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Design of Ternary Logic Circuits Using CNFETs
Published in Brajesh Kumar Kaushik, Nanoscale Devices, 2018
Chetan Vudadha, M. B. Srinivas
One of the computing paradigms that has received considerable attention over the last few decades is multi-valued logic (MVL) [18]. Three-valued logic or ternary logic, which is a special case of MVL, has attracted considerable interest over the last couple of decades. A recent survey presents various contemporary aspects related to MVL [8]. Some of the advantages of MVL include reduced interconnect complexity, less device count, etc. This is due to the fact that more information is embedded per digit. For example, it is possible to represent a 14-digit (N-digit) binary number using only 9 (log3(2N− 1)) ternary digits. Ternary logic is a special case of MVL with three significant states. There have been many CMOS-based implementations for ternary logic [19,20]. It has been shown that the performance of CMOS-based designs is enhanced by adding MVL blocks to binary designs [21,22]. A design for ternary memory units and sequential circuits has been presented in [23]. A CMOS-based ternary Wallace tree multiplier has been implemented in [24]. Apart from the works that focus on novel designs [23–26], there have been many works that focus on synthesis of MVL logic circuits [27–29].
Fuzzy Logic
Published in Praveen Kumar, Jay Alameda, Peter Bajcsy, Mike Folk, Momcilo Markus, Hydroinformatics: Data Integrative Approaches in Computation, Analysis, and Modeling, 2005
Lydia Vamvakeridou-Lyroudia, Dragan Savic
In classical Boolean predicate logic any proposition is either “true” (1) or “false” (0). However this binary black-and-white way is not always successful in real-life problems and reasoning. A system of logic is needed, where for any proposition there can be at least three answers: “True/Yes,” symbolically represented as (1), “False/No,” represented as (0) and “Uncertain/maybe/we do not know,” represented as (0.5). This is formally called three-valued logic. Three valued logic (and its extension to multiple n-valued logic) has been introduced before fuzzy logic, in the 1920s and 1930s. For a logic system to be fully determined, basic operations, called primitives, have to be defined. These primitives are: Conjuction (∧), the logical AND (P Λ Q)Disjuction (∨), the logical OR (P V Q)Negation (-), the logical NOT (-P)Implication (→)(P implies Q: P → Q ≡ (−P) ∨ Q)Equivalence (↔) (If P → Q and Q → P, then P ↔ Q)
Fuzzy cluster approach for area FWD representative basin from deflection measurement spatial variability
Published in International Journal of Pavement Engineering, 2019
Alessandra Bianchini, Haley P. Bell
With the introduction of the fuzzy logic, or three-valued logic, the membership of each element to a set is not crisp and is defined by a value ranging from 0 (the element does not belong to the set) to 1 (the element fully belongs to the set). The element membership to a class is defined by the membership function that quantifies how similar the characteristics of an element are to those characteristics of the class and to those elements already enclosed in the set. The membership function is Equation (6). Any function can be used as a membership function with the limitation that its range varies between 0 and 1 (Ross 2004).
Novel Circuit Model of Multi-walled CNT Bundle Interconnects Using Multi-valued Ternary Logic
Published in IETE Journal of Research, 2023
V. Sulochana, C. Venkataiah, Sunil Agrawal, Balwinder Singh
As the technology is advancing day by day, the performance of digital circuits depends on the binary logic is overpowered by the MVL logics due to pin-out connection problems in integrated circuits. The primary advantage of the MVL systems is that each wire can transmit more information than the binary systems that leads to a reduced number of connections and complexity. Furthermore, the speed of transmitted information is also increased. Ternary (three valued) logic is one of the well-known logic in MVL system because 3 is the smallest radix than binary logic. Ternary logic systems are more economical because 3 is very close to e =2.718. In [21], it has been observed that the MWCNT interconnects demonstrate lesser crosstalk delay than conventional Cu. In [22], an encoder design was implemented for the ternary logic system to convert intermediated binary signals to final ternary outputs. A multi-diameter CNTFET-based ternary logic system has also been implemented in [23]. However, the previous works [21–23] have not reported on temperature-based active shielding of MWCNT interconnect with CNTFET driver. Therefore, the objective of this work is to demonstrate the performance of active shielding under the influence of temperature variation using an MWCNT interconnect line. The paper is organized as follows: Section 1 introduces the current research scenario and importance of the proposed work. The interconnect geometry and the proposed MWCNT transmission line model with a CNTFET driver are presented in Section 2. The crosstalk reliability with and without the shielding is demonstrated in Section 3. This section also illustrates the performance based on the temperature and noise variations. Finally, Sections 4 draws a brief summary of the paper.
Non-commutative propositional logic with short-circuit evaluation
Published in Journal of Applied Non-Classical Logics, 2021
Jan A. Bergstra, Alban Ponse, Daan J. C. Staudt
In this section, we discuss some other variants of sequential connectives. Next, we relate to McCarthy's three-valued logic and observe that we cannot relate to any well-known three-valued logic. We conclude with a note on two-valued (which comprises an axiomatisation).