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MSBFirst Digit Serial Arithmetic
, 1995
"... : We develop a formal account of digit serial number representations by describing them as strings from a language. A prefix of a string represents an interval approximating a number by enclosure. Standard online representations are shown to be a special case of the general digit serial representat ..."
Abstract

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: We develop a formal account of digit serial number representations by describing them as strings from a language. A prefix of a string represents an interval approximating a number by enclosure. Standard online representations are shown to be a special case of the general digit serial representations. Matrices are introduced as representations of intervals and a finitestate transducer is used for mapping strings into intervals. Homographic and bihomographic functions are used for representing basic arithmetic operations on digit serial numbers, and finally a digit serial representation of floating point numbers is introduced. Key Words: Computer Arithmetic, Online Computation, Number Representations, Redundant Digit sets, Continued Fractions, Intervals. Category: B.2 1 Introduction A number is usually represented as a string of digits belonging to some digit set \Sigma . The number representation specifies a function that maps the string to its value. In the context of this pa...
Some characterizations of functions computable in online arithmetic
 I.E.E.E. Trans. on Computers
, 1994
"... AbsfmctAfter a short introduction to online computing, we prove that the functions computable in online by a finite automaton are piecewise afthe functions whose coefikients are rational numbers (i.e., the fnnctions f(s) = UP + b, or f(z, y) = nx + by + c where a. b, and c are rational). A con ..."
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Cited by 16 (0 self)
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AbsfmctAfter a short introduction to online computing, we prove that the functions computable in online by a finite automaton are piecewise afthe functions whose coefikients are rational numbers (i.e., the fnnctions f(s) = UP + b, or f(z, y) = nx + by + c where a. b, and c are rational). A consequence of this study is that multiplication, division, and elementary functions of operands of arbitrarily long length cannot be performed using boundedshe operators. Index Zhts4omputer arithmetic, finite automata, online arithmetic. I.
An Efficient BitSerial FIR Filter Architecture
 In Circuits, Systems, and Signal Processing
, 1993
"... A new bitserial architecture for implementation of high order FIR filters, as well as example FPGA and CMOS realizations are introduced. This structure exploits the simplicity of coefficients which consist of two poweroftwo terms to yield efficient implementations. Quantization effects are discus ..."
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Cited by 2 (0 self)
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A new bitserial architecture for implementation of high order FIR filters, as well as example FPGA and CMOS realizations are introduced. This structure exploits the simplicity of coefficients which consist of two poweroftwo terms to yield efficient implementations. Quantization effects are discussed and a simple block scaling method for reducing rounding and truncation noise in high order filters is also presented. This research is supportedby the Office of Naval ResearchunderGrant N0001489J1327,NSFGrant ECS8713598,byan AT&T Bell Laboratories Graduate Fellowship, and by University of Kansas General Research allocation 3775200038. Portions of this work were presented at ICASSP90 in Albequerue, New Mexico. 1 Introduction In recent years, considerable attention has been placed on the implementation of signal processing algorithms in VLSI [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 16, 17, 19, 21], ranging from full custom VLSI to general purpose digital signal processors. A variety of app...
Number systems and Digit Serial Arithmetic
, 1997
"... this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. T ..."
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Cited by 1 (1 self)
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this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. The cube modeling a function of two variables, can be generalized to a hypercube modeling a polyhomographic function of n variables. For n = 3 the function is defined as: