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This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in the field of multiple-valued logic prior to 1975 - this supplements and extends an earlier bibliography of works prior to 1965, by Nicholas Rescher in his book Many-Valued Logic, McGraw-Hill, 1969. There are a number of possible reasons for interest in the present volume. First, the range of various uses covered in this collection of papers may be taken as indicative of a breadth which occurs in the field of multiple-valued logic as a whole - the papers here can do no more than cover a small sample: question-answering systems, analysis of computer hazards, algebraic structures relating to multiple-valued logic, algebra of computer programs, fuzzy sets. Second, a large part of the interest in such uses and applications has occurred in the last twenty, even ten years. It would be too much to expect this to be reflected in Rescher's 1969 book. Third, in the 1970's a series of annual symposia have been held on multiple-valued logic, which have brought much of this into a sharp focus. * The 1971 and 1972 symposia were held at the SUNY at Buffalo, the 1973 symposium at the Uni versity of Toronto, and the 1974 symposium at West Virginia Uni versity. Papers from these symposia are included in the bibliography which may be found in an appendix of this book.
Timing research in high performance VLSI systems has advanced at a steady pace over the last few years, while tools, especially theoretical mechanisms, lag behind. Much present timing research relies heavily on timing diagrams, which, although intuitive, are inadequate for analysis of large designs with many parameters. Further, timing diagrams offer only approximations, not exact solutions, to many timing problems and provide little insight in the cases where temporal properties of a design interact intricately with the design's logical functionalities. This book presents a methodology for timing research which facilitates analy sis and design of circuits and systems in a unified temporal and logical domain. In the first part, we introduce an algebraic representation formalism, Timed Boolean Functions (TBF's), which integrates both logical and timing informa tion of digital circuits and systems into a single formalism. We also give a canonical form, TBF BDD's, for them, which can be used for efficient ma nipulation. In the second part, we apply Timed Boolean Functions to three problems in timing research, for which exact solutions are obtained for the first time: 1. computing the exact delays of combinational circuits and the minimum cycle times of finite state machines, 2. analysis and synthesis of wavepipelining circuits, a high speed architecture for which precise timing relations between signals are essential for correct operations, 3. verification of circuit and system performance and coverage of delay faults by testing.
Ternary digital system is commonly known as three valued digital system.Three valued logic is an elementary set of Multiple Valued Logic, which is introduced in the book at the beginning. The book provides a detail overview of every concept required for the design and applications of ternary circuits. It covers the basic concepts for ternary logic fundamentals,ternary logic gates, its logic gate truth tables, Boolean rules for ternary logic up to ternary logic families, function synthesis and minimization techniques and an applications like one trit T-ALU, Two trit T-ALU Slice, Ternary R-S and D memory elements and an analog to ternary converter for DSP application as a fundamental block are developed and simulated using EDA tool. Finally computer simulation using EDA (Electronic Design Automation) tools like Tanner, spice and VHDL is also illustrated. In the first half of 19 th century G.Boolean have proposed the Algebra for two valued (Binary logic) system after that Shanon has expressed the behavior of electrical switches in terms of Boolean algebra and he paved the ramp to an industrial development that is recognized as initiating one of the most revolutionary economic changes ever. MVL is also known as Multi-Valued, Multiple-Valued or Many-Valued logic. Multi-Value logic is regarded as a switch with more than two states. Such as a 3- value switch with states ‘0’, ‘1’ and ‘2’. Or a 4-value switch with states ‘0’, ‘1’, ‘2’ and ‘3’. In case of 3-Valued logic the term ternary logic is used & term quaternary logic for 4-Valued logic. Alexander (1964) showed that the most efficient radix for implementation of switching systems is the natural base (e ≈2.71828), it seems likely that the best integral radix is 3 rather than 2.It should be noted that this book emphasis on Ternary logic with concepts and applications. The fundamental work on Multiple Valued Logic (MVL) System was done by E.L.Post in the beginning of 19 th centuries and based on that work P.C.Rosen Bloom modeled the Algebra for MVL is called Post Algebra.