Search results for: Residue arithmetic

Authors: Hossein Khademolhosseini, Mehdi Hosseinzadeh

Abstract:

The residue number system (RNS), due to its properties, is used in applications in which high performance computation is needed. The carry free nature, which makes the arithmetic, carry bounded as well as the paralleling facility is the reason of its capability of high speed rendering. Since carry is not propagated between the moduli in this system, the performance is only restricted by the speed of the operations in each modulus. In this paper a novel method of number representation by use of redundancy is suggested in which {rn- 2,rn-1,rn} is the reference moduli set where r=2k+1 and k =1, 2,3,.. This method achieves fast computations and conversions and makes the circuits of them much simpler.

Keywords: Binary to RNS converter, Carry save adder, Computer arithmetic, Residue number system.

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

Abstract:

In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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Authors: Mehdi Hosseinzadeh, Somayyeh Jafarali Jassbi, Keivan Navi

Abstract:

Residue Number System (RNS) is a modular representation and is proved to be an instrumental tool in many digital signal processing (DSP) applications which require high-speed computations. RNS is an integer and non weighted number system; it can support parallel, carry-free, high-speed and low power arithmetic. A very interesting correspondence exists between the concepts of Multiple Valued Logic (MVL) and Residue Number Arithmetic. If the number of levels used to represent MVL signals is chosen to be consistent with the moduli which create the finite rings in the RNS, MVL becomes a very natural representation for the RNS. There are two concerns related to the application of this Number System: reaching the most possible speed and the largest dynamic range. There is a conflict when one wants to resolve both these problem. That is augmenting the dynamic range results in reducing the speed in the same time. For achieving the most performance a method is considere named “One-Hot Residue Number System" in this implementation the propagation is only equal to one transistor delay. The problem with this method is the huge increase in the number of transistors they are increased in order m² . In real application this is practically impossible. In this paper combining the Multiple Valued Logic and One-Hot Residue Number System we represent a new method to resolve both of these two problems. In this paper we represent a novel design of an OHRNS-based adder circuit. This circuit is useable for Multiple Valued Logic moduli, in comparison to other RNS design; this circuit has considerably improved the number of transistors and power consumption.

Keywords: Computer Arithmetic, Residue Number System, Multiple Valued Logic, One-Hot, VLSI.

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Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi

Abstract:

The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {rn - 2, rn - 1, rn}, based on simple mathematical relationships. Also an efficient hardware realization of this algorithm is presented. Our proposed converter is very faster and results to hardware savings, compared to the other reverse converters.

Keywords: Reverse converter, residue to weighted converter, residue number system, multiple-valued logic, computer arithmetic.

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Authors: Yavar Safaei Mehrabani, Mehdi Hosseinzadeh

Abstract:

As embedded and portable systems were emerged power consumption of circuits had been major challenge. On the other hand latency as determines frequency of circuits is also vital task. Therefore, trade off between both of them will be desirable. Modulo 2n+1 adders are important part of the residue number system (RNS) based arithmetic units with the interesting moduli set (2n-1,2n, 2n+1). In this manuscript we have introduced novel binary representation to the design of modulo 2n+1 adder. VLSI realization of proposed architecture under 180 nm full static CMOS technology reveals its superiority in terms of area, power consumption and power-delay product (PDP) against several peer existing structures.

Keywords: Computer arithmetic, modulo 2n+1 adders, Residue Number System (RNS), VLSI.

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Authors: Chithra R, Pallab Maji, Sarat Kumar Patra, Girija Sankar Rath

Abstract:

The successful use of CDMA technology is based on the construction of large families of encoding sequences with good correlation properties. This paper discusses PN sequence generation based on Residue Arithmetic with an effort to improve the performance of existing interference-limited CDMA technology for mobile cellular systems. All spreading codes with residual number system proposed earlier did not consider external interferences, multipath propagation, Doppler effect etc. In literature the use of residual arithmetic in DS-CDMA was restricted to encoding of already spread sequence; where spreading of sequence is done by some existing techniques. The novelty of this paper is the use of residual number system in generation of the PN sequences which is used to spread the message signal. The significance of cross-correlation factor in alleviating multi-access interference is also discussed. The RNS based PN sequence has superior performance than most of the existing codes that are widely used in DS-CDMA applications. Simulation results suggest that the performance of the proposed system is superior to many existing systems.

Keywords: Direct-Sequence Code Division Multiple Access (DSCDMA), Multiple-Access Interference (MAI), PN Sequence, Residue Number System (RNS).

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Authors: Xing-Jian Li, Shen Qu

Abstract:

The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.

Keywords: Elementary row transformation, Euler function, Matrix decomposition, Smith arithmetic determinant.

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Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi

Abstract:

In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than the latest introduced reverse converter for moduli set {2n, 2n–1, 2n–1–1}. Also, it has better performance than the reverse converters for the recently introduced moduli set {2n+1–1, 2n, 2n–1}

Keywords: Residue arithmetic, Residue number system, Residue-to-Binary converter, Reverse converter

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Authors: Yukinari Minagi , Akinori Kanasugi

Abstract:

This paper describes about dynamic reconfiguration to miniaturize arithmetic circuits in general-purpose processor. Dynamic reconfiguration is a technique to realize required functions by changing hardware construction during operation. The proposed arithmetic circuit performs floating-point arithmetic which is frequently used in science and technology. The data format is floating-point based on IEEE754. The proposed circuit is designed using VHDL, and verified the correct operation by simulations and experiments.

Keywords: dynamic reconfiguration, floating-point arithmetic, double precision, FPGA

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Authors: Naruemon Prapasuwannakul

Abstract:

Soymilk residue is obtained as a byproduct from soymilk and tofu production with little economic value. It contains high protein and fiber as well as various minerals and phyto-chemical compounds. The objective of this research was to substitute soymilk residue for wheat flour in gyoza skin in order to enhance value of soymilk residue and increase protein and fiber content of gyoza skin. Wheat flour was replaced with soymilk residue from 0 to 40%. The soy milk residue prepared in this research contains 26.92%protein, 3.58% fiber, 2.88% lipid, 6.29% ash and 60.33% carbohydrate. The results showed that increasing soymilk residue decreased lightness (L*value), tensile strength and sensory attributes but increased redness (a*), yellowness (b*), protein and fiber contents of product. The result also showed that the gyoza skin substituted with 30% soymilk residue was the most acceptable (p≤0.05) and its protein and fiber content increased up to 45 % and 867 % respectively.

Keywords: Gyoza skin, sensory, soymilk residue, wheat flour.

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Authors: K. Ganesan

Abstract:

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.

Keywords: Interval arithmetic, Interval matrix, linear equations.

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Authors: Haruo Shimada, Akinori Kanasugi

Abstract:

This paper proposes an architecture of dynamically reconfigurable arithmetic circuit. Dynamic reconfiguration is a technique to realize required functions by changing hardware construction during operations. The proposed circuit is based on a complex number multiply-accumulation circuit which is used frequently in the field of digital signal processing. In addition, the proposed circuit performs real number double precision arithmetic operations. The data formats are single and double precision floating point number based on IEEE754. The proposed circuit is designed using VHDL, and verified the correct operation by simulations and experiments.

Keywords: arithmetic circuit, complex number, double precision, dynamic reconfiguration

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Authors: Pitcha Wongskeo, Pramoch Rangsunvigit, Sumaeth Chavadej

Abstract:

The possibility of using cassava residue containing 49.66% starch, 21.47% cellulose, 12.97% hemicellulose, and 21.86% lignin as a raw material to produce glucose using enzymatic hydrolysis was investigated. In the experiment, each reactor contained the cassava residue, bacteria cells, and production medium. The effects of particles size (40 mesh and 60 mesh) and strains of bacteria (A002 and M015) isolated from Thai higher termites, Microcerotermes sp., on the glucose concentration at 37°C were focused. High performance liquid chromatography (HPLC) with a refractive index detector was used to determine the quantity of glucose. The maximum glucose concentration obtained at 37°C using strain A002 and 60 mesh of the cassava residue was 1.51 g/L at 10 h.

Keywords: Hydrolysis, termites, glucose, cassava

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Authors: Harpreet Singh Dhillon, Abhijit Mitra

Abstract:

A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

Keywords: Multiplication, algorithm, Vedic mathematics, digital arithmetic, reduced-bit.

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Authors: Somayeh Timarchi, Keivan Navi

Abstract:

Efficient modulo 2n+1 adders are important for several applications including residue number system, digital signal processors and cryptography algorithms. In this paper we present a novel modulo 2n+1 addition algorithm for a recently represented number system. The proposed approach is introduced for the reduction of the power dissipated. In a conventional modulo 2n+1 adder, all operands have (n+1)-bit length. To avoid using (n+1)-bit circuits, the diminished-1 and carry save diminished-1 number systems can be effectively used in applications. In the paper, we also derive two new architectures for designing modulo 2n+1 adder, based on n-bit ripple-carry adder. The first architecture is a faster design whereas the second one uses less hardware. In the proposed method, the special treatment required for zero operands in Diminished-1 number system is removed. In the fastest modulo 2n+1 adders in normal binary system, there are 3-operand adders. This problem is also resolved in this paper. The proposed architectures are compared with some efficient adders based on ripple-carry adder and highspeed adder. It is shown that the hardware overhead and power consumption will be reduced. As well as power reduction, in some cases, power-delay product will be also reduced.

Keywords: Modulo 2n+1 arithmetic, residue number system, low power, ripple-carry adders.

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Authors: Chan Weng Howe, Mohd Saberi Mohamad

Abstract:

Protein residue contact map is a compact representation of secondary structure of protein. Due to the information hold in the contact map, attentions from researchers in related field were drawn and plenty of works have been done throughout the past decade. Artificial intelligence approaches have been widely adapted in related works such as neural networks, genetic programming, and Hidden Markov model as well as support vector machine. However, the performance of the prediction was not generalized which probably depends on the data used to train and generate the prediction model. This situation shown the importance of the features or information used in affecting the prediction performance. In this research, support vector machine was used to predict protein residue contact map on different combination of features in order to show and analyze the effectiveness of the features.

Keywords: contact map, protein residue contact, support vector machine, protein structure prediction

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Authors: Dhruba Das

Abstract:

In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: Imprecise number, Imprecise vector, Membership surface, Imprecise matrix.

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Authors: Yong-Je Choi, Moo-Seop Kim, Hang-Rok Lee, Ho-Won Kim

Abstract:

Polynomial bases and normal bases are both used for elliptic curve cryptosystems, but field arithmetic operations such as multiplication, inversion and doubling for each basis are implemented by different methods. In general, it is said that normal bases, especially optimal normal bases (ONB) which are special cases on normal bases, are efficient for the implementation in hardware in comparison with polynomial bases. However there seems to be more examined by implementing and analyzing these systems under similar condition. In this paper, we designed field arithmetic operators for each basis over GF(2233), which field has a polynomial basis recommended by SEC2 and a type-II ONB both, and analyzed these implementation results. And, in addition, we predicted the efficiency of two elliptic curve cryptosystems using these field arithmetic operators.

Keywords: Elliptic Curve Cryptosystem, Crypto Algorithm, Polynomial Basis, Optimal Normal Basis, Security.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a general overview of this type of generalization and study some of their main properties such as the distinction between descending and ascending orders. We also consider different families of Quasi-OWAD operators such as the Minkowski ordered weighted averaging distance (MOWAD) operator, the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized quasi-arithmetic distance, etc.

Keywords: Aggregation operators, Distance measures, Quasi- OWA operator.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: Girija Chetty, Renuka Biswas

Abstract:

In this paper, we propose novel algorithmic models based on information fusion and feature transformation in crossmodal subspace for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quantization features, their transformation in cross-modal subspace, and their multimodal fusion, for emulated copy-move tamper scenario shows a significant improvement in tamper detection accuracy as compared to single mode features without transformation in cross-modal subspace.

Keywords: image tamper detection, digital forensics, correlation features image fusion

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Authors: Shahana T. K., Babita R. Jose, K. Poulose Jacob, Sreela Sasi

Abstract:

The modern telecommunication industry demands higher capacity networks with high data rate. Orthogonal frequency division multiplexing (OFDM) is a promising technique for high data rate wireless communications at reasonable complexity in wireless channels. OFDM has been adopted for many types of wireless systems like wireless local area networks such as IEEE 802.11a, and digital audio/video broadcasting (DAB/DVB). The proposed research focuses on a concatenated coding scheme that improve the performance of OFDM based wireless communications. It uses a Redundant Residue Number System (RRNS) code as the outer code and a convolutional code as the inner code. Here, a direct conversion of analog signal to residue domain is done to reduce the conversion complexity using sigma-delta based parallel analog-to-residue converter. The bit error rate (BER) performances of the proposed system under different channel conditions are investigated. These include the effect of additive white Gaussian noise (AWGN), multipath delay spread, peak power clipping and frame start synchronization error. The simulation results show that the proposed RRNS-Convolutional concatenated coding (RCCC) scheme provides significant improvement in the system performance by exploiting the inherent properties of RRNS.

Keywords: Analog-to-residue converter, Concatenated codes, OFDM, Redundant Residue Number System, Sigma-delta modulator, Wireless communication

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Authors: Mohamed Al Mahdi Eshtawie, Masuri Bin Othman

Abstract:

Finite impulse response (FIR) filters have the advantage of linear phase, guaranteed stability, fewer finite precision errors, and efficient implementation. In contrast, they have a major disadvantage of high order need (more coefficients) than IIR counterpart with comparable performance. The high order demand imposes more hardware requirements, arithmetic operations, area usage, and power consumption when designing and fabricating the filter. Therefore, minimizing or reducing these parameters, is a major goal or target in digital filter design task. This paper presents an algorithm proposed for modifying values and the number of non-zero coefficients used to represent the FIR digital pulse shaping filter response. With this algorithm, the FIR filter frequency and phase response can be represented with a minimum number of non-zero coefficients. Therefore, reducing the arithmetic complexity needed to get the filter output. Consequently, the system characteristic i.e. power consumption, area usage, and processing time are also reduced. The proposed algorithm is more powerful when integrated with multiplierless algorithms such as distributed arithmetic (DA) in designing high order digital FIR filters. Here the DA usage eliminates the need for multipliers when implementing the multiply and accumulate unit (MAC) and the proposed algorithm will reduce the number of adders and addition operations needed through the minimization of the non-zero values coefficients to get the filter output.

Keywords: Pulse shaping Filter, Distributed Arithmetic, Optimization algorithm.

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Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul

Abstract:

In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.

Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.

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Authors: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: Cheewaphongphan P., Garivait S., Pongpullponsak A., Patumsawad S.

Abstract:

Thailand is one of the world-s leaders of rice producers and exporters. Farmers have to increase the rice cultivation frequency for serving the national increasing of export-s demand. It leads to an elimination of rice residues by open burning which is the quickest and costless management method. The open burning of rice residue is one of the major causes of air pollutants and greenhouse gas (GHG) emission. Under ASEAN agreement on trans-boundary haze, Thailand set the master plan to mitigate air pollutant emission from open burning of agricultural residues. In this master plan, residues incorporation is promoted as alternative management method to open burning. However, the assessment of both options in term of GHG emission in order to investigate their contribution to long-term global warming is still scarce or inexistent. In this study, a method on rice residues assessment was first developed in order to estimate and compare GHG emissions from rice cultivation under rice residues open burning and the case with incorporation of the same amount of rice residues, using 2006 IPCC guidelines for emission estimation and Life Cycle Analysis technique. The emission from rice cultivation in different preparing area practice was also discussed.

Keywords: Greenhouse gases, Incorporation, Rice cultivation, Rice field residue, Rice residue management

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Authors: O. Farobie, S S. Achmadi, L K. Darusman

Abstract:

Biodiesel production results in glycerol production as the main by-product in biodiesel industry.One of the utilizations of glycerol obtained from biodiesel production is as a cement grinding aid (CGA). Results showed that crude glycerol content was 40.19% whereas pure glycerol content was 82.15%. BSS value of the cement with CGA supplementation was higher than that of nonsupplemented cement (blank) indicating that CGA-supplemented cement had higher fineness than the non-supplemented one. It was also found that pure glycerol 95% and TEA 5% at 80ºC was the optimum CGA used to result in finest cement with BSS value of 4.836 cm2/g. Residue test showed that the smallest percent residue value (0.11%) was obtained in cement with supplementation of pure glycerol 95% and TEA 5%. Results of residue test confirmed those of BSS test showing that cement with supplementation of pure glycerol 95% and TEA 5% had the finest particle size.

Keywords: biodiesel, cement grinding aid, glycerol, Jatropha curcas

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Authors: Davod Khojasteh Salkuyeh

Abstract:

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

Keywords: Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.

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Authors: Lidia Obojska

Abstract:

This paper has, as its point of departure, the foundational axiomatic theory of E. De Giorgi (1996, Scuola Normale Superiore di Pisa, Preprints di Matematica 26, 1), based on two primitive notions of quality and relation. With the introduction of a unary relation, we develop a system totally based on the sole primitive notion of relation. Such a modification enables a definition of the concept of dynamic unary relation. In this way we construct a simple language capable to express other well known theories such as Robinson-s arithmetic or a piece of a theory of concatenation. A key role in this system plays an abstract relation designated by “( )", which can be interpreted in different ways, but in this paper we will focus on the case when we can perform computations and obtain results.

Keywords: language, unary relations, arithmetic, computability

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Authors: Shiv Shankar Mishra, S. Wairya, R. K. Nagaria, S. Tiwari

Abstract:

New methodologies for XOR-XNOR circuits are proposed to improve the speed and power as these circuits are basic building blocks of many arithmetic circuits. This paper evaluates and compares the performance of various XOR-XNOR circuits. The performance of the XOR-XNOR circuits based on TSMC 0.18μm process models at all range of the supply voltage starting from 0.6V to 3.3V is evaluated by the comparison of the simulation results obtained from HSPICE. Simulation results reveal that the proposed circuit exhibit lower PDP and EDP, more power efficient and faster when compared with best available XOR-XNOR circuits in the literature.

Keywords: Exclusive-OR (XOR), Exclusive-NOR (XNOR), High speed, Low power, Arithmetic Circuits.

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