Journal ArticleDOI
Ternary Threshold Logic
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In this article, a ternary threshold logic is proposed to represent all three-valued functions, and two methods of synthesizing these functions from their truth tables are given, one of the methods produces a normal form that is analogous to the disjunctive normal form of Boolean algebra.Abstract:
A new logical algebra, ternary threshold logic, is defined and developed. The system is shown to be capable of representing all three-valued functions, and two methods of synthesizing these functions from their truth tables are given. One of the methods produces a normal form that is analogous to the disjunctive normal form of Boolean algebra. A list of single-threshold-operator equivalents of certain normal forms is given. It is pointed out that magnetic film parametrons may be made to exhibit the logical properties of the operators of the system. Designs for ternary adder and comparator stages are given that could be constructed out of magnetic film parametrons.read more
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Journal ArticleDOI
Multiple-Valued Logic—its Status and its Future
TL;DR: This tutorial/survey paper will review the historical developments in this field, both in circuit realizations and in methods of handling multiple-valued design data, and consider the present state-of-the-art and future expectations.
Journal ArticleDOI
Three-valued digital systems
TL;DR: A survey is presented of the developments in algebras and techniques for the realisation of 3-valued switching functions, including digital arithmetic, ternary codes, composition alagbras, minimisation, circuits and sequential circuit design.
Journal ArticleDOI
The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement
Stephen Y. H. Su,A.A. Sarris +1 more
TL;DR: It is shown that DeMorgan's theorem holds for all four definitions of complement given in this paper, which allow us to map the multivalued variables into binary variables.
Journal ArticleDOI
Analysis of weighted median filters based on inequalities relating the weights
Mohit K. Prasad,Yong Hoon Lee +1 more
TL;DR: It is shown that a weighted median (WM) filter of spanN can be specified unambiguously by 2N−1 consistent linear inequalities relating the weights, and it is also shown that WM filters with symmetric weights can be specifying by ternary threshold functions.
References
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Journal ArticleDOI
Several-valued combinational switching circuits
C. Y. Lee,W. H. Chen +1 more
TL;DR: A survey of the literature will show that it is generally (tacitly) assumed that the states of transmission through a switching network are limited to two values.
Journal ArticleDOI
Axiomatic Majority-Decision Logic
Martin Cohn,R. Lindaman +1 more
TL;DR: An algebra suited to logical design with majority-decision elements (parametrons, Esaki diodes, etc.) is developed axiomatically and demonstrated by resolving sample problems.
Proceedings Article
A three-valued system of logic and its application to base three digital circuits.
Journal ArticleDOI
Some Applications of Magnetic Film Parametrons as Logical Devices
TL;DR: High-frequency magnetic film parametrons have been made and observed to exhibit two- or three-state operation for a single bias condition, and proposed logical designs for a two-element binary adder, a binary shift counter, and a shift register are presented.