Switching Theory: Insight through Predicate Logic

ISBN-13: 9783642073182 / Angielski / Miękka / 2010 / 428 str.

Shimon Peter Vingron

Opis

This new approach to an established field introduces the concept of predicate logic in order to supersede propositional logic in switching theory. The author gives new insight into the theory of latches (memory circuits) for use in undergraduate and graduate courses.

Spis treści

Division One Fundamental Concepts.- 1 Outline and Basics.- 2 Switching Devices.- 3 Functions.- 4 Logic Functions and Gates.- 5 Synthesis and Duality.- 6 Karnaugh Maps.- 7 Utilising Karnaugh Maps.- Division Two Logic.- 8 Tautologies.- 9 Propositional Logic.- 10 Summary of Theorems.- 11 Algebraic Proofs.- 12 On Predicate Logic.- 13 Predicate Logic.- Division Three Combinational Circuits.- 14 Canonical Normal Forms.- 15 Shegalkin Normal Form.- 16 Synthesis Examples.- 17 Concepts Old and New.- 18 Minimisation Preliminaries.- 19 Minimisation—an Excerp.- 20 Reduced Karnaugh Maps.- 21 NOT-AND and NOT-OR.- 22 Composition of Circuits.- 23 Hazards.- Division Four Latches.- 24 Memorising by Feedback.- 25 Basic Theory of Latches.- 26 Optimised Latches.- 27 Elementary Latches.- 28 Composition of Latches.- Division Five Sequential Circuits with Continuously Read Inputs.- 29 Automata and Programs.- 30 Word-Recognition Tables.- 31 Catenation Model.- 32 Toggle Circuits.- 33 Triggering and Synchronising.- 34 Verifying a Logic Design.- 35 Discussing Huffman’s Theory.- 36 State Encoding Techniques.

Blurb

The author’s main concern is to promote understanding of the basic ideas underlying switching theory. Nothing is taken for granted, whether it is the concept of a logic variable, that of feedback in a latch or sequential circuit, or the necessity to encode internal states. This very basic and thorough approach enables the development of new concepts such as Composition, or Verification. The theoretical side is enhanced by using predicate (instead of propositional) logic allowing for formal proofs till now unattainable. On the practical side, sequential circuits that hitherto were obtained intuitively are now open to a formal synthesis procedure.