Showing papers on "Binary number published in 1998"

On the Conversion between Non-Binary and Binary Constraint Satisfaction Problems

Abstract: It is well known that any non-binary discrete constraint satisfaction problem (CSP) can be translated into an equivalent binary CSP. Two translations are known: the dual graph translation and the hidden variable translation. However, there has been little theoretical or experimental work on how well backtracking algorithms perform on these binary representations in comparison to their performance on the corresponding non-binary CSP. We present both theoretical and empirical results to help understand the tradeoffs involved. In particular, we show that translating a non-binary CSP into a binary representation can be a viable solution technique in certain circumstances. The ultimate aim of this research is to give guidance for when one should consider translating between non-binary and binary representations. Our results supply some initial answers to this question.

A note on generating correlated binary variables

Abstract: SUMMARY It is important to be able to generate correlated binary data in an efficient, easily programmed manner for, among other things, the generation of large bootstrap samples. In this note nothing more than the basic ingredient of the uniform random number generator is required for simulating binary data from the most commonly occurring correlation structures.

Residue-to-Binary Arithmetic Converter for the Moduli Set ( )

Abstract: This paper presents a new algorithm which converts moduli residue numbers to their binary equivalents; it is the first converter which has been dedicated to this particular moduli set. The complexity of conversion has been greatly reduced using new compact forms for the multiplicative inverses and the properties of modular arithmetic. A hardware implementation which utilizes adders only is also proposed. With a pipelined system, the throughput rate is that of a single - bit binary adder. Comparison results showed that the hardware requirements and the execution time of the new converter are less than half that needed by other converters.

Residue-to-binary arithmetic converter for the moduli set (2/sup k/, 2/sup k/-1, 2/sup k-1/-1)

Abstract: This paper presents a new algorithm which converts moduli (2/sup k/, 2/sup k/-1, 2/sup k-1/-1) residue numbers to their binary equivalents; it is the first converter which has been dedicated to this particular moduli set. The complexity of conversion has been greatly reduced using new compact forms for the multiplicative inverses and the properties of modular arithmetic. A hardware implementation which utilizes adders only is also proposed. With a pipelined system, the throughput rate is that of a single (2k-1)-bit binary adder. Comparison results showed that the hardware requirements and the execution time of the new converter are less than half that needed by other converters.

Long-Term Stability of Planets in Binary Systems

Abstract: A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the system's center of mass, are examined. From the results, empirical expressions are developed for both 1) the largest orbit around each of the stars, and 2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10^4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0 <= e <= 0.7-0.8 and 0.1 <= mu <= 0.9 in both regions, and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually-interacting system of planets orbiting one star of a binary system is examined, though in less detail.

A fast renormalisation for arithmetic coding

Abstract: Summary form only given. All integer based arithmetic coding consists of two steps: proportional range restriction and range expansion (renormalisation). Here a method is presented that significantly reduces the complexity of renormalisation, allowing a speedup of arithmetic coding by a factor of up to 2. The main idea is to treat the output not as a binary number, but as a base 256 (or other) number. This requires less renormalisation and no bitwise operations.

On binary constructions of quantum codes

Abstract: Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.

Residue-to-binary arithmetic converter for the moduli set (2k, 2k - 1, 2k-1 - 1)

Abstract: This paper presents a new algorithm which converts moduli (2 k , 2 k - 1, 2 -1 - 1) residue numbers to their binary equivalents; it is the first converter which has been dedicated to this particular moduli set. The complexity of conversion has been greatly reduced using new compact forms for the multiplicative inverses and the properties of modular arithmetic. A hardware implementation which utilizes adders only is also proposed. With a pipelined system, the throughput rate is that of a single (2k-1)-bit binary adder. Comparison results showed that the hardware requirements and the execution time of the new converter are less than half that needed by other converters.

Duobinary coding and modulation technique for optical communication systems

Abstract: A method for encoding a binary input sequence x(0,1) to obtain a duobinary output sequence y(+1,0,-1) is provided. The duobinary coding technique always provides an output bit yk =0 when the corresponding bit xk =0; bits yk alternatively assume a logical level '+1' and '-1' whenever an input bit xk-1=0 changes to xk=1, and the output bit yk maintains the logical level '+1' or '-1' whenever the corresponding bit xk maintains the logical level '1'. A coding device for encoding a binary input sequence x(0,1) to a duobinary output sequence y(+1,0,-1) is also provided, comprising a D-type flip-flop for generating a binary switch signal. A first AND circuit receives the input sequence and the switch signal, and provides a first binary sequence a(0,1), while a second AND circuit receives the input sequence and the complement of the switch signal and provides a second binary sequence b(0,1). These first and second binary sequences are applied to a summer to obtain the output sequence y(+1,0,-1). A method for differentially driving an M-Z modulator using a virtual ground level is also provided, which reduces the peak-to-peak drive voltage by a factor of two.

Binary integration for Swerling target fluctuations

Abstract: Binary Integration is a suboptimal approach offering most of the benefits of integration with a simpler and less expensive receiver implementation than optimum coherent integration. We develop accurate, reliable, and efficient methods for binary integration computations for both the constant and Swerling target models. Binary integration introduces a new parameter M, the required number of threshold crossings to declare a detection. With these programs, we can readily do all the calculations necessary to determine the optimum values for M. We find that the assumed loss of 1.5 dB signal-to-noise ratio (SNR) per pulse for binary integration holds for small and large N, not only for the constant targets, but also for the Swerling target fluctuations.

Bit-stuffing bounds on the capacity of 2-dimensional constrained arrays

Abstract: Bit-stuffing constructions of binary 2-dimensional constrained arrays satisfying (d,/spl infin/) or (0,k) runlength constraints in both horizontal and vertical dimensions are described. Lower bounds on the capacity of these constrained arrays are derived.

Chaotic sequences for multiple access

Abstract: The use of chaotic signals as generators of binary and multilevel sequences suitable for code division multiple access (CDMA) is proposed. The number of obtained sequences is found to be greater than the number of m-sequences of the same length. These new chaotic sequences are used as spreading codes in a CDMA system. Simulation results are presented and compared with those obtained for m-sequences in terms of BER performance.

Dynamics of the Binary Euclidean Algorithm: Functional Analysis and Operators

Abstract: We provide here a complete average-case analysis of the binary continued fraction representation of a random rational whose numerator and denominator are odd and less than N . We analyze the three main parameters of the binary continued fraction expansion, namely, the height, the number of steps of the binary Euclidean algorithm, and finally the sum of the exponents of powers of 2 contained in the numerators of the binary continued fraction. The average values of these parameters are shown to be asymptotic to A i log N , and the three constants A i are related to the invariant measure of the Perron—Frobenius operator linked to this dynamical system. The binary Euclidean algorithm was previously studied in 1976 by Brent who provided a partial analysis of the number of steps, based on a heuristic model and some unproven conjecture. Our methods are quite different, not relying on unproven assumptions, and more general, since they allow us to study all the parameters of the binary continued fraction expansion.

Competitive Learning for Binary Valued Data

Abstract: We propose a new approach for using online competitive learning on binary data. The usual Euclidean distance is replaced by binary distance measures, which take possible asymmetries of binary data into account and therefore provide a “different point of view” for looking at the data. The method is demonstrated on two artificial examples and applied on tourist marketing research data.

Highly parallel, fast scaling of numbers in nonredundant residue arithmetic

Abstract: A new approach to scaling in the nonredundant residue number system (RNS) with the use of the Chinese remainder theorem (CRT) is presented. The auxiliary scaling by M, where M is the number range, is performed in parallel with scaling by the scale factor K in order to avoid the number range overflow. The scaler design utilizes small look-up tables and multioperand (both modulo and binary) adders. The new approach does not impose restrictions on the form, size, and number of moduli n. The only proviso is that K>n. The scaling error is bounded by n and can be reduced to 1 or 1.5 if a correction circuit is employed. Hardware complexity expressed by the number of transistors is approximately one order smaller than that for the earlier design, whereas the scaler latency is similar.

Galactic microlensing with rotating binaries

Abstract: The influence of rotating binary systems on the light curves of galactic microlensing events is studied Three dif- ferent rotating binary systems are discussed: a rotating binary lens, a rotating binary source, and the earth's motion around the sun (parallax effect) The most dramatic effects arise from the motion of a binary lens because of the changes of the caustic structurewithtimeIdiscusswhenthetreatmentofamicrolens- ing event with a static binary model is appropriate It is shown that additional constraints on the unknown physical quantities of the lens system arise from a t with a rotating binary lens as well as from the earth-around-sun motion For the DUO#2 event, a t with a rotating binary lens is presented

RNS-to-binary conversion for efficient VLSI implementation

Abstract: Conversion from a residue number system (RNS) to binary is a crucial point in the implementation of modular processors. The choice of the moduli is strictly related to conversion performance and influences the processor complexity. In this paper, a conversion method based on a class of couples of coprime moduli defined as (n - 2 k , n + 2 k ) is presented. The method and the related architecture can easily be extended to a larger number of moduli. Since it is based on very small look-up tables, the proposed method can be implemented by fast and low complex architectures.

Absolute position measurement using pseudo-random binary encoding

Abstract: This paper will present a non-traditional encoding method which represents a more efficient alternative to absolute position measurement applications. The new method is based on the properties of pseudo-random binary sequences and has the notable advantage of requiring only one bit of code per quantization interval. This advantage makes absolute position measurement more accessible for very high resolution applications.

Breaking the 2n-bit carry propagationbarrier in residue to binary conversion for the [2n-1. 2n, 2n + 1] modula set

Abstract: This brief presents a high speed realization of a residue to binary converter for the {2 n-1 , 2 n , 2 n + 1} moduli set, which improves upon the best known implementation by almost twice in terms of overall conversion delay. This significant speedup is achieved by using just three extra two input logic gates. Interestingly, by exploiting certain symmetry in operands, we also reduce the hardware requirement of the best known implementation by n - 1 full adders. Finally, the proposed converter eliminates the redundant representation of zero using no extra logic.

Error correction and detection for faults on time multiplexed data lines

Abstract: Error correction and detection for time-multiplexed binary 72-tuples over 18 wires to detect a wire fault. A syndrome is computed using a parity check matrix, where circuits for realizing the parity check matrix multiplication can be realized with only two levels of XOR gates and in which the computation is pipelined to process the time-multiplexed binary 72-tuple.

Shift—Nets: a New Class of Binary Digital (t, m, s)--Nets

Abstract: Digital nets and sequences play an important role in the theory of low-discrepancy point sets and sequences in the s-dimensional unit cube. This paper is devoted to the binary case. We first will improve the lower bound for the quality parameter of binary digital sequences. The main aim is to introduce a new class of binary digital nets, the so-called shift—nets, which in many cases are nets of improved quality.

Efficient algorithms for binary logarithmic conversion and addition

Abstract: Logarithm number system is an attractive alternative to the conventional number systems when data need to be manipulated at very high rate over a wide data range. However, the major problem is deriving logarithm and anti-logarithm quickly and accurately enough to allow conversions to and from the conventional number representations. In this paper, efficient algorithms that convert the conventional number representation to binary logarithm representation are proposed. The algorithms adopt a factorization approach to reduce the look-up table size and a nonlinear approximation method to reduce the computational complexity. Simulation results on IEEE single precision (24 bits) conversion are presented, and the conversion requires only one ROM table with 2/sup 13//spl times/26 bits, one with 2/sup 13//spl times/14 bits, and one with 2/sup 13//spl times/5 bits, or a total of 360 kbits. The algorithm can also be adopted for binary logarithmic addition.

Precise edge detection: representation by Boolean functions, implementation on the CNN

Abstract: An edge detection problem is considered in the paper It is proposed to reduce the edge detection problem on binary images to evaluation of the Boolean functions A separate processing of the binary planes with their further integration into resulting image is used for edge detection on the gray-scale images The different Boolean functions for detection of edges corresponding to the upward and downward brightness overleaps, to the narrow directions (south-north, south-east-north-west, etc) are considered All the processing functions are non-threshold Boolean functions of nine variables (such a number of variables corresponds to the processing within a 3/spl times/3 local window around the each pixel) Since all the functions are not threshold, CNN with universal binary neurons are proposed to be used for their implementation The weighting templates for all functions are obtained by learning The software simulation results are also presented

Context-based arithmetic encoding/decoding method and apparatus

Abstract: An apparatus encodes a binary shape signal by using a modified context-based arithmetic encoding technique. The apparatus computes a context number of each binary pixel in the binary shape signal based on its corresponding context. Then, a probability corresponding to the context number is detected and a state of each binary pixel is determined by comparing the probability with a preset threshold value. Furthermore, a predicted pixel value corresponding to each binary pixel is decided based on the probability. The predicted pixel value is compared with an original pixel value of each binary pixel to thereby output a mapping value representing whether the predicted pixel value is identical to the original pixel value or not. The apparatus generates a first and a second sequences by rearranging the mapping values of the binary pixels in the binary shape signal according to the states of the binary pixels and assigns adaptive probability sets to the first and the second sequences, respectively. The first and the second sequences are arithmetically encoded based on the adaptive probability sets to thereby produce an encoded binary shape signal.

Stationary states of irrotational binary neutron star systems and their evolution as a result of gravitational wave emission

Abstract: We have succeeded in obtaining exact configurations of irrotational binary systems for compressible (polytropic) equations of state. Our models correspond to binary systems of equal-mass neutron stars in the viscosity free limit. By using the obtained sequences of stationary states, the evolution of binary systems of irrotational neutron stars resulting from gravitational wave emission has been examined. For inviscid binary systems, the spin angular velocity of each component in a detached phase is smaller than the orbital angular velocity at a contact phase. The irrotational approximation during the evolution of binary neutron stars resulting from gravitational wave emission can therefore be justified. Our computational results show that the binary will never reach a dynamically unstable state before a contact phase, even for rather stiff polytropes with index N≳0.7, as the separation of two components decreases as a result of gravitational wave emission. This conclusion is quantitatively different from that of Lai, Rasio & Shapiro, who employed approximate solutions for polytropic binary systems.