Spectral Logic and Its Applications for the Design of Digital Devices

CHAPTER 6

SPECTRAL METHODS IN SYNTHESIS OF LOGIC NETWORKS

The present chapter is devoted to methods for the design of combinational digital devices realizing systems of logical functions. These methods are based on the orthogonal series expansions of logic functions, with various spectral transforms and correlation functions as the main tools.

All the methods described in this chapter for the design of digital devices realizing systems of logic functions are also applicable to the construction of algorithms for software implementations of logic functions. In other words, spectral methods may be interpreted from both network and programming standpoint. The synthesis methods are illustrated by network interpretations.

As it has been noticed in Reference 299, there is apparent a renewed and considerable interest in spectral techniques after the publication of a report about applications of Walsh functions to technology mapping (655). This interest is due to the development of technology of digital circuits imposing requirements and strong demands regarding complexity and performances of logic networks and digital devices in general, which cannot be met by traditional approaches.

In the last decade, spectral method for synthesis, including testing, has been discussed in a considerable number of publications, see References 37, 54, 57, 98, 204, 228, 283, 295, 297, 318, 319, 345, 346, 356, 385, 434, 458, 475, 481, 497, 600, 602, 604, 656, and 657.

6.1 SPECTRAL METHODS OF SYNTHESIS OF ...