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Computer Arithmetic (ARITH)

作者： S. Ong D. E. Atkins Systems Engineering Laboratory Department of Electrical and Computer Engineering University of Michigan Ann Arbor MI USA Program in Computer Information and Control Engineering University of Michigan Ann Arbor MI USA

This paper describes an evolving Arithmetic Design System (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple consisting of a symbol set (elements are called "digit-vectors"), an interpretation set, a mapping between these two sets, and a set of operators (digit-vector algorithms) defined on its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without overflow detection, for three number systems is given.

关键词： Vectors Complexity theory Computers Algorithm design and analysis Finite element methods Hardware Digital arithmetic

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Time-Component Complexity of Two Approaches to Multioperand Binary Addition

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IEEE Transactions on Computers 1979年第12期C-28卷 918-926页

作者： Atkins, Daniel E. Ong, Shau-Chi Program in Computer Information and Control Engineering the Systems Engineering Laboratory of the Department of Electrical and Computer Engineering University of Michigan Ann Arbor MI 48109 United States

Component and time complexity measures in terms of number of gates and gate delays, respectively, are derived for two multioperand adder structures: a tree of carry-save adders and a tree of carry-lookahead adders. The parameters of the complexity measures are operand length, number of operands, and maximum fanin to the gates. The analysis involves a constructive derivation of the complexity of carry-lookahead networks including optimization by removal of redundant paths. An alternate measure of component complexity, number of packages with a given number of pinouts, rather than number of gates, is also presented. The general conclusion of the paper is that, under the assumptions made, for a large set of design parameters, the carry-save adder structure requires both less time and fewer components than the functionally equivalent carry-lookahead adder structure. Copyright © 1979 by The Institute of electrical and Electronics Engineers, Inc.

关键词： binary addition carry-lookahead adder carry-save adder Index Terms-Adder tree multioperand addition time-component complexity

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8th International Symposium on Multiple-Valued Logic, MVL 1978

作者： Atkins, D.E. Program in Computer Information and Control Engineering Systems Engineering Laboratory Department of Electrical and Computer Engineering University of Michigan Ann ArborMI48109 United States

An approach to the topic of computer arithmetic is suggested which may have a particular conceptual, pedagodical, and practical appeal to the designer of multiple-valued logic processors. Computer arithmetic deals with the physical representation of finite sets of numbers and the design, analysis, and implementation of algorithms for mechanizing arithmetic operations on these sets. Finite number representation systems (FNRS) are specified by defining a set of symbols and a mapping from the elements of this symbol set to a subset of the real numbers. A formal definition of a FNRS provides a basis for a set of definitions which in turn provide the framework for the classification of a large set of number systems. Emphasis in this paper is on the following positive, fixed radix systems: unsigned, sign and magnitude, radix complement, and diminished radix complement. We offer an annotated listing of primitive digit vector algorithms for the four common number representation systems with an arbitrary, positive integer, fixed radix. These digit vector algorithms are ones which the designer of multi-valued logic arithmetic processors will need to implement to provide general arithmetic computation. © 1978 Advanced Automotive Batteries. All rights reserved.

关键词： Numbering systems

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A comparison of two approaches to multi-operand binary addition

A comparison of two approaches to multi-operand binary addit...

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Computer Arithmetic (ARITH)

作者： D. E. Atkins S. C. Ong Program in Computer Information and Control Engineering and Systems Engineering Laboratory Department of Electrical and Computer Engineering University of Michigan Ann Arbor USA University of Michigan Ann Arbor MI US

This paper presents the results of one phase of a study concerning methods for addition of P>;2 numbers, each encoded as a vector of digits (digit vector) of length N. Such multi-operand addition has been studied most often in the context of reducing a set of partial products to a single result in the implementation of multiplication. More generalized multi-operand addition, most notably in the form of inner product calculations is, however, central to numerous scientific applications of digital computers. Although multi-operand addition is trivially accomplished by accumulation (iteration in time) in any general purpose machine, demands for very high-speed computation, typified by 2- and 3-D signal processing prompt implementation of dedicated, hardware-intensive structures for multi-operand addition. This study, for example, is motivated in part by requirements for rapid simultaneous addition of up to 100, 16-bit operands in the design of a dedicated processor for real-time reconstruction of 3-D images of the beating heart and breathing lungs [1].

关键词： Adders Logic gates Vectors Delay Equations Computers Hardware

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BANQUET ADDRESS - BUILT-IN COMBAT READINESS - APPROACH TO FUTURE SHIP DESIGN

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NAVAL ENGINEERS JOURNAL 1976年第3期88卷 40-43页

作者： MARCY, HT The Honorable H. Tyler (“Ty”) Marcy:was born in 1918 in Rochester New York but moved to Baltimore Maryland at an early age where he attended public schools. He is a graduate of the Massachusetts Institute of Technology from which he received both his BS and MS degrees in Electrical Engineering. Subsequent to receiving the latter degree in 1941 he designed and developed gun control systems in the MIT Servomechanism Laboratory until 1946 when he became Associate Director Special Projects Department M. W. Kellogg Company and worked on rocket engine development missile controls and analog air defense systems. In 1951 Mr. Marcy left Kellogg Company to join the IBM Corporation where he remained until 1972 and was employed in various engineering and managerial positions. At IBM his first assignment concerned the bomb/navigational system for the B-52 aircraft. He then moved into commercial development of data processing machines and peripheral devices subsequently being placed in a series of technical management positions which included Assistant Manager of Product Development Corporate Headquarters New York (1956) Manager Poughkeepsie N.Y. Laboratory (1957) Vice-President General Products Division (1962) Vice-President Systems Development Division (1965) and Director of Technology Corporate Headquarters Armonk N. Y. (1968). His last position was held until 1972 when he left IBM to do private consulting work in engineering management technology and program review. In October 1974 he was appointed by the President to his present office as Assistant Secretary of the Navy for Research and Development. Mr. Marcy has been a member of the Instrument Society of America since 1963 serving as its President from 1971 until 1974. In 1967 he became a Fellow of the Institute of Electrical and Electronic Engineers (IEEE) for his leadership in feedback control and for his significant contribution to the management of technical enterprise. In addition to these professional organizations he is also a member of the

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Scattering theory and linear least squares estimation: Part II: Discrete-time problems

Scattering theory and linear least squares estimation: Part ...

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IEEE Conference on Decision and control

作者： B. Friedlander T. Kailath L. Ljung Information Systems Laboratory Department of Electrical Engineering University of Stanford Stanford CA USA Department of Automatic Control Lund Institute of Technology Lund Sweden

A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous-time are noted.

关键词： Least squares approximation information systems Laboratories Time measurement Scattering parameters

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Scattering theory and linear least squares estimation: Part I: Continuous-time problems

Scattering theory and linear least squares estimation: Part ...

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IEEE Conference on Decision and control

作者： L. Ljung T. Kailath B. Friedlander Department of Automatic Control Lund Institute of Technology Lund Sweden Information Systems Laboratory Department of Electrical Engineering University of Stanford Stanford CA USA

The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. We show that this framework is very appropriate also for estimation problems, and that it enables us to give simple derivatitions of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behavior of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.

关键词： Scattering Least squares approximation Riccati equations Smoothing methods

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A Method for Increasing the Resolution of Discrete Optical Sensors

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IEEE Transactions on Industrial Electronics and control Instrumentation 1974年第2期IECI-21卷 71-74页

作者： Henderson, Karl C. McVey, Eugene S. Research Laboratories for Engineering Sciences University of Virginia Charlottesville Va. 22901 United States Control and Information Systems Laboratory Department of Electrical Engineering University of Virginia Charlottesville Va. 22901 United States

The problem of increasing the resolution of discrete optical sensors in information systems is considered. The proposed method uses an overlapping scan and multilevel quantization. The samples thus obtained are processed by a minimum mean square estimator utilizing the pseudoinverse of the transformation matrix. The method is illustrated by a 4/1 enhancement of an 8 X 8 resolution grid. Experimental results are presented. Copyright © 1974 by The Institute of electrical and Electronics Engineers, Inc.

关键词： Optical sensors Sensor arrays Optical devices Optical arrays Quantization Additive noise Image resolution Solid state circuits Detectors Costs

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INVESTIGATION OF WORST-CASE ERRORS WHEN INPUTS AND THEIR RATE OF CHANGE ARE BOUNDED

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IEEE TRANSACTIONS ON AUTOMATIC control 1966年第2期AC11卷 296-+页

作者： SARIDIS, G REKASIUS, ZV Control and Information Systems Laboratory School of Electrical Engineering Purdue University Lafayette IN USA Department of Electrical Engineering Technological Institute North western University Evanston IL USA

The worst-case error analysis is extended to include the problem of bounded input r(t) and its rate of change dr/dt for a a dynamical system described by a set of differential equations with separable forcing function. The problem is reformulated as a bounded-input, bounded-state variable problem, and Pontryagin's Maximum Principle is applied to maximize a given error function. For a wide class of systems, the time derivative of the worst forcing function is shown to be "bang-bang" for the open region defined by the constraint of r(t) and zero on its boundary. A computational algorithm is developed to solve the resulting two-point boundary value problem.

关键词： Error analysis Differential equations Error correction Optimal control Variable speed drives Missiles control systems information systems Laboratories Military computing

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A NONBULK ADDITION TECHNIQUE FOR ASSOCIATIVE PROCESSORS

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IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS 1966年第6期EC15卷 938-+页

作者： YAU, SS YANG, CC Information-Processing and Control Systems Laboratory and Department of Electrical Engineering Northwestern University Evanston IL USA Program of Information Science and the Department of Electrical Engineering Washington State University Pullman USA Information-processing and Control Systems Laboratory and Department of Electrical Engineering Northwestern University Evanston IL USA

A process is described for continuing adaptation, after hyperplanes that separate pattern classes in pattern space have been found, in order to increase the distance between sample patterns and hyperplanes.

关键词： Boolean functions Logic Network synthesis Testing Silicon carbide Sufficient conditions Arithmetic Software performance Associative memory Hardware

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