Journal Article10.1109/T-C.1975.224216
A Note on Base –2 Arithmetic Logic
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TL;DR: Circuits for performing arithmetic operations using base –2 representations are considered, study of the counting process leads to a negative binary up-down counter and new simple methods for positive-negative base conversions.
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Abstract: Circuits for performing arithmetic operations using base –2 representations are considered. Study of the counting process leads to a negative binary up-down counter and new simple methods for positive-negative base conversions. The advantage of employing carry-borrow rather than carry-only during additions is pointed out. Certain special features of negation, arithmetic shift, multiplication, and division in base –2 are described.
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Citations
Parallel optical negabinary signed-digit computing: algorithm and optical implementation
TL;DR: A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/ Subtraction algorithm based onnegabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normalNegabinary in the carry-look-ahead mode.
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On Classes of Positive, Negative, and Imaginary Radix Number Systems
TL;DR: A unified approach to a broad class of finite number representation systems that contains aDl positive and negative radix systems and other well-known number systems is proposed and enables us to develop a single set of algoritims for arithmetic operations.
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An Algorithm for Sequency Ordering of Hadamard Functions
TL;DR: A simple algorithm is developed for obtaining the sequency vector of high-order Hadamard transform matrices without the need for converting the order of individual hadamard functions to sequency.
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A recursive radix conversion formula and its application to multiplication and division
TL;DR: The recursive formula presented here is suitable for parallel computation, so that the length of time necessary for number conversion can be shortened, and the longer the digit number, the more appreciation in conversion time-saving will result.
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On Negabinary-Binary Arithmetic Relationships and Their Hardware Reciprocity
TL;DR: This correspondence emphasizes the close relationship between binary addition and negative negabinary addition (n.n.b.a.).
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References
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TL;DR: In this paper, the bit-level operations involved in the convolution realization of a non-recursive digital filter are analyzed, leading to hardware designs of digital filters based on the operation of counting.
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Negative Radix Conversion
TL;DR: Adoption of a negative radix for number representation results in a system that is totally indifferent to the sign of the number, compared to theSign-magnitude representation, which requires one extra digit.
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Arithmetic Algorithms in a Negative Base
TL;DR: Algorithms are described for the basic arithmetic operations and square rooting in a negative base and a new operation called polarization that reverses the sign of a number facilitates subtraction, using addition.
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Fast Hardware Fourier Transformation Through Counting
TL;DR: Hardware Fourier transformations are considered with the goal of increasing speed through parallel operation and two designs in which the basic element is a fast counter are developed.
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