Showing papers on "Binary number published in 1999"

Several classes of binary sequences with three-level autocorrelation

Abstract: In this correspondence we describe several classes of binary sequences with three-level autocorrelation. Those classes of binary sequences are based on cyclic almost difference sets. Some classes of binary sequences have optimum autocorrelation.

Binary Digital Image Processing: A Discrete Approach

Abstract: Foreword. Acknowledgements. Notation. Preface. Digital topology. Discrete geometry. Algorithmic graph theory. Acquisition and storage. Distance transformations. Binary digital image characteristics. Image thinning. Some applications. References. Index.

Method and constructions for space-time codes for psk constellations for spatial diversity in multiple-element antenna systems

Abstract: General binary design criteria for PSK-modulated space-time codes are provided. For linear binary PSK (BPSK) codes and quadrature PSK (QPSK) codes, the rank (i.e., binary projections) of the unmodulated code words, as binary matrices over the binary field, is used as a design criterion. Fundamental code constructions for both quasi-static and time-varying channels are provided.

The mass of X-Ray Nova Scorpii 1994 (=GRO J1655--40)]

Abstract: We have obtained high and intermediate resolution optical spectra of the black-hole candidate Nova Sco 1994 in May/June 1998, when the source was in complete (X-ray) quiescence. We measure the radial velocity curve of the secondary star and obtain a semi-amplitude of K_2=215.5+/-2.4 km/s, which is 6 per cent lower than the only previously determined value. This new value for K_2 thus reduces the binary mass function to f(M) = 2.73+/-0.09 Mo. Using only the high resolution spectra we constrain the rotational broadening of the secondary star, vsini, to lie in the range 82.9-94.9 km/s (95 per cent confidence) and thus constrain the binary mass ratio to lie in the range 0.337--0.436 (95 per cent confidence). We can also combine our results with published limits for the binary inclination to constrain the mass of the compact object and secondary star to the ranges 5.5 -- 7.9 and 1.7 -- 3.3 Mo respectively (95 per cent confidence). Finally, we report on the detection of the Lithium resonance line at 6707.8 A, with an equivalent width of 55+/-8 mA.

Binary Star Orbits from Speckle Interferometry. I. Improved Orbital Elements of 22 Visual Systems

Abstract: Improved orbital elements for 22 binary systems are presented. For 12 systems, masses are calculated using available trigonometric parallaxes and making certain assumptions regarding the mass ratio. For the other 10 systems, provisional elements are provided that should provide relatively accurate ephemerides for the next decade.

Non-Binary Constraints

Abstract: Since the origins of the constraint satisfaction paradigm, its restriction to binary constraints has concentrated a significant part of the work. This is understandable because new ideas/techniques are usually much simpler to present/ elaborate by first restricting them to the binary case. (See for example the arc consistency algorithms, such as AC-3 or AC-4, which have been presented first in their binary version [10,12], before being extended to non-binary constraints [11,13].) But this inclination has highly increased in the early nineties. Authors indeed justified this restriction by the fact that any non-binary constraint network can polyniomally be converted into an equivalent binary one [6,8,5,19]. And, in most cases, they never extended their work to non-binary constraints.

Sparse modulation codes for holographic data storage

Abstract: A method for storing data in a holographic storage medium comprises the steps of dividing a bit stream of binary data into data groups, encoding the data groups as binary patterns, and storing the binary patterns holographically as data pages. Each binary pattern comprises channel bits, wherein the number of “off” channel bits is greater than the number of “on” channel bits. To retrieve information from the storage medium, the medium is illuminated and resultant light signals are gathered. The light signals are converted to the binary patterns, and the binary patterns are converted to the data groups. Binary patterns stored in the storage medium only slightly perturb subsequent reading and writing of data, since the patterns have fewer “on” channel bits than “off” channel bits.

The binary gravitational lens and its extreme cases

Abstract: The transition of the binary gravitational lens from the equal mass case to small (planetary) mass ratios q is studied. It is shown how the limit of a (pure shear) Chang-Refsdal lens is approached, under what conditions the Chang-Refsdal approximation is valid, and how the 3 different topologies of the critical curves and caustics for a binary lens are mapped onto the 2 different topologies for a Chang-Refsdal lens with pure shear. It is shown that for wide binaries, the lensing in the vicinity of both lens objects can be described by a Taylor-expansion of the deflection term due to the other object, where the Chang-Refsdal approximation corresponds to a truncation of this series. For close binaries, only the vicinity of the secondary, less massive, object can be described in this way. However, for image distances much larger than the separation of the lens objects, any binary lens can be approximated by means of multipole expansion, where the first non-trivial term is the quadrupole term. It is shown that an ambiguity exists between wide and close binary lenses, where the shear at one of the objects due to the other object for the wide binary is equal to the absolute value of the eigenvalues of the quadrupole moment for the close binary. This analysis provides the basis for a classification of binary lens microlensing events, especially of planetary events, and an understanding of present ambiguities.

Circuitry for performing operations on binary numbers

Abstract: Circuitry for adding a first binary number (A) having a plurality of bits (a 0 , a 1 , . . . ) to a second binary number (B) having a plurality of bits (b 0 , b 1 , . . . ) to produce a third binary number (A+B) having a plurality of bits (s 0 , s 1 , . . . ) and/or a fourth binary number (A+B+1) having a plurality of bits (s 0 ′, s 1 ′, . . . ) and corresponding to the addition of the third binary number and one. The circuitry includes a plurality of stages wherein each stage has a first input for receiving a bit (a i ) of the first binary number (A), a second input for receiving a bit (b i ) of the second binary number (B) having the same binary weight (i) as the bit received at the first input and output means for producing a bit (s i ) of the third binary number (A+B) and/or a bit (s′ i ) of the fourth binary number (A+B+1), wherein said output means comprises exclusive OR means for combining a first signal and a second signal to produce a bit of the third binary number and the first signal and a third signal to produce a bit of the fourth binary number wherein said third signal is equivalent to said second signal if both the bits received at the first and second inputs have a LOW logic value, or for any stage having a lower binary weight, both the bits received at the first and second inputs have a LOW logic value and is otherwise equivalent to a predetermined logic value.

Parallel optical negabinary signed-digit computing: algorithm and optical implementation

Abstract: Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

The binary gravitational lens and its extreme cases

Abstract: The transition of the binary gravitational lens from the equal mass case to small (planetary) mass ratios q is studied. It is shown how the Limit of a (pure shear) Chang-Refsdal lens is approached, under what conditions the Chang-Refsdal approximation is valid, and how the 3 different topologies of the critical curves and caustics for a binary lens are mapped onto the 2 different topologies for a Chang-Refsdal lens with pure shear. It is shown that for wide binaries, the lensing in the vicinity of both lens objects can be described by a Taylor-expansion of the deflection term due to the other object, where the Chang-Refsdal approximation corresponds to a truncation of this series. For close binaries, only the vicinity of the secondary, less massive, object can be described in this way. However, for image distances much larger than the separation of the lens objects, any binary lens can be approximated by means of multipole expansion, where the first non-trivial term is the quadrupole term. It is shown that an ambiguity exists between wide and close binary lenses, where the shear at one of the objects due to the other object for the wide binary is equal to the absolute value of the eigenvalues of the quadrupole moment for the close binary. This analysis provides the basis for a classification of binary lens microlensing events, especially of planetary events, and an understanding of present ambiguities.

CD Tau: a detached eclipsing binary with a solar-mass companion

Abstract: We present a detailed analysis of the detached eclipsing binary CD Tau. A largevariety of observational data, in form of IR photometry, CORAVEL radial velocityobservations and high-resolution spectra, are combined with the published light curvesto derive accurate absolute dimensions and effective temperature of the components,as well as the metal abundance of the system. We obtain: M A = 1.442(16) M ⊙ ,R A = 1.798(17)R ⊙ , T eff = 6200(50)K,M B = 1.368(16)M ⊙ ,R B = 1.584(20)R ⊙ andT effB = 6200(50) K. The metal content of the system is determined to be [Fe/H] =+0.08(15) dex.In addition, the eclipsing binary has a K-type close visual companion at about10-arcsec separation, which is shown to be physically linked, thus sharing a commonorigin. The effective temperature of the visual companion (T effC = 5250(200) K) isdetermined from synthetic spectrum fitting, and its luminosity (logL/L ⊙ = −0.27(6)),and therefore its radius (R = 0.89(9) R ⊙ ), are obtained from comparison with theapparent magnitude of the eclipsing pair.The observed fundamental properties of the eclipsing components are comparedwith the predictions of evolutionary models, and we obtain good agreement for an ageof 2.6 Gyr and a chemical composition of Z = 0.026 and Y = 0.26. Furthermore, wetest the evolutionary models for solar-mass stars and we conclude that the physicalproperties of the visual companion are very accurately described by the same isochronethat fits the more massive components.Key words: stars: individual: CD Tau – binaries: eclipsing – binaries: visual – stars:evolution – stars: abundances – stars: late-type.

Method for detecting edges in an image signal

Abstract: An edge detection method employs binary morphological erosion. A binary image is generated from the gray-scale-value input image. A structure element is guided in a step-by-step manner across the binary image and generates an eroded binary image in accordance with an erosion rule. By forming the difference between the binary image and the eroded binary image, an output image containing the edges is generated. An output image which contains masked edges is generated through the use of a further erosion rule. The further erosion rule is based on a gray-scale value threshold and is applied to the eroded binary image to form a twice-eroded binary image. The difference between the twice-eroded binary image and the binary image forms the image which contains masked edges.

Method for the orthogonal and offset transmission-reception of a signal and device for realizing the same

Abstract: An information stream of binary symbols is divided into serial packets of N binary symbols. The method further includes serial-parallel conversion of binary symbols in each serial packet and repeating N times the parallel packet thus obtained in order to form a serial-parallel packet of binary symbols. The binary symbols are permuted in the duration interval of each serial-parallel packet, and orthogonal codes generated according to the above binary symbol permutation are then applied. A space-diversity channel is then assigned to each serial group of the serial-parallel packet of coded binary symbols thus obtained. All the serial groups of coded binary symbols, each coded binary symbol having been previously spread by a user spreading code, as well as pilot signals of the corresponding space diversity channels are simultaneously transmitted. The method also involves generating on the reception side a serial packet of soft decisions that corresponds to the serial packet of binary symbols on the transmission side.

Orbital periods of the binary sdB stars PG0940+068 and PG1247+554

Abstract: We have used the radial velocity variations of two sdB stars previously reported to be binaries to establish their orbital periods. They are PG0940+068, (P=8.33d) and PG1247+554 (P=0.599d). The minimum masses of the unseen companions, assuming a mass of 0.5 solar masses for the sdB stars, are 0.090 +/- 0.003 solar masses for PG1247+554 and 0.63 +/- 0.02 solar masses for PG0940+068. The nature of the companions is not constrained further by our data.

Classification of binary textures using the 1-D Boolean model

Abstract: The one-dimensional (1-D) Boolean model is used to calculate features for the description of binary textures. Each two-dimensional (2-D) texture is converted into several 1-D strings by scanning it according to raster vertical, horizontal or Hilbert sequences. Several different probability distributions for the segment lengths created this way are used to model their distribution. Therefore, each texture is described by a set of Boolean models. Classification is performed by calculating the overlapping probability between corresponding models. The method is evaluated with the help of 32 different binary textures, and the pros and cons of the approach are discussed.

Method and device for coding and transmission using a sub-code of a product code

Abstract: A method is provided for coding information representing a physical quantity and represented by first binary symbols, having an operation of calculating second binary symbols from the information, the second binary symbols being called calculated binary symbols and being provided in order to be disposed in a square table. For each calculated binary symbol, there exist at least three distinct diagonals in the table which contain this calculated binary symbol and which, deprived of this calculated binary symbol, still allow each one on its own to recalculate the calculated binary symbol. A coding device, a decoding method, a decoding device, a transmission method, and a transmission device are provided, as well as a camera, a facsimile machine, photographic apparatus, and a computer, implementing the invention.

All-optical pseudorandom number generator

Abstract: We demonstrate an all-optical pseudorandom binary number generator comprised of two coupled regenerative opticalmemories and an XOR gate. Both sub-maximal binary sequences and maximal length pseudorandom sequences weresuccessfully demonstrated. q1999 Elsevier Science B.V. All rights reserved. Keywords: All-optical digital processing; XOR; TOAD In future high speed photonic networks, it is envisagedthat all-optical signal processing will be required in orderto reduce latency and maintain the high bandwidth of thenetwork 1 . Recently, the practical prospect of performingwxall-optical digital processing has been advanced with theuse of semiconductor optical amplifier SOA based inter-.ferometric switching gates 2 . The low switching energieswxtypically ;100–200 fJ per pulse 2–4 and the highwx.switching speed of up to 100 Gbits 5–7 has led to a y1 wxvariety of all-optical digital circuits being realised. Thesehave included a shift register with inverter 8,9 , a regener-wxative memory with logic level restoration 10,11 , an opti-wxcal memory with readrwrite ability 12 and a binarywxhalf-adder 13 . The use of bit-serial time-of-flight opticalwxarchitectures has allowed complex circuits to be demon-strated with a simple scaling to operation at higher switch-ing speeds 14 . In this paper, we further extend thewxfunctionality of all-optical digital circuits with a demon-stration of an all-optical digital pseudorandom numbergenerator. The concept of a digital pseudorandom numbergenerator is well known in electronics 15 . Binary pseudo-wxrandom bit sequences PRBS can be obtained by using a.shift register and feeding back the logical XOR of the endof the register and a tap point as shown in Fig. 1. The

Efficient algorithms for binary logarithmic conversion and addition

Abstract: The logarithm number system is an attractive alternative to the conventional number systems when data needs to be manipulated at a very high rate over a wide range. The major problem is deriving logarithms and antilogarithms quickly and accurately enough to allow conversions to and from conventional number representations. Efficient algorithms that convert the conventional number representation to binary logarithm representations are proposed. The algorithms adopt a factorisation 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.

Constructions of intersecting codes

Abstract: New constructions of binary linear intersecting codes are presented. Some codes with high distances are shown to be intersecting.

Non-power-of-two Gray-code counter and binary incrementer therefor

Abstract: Non-power-of-two Gray-code counters, including modulos 10, 12, 14, and 22 are disclosed, along with a sequencing method they employ. Each counter includes a register for storing an N-bit, e.g., 4-bit, Gray-code count. The count is converted to binary code by a Gray-to-binary-code counter. The resulting binary count is incremented by an N-bit incrementer that skips certain binary values by toggling least-significant bits in unison when indicated by certain most-significant binary bits. The result is converted to Gray-code by a binary-to-Gray-code translator. The translated result is stored in the register as the next count. An algorithm is disclosed for designing such a Gray-code counter for any even modulo. The modulo is expressed as a sum of positive and negative terms, each term being a power of two. The exponents of the terms determine the counter design.

Guest Editorial: Special Section on Computer Arithmetic for Optical Computing

Abstract: Around the same time, non-binary systemssuch as multiple valued logic ~MVL!~Ref. 3! alsoachieved prominence both in optics and digital comput-ing. Since then a large number of papers have been pub-lished in optical computer arithmetic. This special sectionis an attempt to capture current research in computerarithmetic for optical computing. The five major areasthat are presented in this section are MSD-based algo-rithm and systems, optimization of MVL, novel architec-tures for binary optical computing, high accuracy analogoptical system implementations, and system studies forfault-tolerance and accuracy. Some of the papers mayhave overlap of two or more areas with one primary fo-cus; they are pointed out in the following discussion.The largest cluster of papers appears in the area ofsigned-digit arithmetic and its implementation. A numberof different techniques for addition, multiplication and di-vision are proposed by several authors. The number sys-tems addressed include redundant binary, MSD binary,negabinary, MSD trinary, recoded trinary and MSD qua-ternary. In terms of number of steps, addition/subtractionin single, dual and triple step has been proposed. Whilethe MSD number system leads to higher information den-sity, if the number of steps is reduced, the truth tablesmay become humongous, which may impose challengingrequirements on the actual implementation. Techniquesfor reducing the cost of such implementations have beenaddressed by some authors. Proposed implementations in-clude space-variant logic array, correlator~composite andpseudo-inverse filter! and non-holographic content ad-dressable memory ~CAM! using electron-trapping mate-rial. Several authors have proposed novel algorithms andtheir possible optical implementations while others havesuggested implementations and/or optimization on knownalgorithms.The first paper in the area of signed-digit arithmetic byLi et al. presents negabinary arithmetic operations for ad-dition, subtraction and multiplication and implementsthem using electron trapping material. A carry free addi-tion technique in signed-digit negabinary ~SDN! is pre-sented with a conversion technique from SDN to normalnegabinary. Zhang and Karim propose modified two-step,one-step, canonical and three-input algorithms for addi-tion of redundant binary numbers and provide architectureand encoding for corresponding optical space-variantimplementation. Cherri demonstrates single step trinaryand quaternary signed-digit circuits. In general, the reduc-tion in step increases the complexity of the truth table.However, Cherri overcomes the problem by smart digitgrouping to reduce the number of rules and an intelligentpixel encoding to implement the system within a certainspace-bandwidth product. Huang, Itoh and Yatagai pro-pose a new technique for high-speed 2-D data array addi-tion and multiplication based on binary MSD addition anddigit-decomposition-plane representation. Huang, Itohand Yatagai generate all the partial products in paralleland propose to add them using an MSD adder tree. It isinteresting to note that they perform multiplication opera-tion using five elementary operations such as bitwiseproduct, duplication, shifting, masking and magnification.In the next paper, Alam introduces trinary division tech-nique based on recoded trinary addition and multiplica-tion. The proposed implementation uses a pseudo-inversefilter correlator. The last two papers in this group byAhmed, Awwal and Power and by Zhang and Karim pro-pose novel implementations of trinary and binary MSDalgorithm. Ahmed, Awwal and Power implement an MSDtrinary adder using composite phase-only-filter correlatorarchitecture. In this framework, the truth table rules are

Binary sequences with two-level autocorrelation

Abstract: We derive the values of the Fourier spectrum, a decomposition, and an achievable upper bound on the linear span, for binary sequences with two-level autocorrelation.

Ideals and the binary discriminator in universal algebra

Abstract: We introduce the binary discriminator and the dual binary discriminator and the corresponding universal algebras with 0. The latter are related to permutability and distributivity at 0. For A finite the dual binary discriminator is in the intersection of all maximal subclones of the clone of all f satisfying f (0,...,0) = 0 (except certain maximal subclones if A is of prime power cardinality). An algebra with a special binary term function and a special unary term function is a dual binary discriminator algebra if and only if it is ideal-free. Finally we characterize binary and dual binary discriminator varieties.

Optical scalable parallel modified signed-digit algorithms for large-scale array addition and multiplication using digit-decomposition-plane representation

Abstract: Optical scalable parallel and high-speed 2D-data array com- puting based on modified signed-digit arithmetic and digit- decomposition-plane representation is presented. The digit- decomposition-plane coding uses m binary planes or m blocks of a binary plane to code an m-digit data array. Therefore, we can easily access each digit individually and can implement array addition with only 13 combinatorial logic formulas. A duplication-shifting-superimposition algorithm for digital array multiplication is proposed. The algorithm gen- erates and records all the bitwise products in mn binary planes simulta- neously, and then processes them based on a modified signed-digit (MSD) adder tree. Only five basic operations of bitwise product, duplica- tion, shifting, masking and magnification are required for digital comput- ing. The features of the proposed algorithm are that it requires no bistable devices, no decimal point, no sign, and no carry. The algorithm and its implementing scheme are scalable because they are indepen- dent to the sizes of data arrays. Therefore it has great promise for large- scale array computing. Optical implementation with classical optical ele- ments, such as beamsplitters, parallel plates, and mirrors, is discussed. A preliminary demonstration experiment with an optoelectronic scheme is described. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)00503-6)

Hybrid weighted-density approximation for nonuniform fluid mixtures.

Abstract: A hybrid weighted-density approximation (HWDA), which is based on both local density and globally averaged density, has been proposed to study the structural properties of nonuniform fluid mixtures. The advantage is that the HWDA is computationally much simpler than the extended weighted-density approximation proposed by Davidchack and Laird. The HWDA has been applied to calculate the density profiles of binary hard-sphere mixtures near a structureless hard wall. Comparison between the theoretical results and simulations for the confined binary hard-sphere mixtures demonstrates the reliable accuracy of the HWDA.

Binary Steering of Nonbinary Iterative Algorithms

Abstract: Existing algorithms for binary image reconstruction that can handle two-dimensional problems are mainly of a combinatorial nature. This has,so far, hindered their direct application to fully three-dimensional binary problems. This chapter proposes a steering scheme by which non-binary iterative reconstruction algorithms can be steered towards a binary solution of a binary problem. Experimental studies show the viability of this approach.