector-valued switching functions -- 7.2.3 Chrestenson spectral response matrices -- 7.2.4 Computing Chrestenson spectral coefficients from a netlist --

8. Implementation considerations -- 8.1 Transfer and justification matrix representations -- 8.1.1 Cubelist representations of transfer matrices -- 8.1.2 BDD representations of transfer matrices -- 8.1.3 Structural representations of transfer matrices -- 8.2 Computing the transfer matrix from a structural netlist -- 8.2.1 Switching network partitioning -- 8.2.2 Computing the transfer matrix and crossover detection -- 8.3 Computational results --

9. Summary -- Bibliography -- Author's biography -- Index.

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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 f0; 1g allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use 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.

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Title from PDF title page (viewed on May 20, 2014).

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