Spectral Logic and Its Applications for the Design of Digital Devices

CHAPTER 9

SPECTRAL METHODS OF ANALYSIS AND SYNTHESIS OF RELIABLE DEVICES

The spectral approach developed in previous chapters will now be applied to the analysis of the reliability of digital devices and to the synthesis of reliable devices. These problems will be discussed both for digital devices including memory elements and for combinational (memoryless) networks. The analysis of correcting capability (Sections 9.1–9.3) will consider only “nonredundant” digital devices, that is, devices containing no special “redundant” logic elements or memory elements designed to increase reliability. The basic working tools in this chapter will be various correlation characteristics of the functions describing the operation of the digital devices.

9.1 SPECTRAL METHODS FOR ANALYSIS OF ERROR CORRECTING CAPABILITIES

9.1.1 Errors in Combinatorial Devices

We first analyze the types of errors that can be detected or corrected by switching (combinational) networks with no memory elements. The behavior of such networks is described by systems of logic functions.

In this context, the term “error” is reserved for errors at the input of a network realizing a given logic function (in particular, these may be owing to errors in previous logic networks or in communication channels). A knowledge of the types of errors that a network is capable of correcting is of paramount importance, both to estimate its reliability and to use it for synthesis of another network realizing the same system of logic functions, ...