scholarly journals Binomial Number System

2021 ◽  
Vol 11 (23) ◽  
pp. 11110
Author(s):  
Oleksiy Borysenko ◽  
Svitlana Matsenko ◽  
Vjaceslavs Bobrovs
Keyword(s):  
Data Storage ◽  
Error Detection ◽  
Digital Signal ◽  
Number System ◽  
Binomial Coefficients ◽  
Property A ◽  
Constant Weight ◽  
Combinatorial Objects ◽  
Digital Devices ◽  
Number Systems

This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number systems (PNS) with conditions and number functions for converting BNS with a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, and multivalued number systems. Generated by BNS, binomial numbers possess the error detection property. A characteristic property of binomial numbers is the ability, on their basis, to form various combinatorial configurations based on the binomial coefficients, e.g., compositions or constant-weight (CW) codes. The theory of positional binary BNS construction and generation of binary binomial numbers are proposed. The basic properties and possible areas of application of BNS researched, particularly for the formation and numbering of combinatorial objects, are indicated. The CW binomial code is designed based on binary binomial numbers with variable code lengths. BNS is efficiently used to develop error detection digital devices and has the property of compressing information.

scholarly journals Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

2022 ◽  
Vol 12 (1) ◽  
pp. 463
Author(s):  
Mikhail Babenko ◽  
Anton Nazarov ◽  
Maxim Deryabin ◽  
Nikolay Kucherov ◽  
Andrei Tchernykh ◽  
...  
Keyword(s):  
Error Detection ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Maximum Likelihood Decoding ◽  
Number Systems ◽  
Residue Number Systems ◽  
Error Detection And Correction ◽  
Residue Number ◽  
Weighted Number ◽  
Multiple Error

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

scholarly journals Number systems in modular rings and their applications to "error-free" computations

2019 ◽  
Vol 43 (5) ◽  
pp. 901-911 ◽  
Author(s):  
V.M. Chernov
Keyword(s):  
Golden Ratio ◽  
Digital Signal ◽  
Number System ◽  
Parallel Machine ◽  
New Class ◽  
Number Systems ◽  
Residue Number ◽  
Discrete Orthogonal ◽  
Redundant Number System ◽  
Modular Reductions

The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.

Analysis of 6T SRAM Cell in Different Technologies

2017 ◽  
Vol MCSP2017 (01) ◽  
pp. 7-10 ◽  
Author(s):  
Subhashree Rath ◽  
Siba Kumar Panda
Keyword(s):  
Low Power ◽  
Data Storage ◽  
Low Voltage ◽  
Random Access ◽  
Storage Device ◽  
Cmos Process ◽  
Process Technology ◽  
Digital Devices ◽  
Noise Margin ◽  
Sram Cell

Static random access memory (SRAM) is an important component of embedded cache memory of handheld digital devices. SRAM has become major data storage device due to its large storage density and less time to access. Exponential growth of low power digital devices has raised the demand of low voltage low power SRAM. This paper presents design and implementation of 6T SRAM cell in 180 nm, 90 nm and 45 nm standard CMOS process technology. The simulation has been done in Cadence Virtuoso environment. The performance analysis of SRAM cell has been evaluated in terms of delay, power and static noise margin (SNM).

Inverse number in dagaare

2021 ◽  
pp. 444-462
Author(s):  
Scott Grimm
Keyword(s):  
Number System ◽  
Formal Semantic ◽  
Semantic Classification ◽  
Lexical Semantic ◽  
Semantic Account ◽  
Number Systems ◽  
System P ◽  
Functional Grounding

This chapter examines the inverse number system in Dagaare (Gur; Niger–Congo). Inverse number systems possess a number morpheme which for some nouns encodes the plural interpretation while for others it encodes the singular interpretation. This chapter argues that a principled lexical semantic classification underlies the inverse number strategy in Dagaare, guiding whether for a particular noun the inverse morpheme codes the singular or the plural interpretation. The chapter further explores the functional grounding of inverse number, in terms of frequency and individuation, and presents a formal semantic account of the inverse number system.

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