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Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.


Papers
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Patent
Bianchini Ronald P1
15 Jun 1999
TL;DR: In this article, a switching system for a data stream utilizing striping with a parity stripe is presented, so if a fabric of the system fails, the data stream can still be reconstructed with the parity stripe.
Abstract: A switching system for a data stream utilizing striping with a parity stripe, so if a fabric of the system fails, the data stream can still be reconstructed with the parity stripe. The system uses receive and transmit interfaces which implement space division, and fabrics which implement hybrid space/time division.

51 citations

Proceedings ArticleDOI
16 May 1972
TL;DR: This paper describes the design of a cyclic redundancy checking circuit using generalized systems containing more logic than the specialized systems used in the past, implemented in unit logic, and at even lower cost.
Abstract: Recent innovations in circuit technology have allowed design alternatives that previously would have been economically unsound. LSI technology permits the use of generalized systems containing more logic than the specialized systems used in the past, implemented in unit logic, and at even lower cost. Five years ago an engineer would not have even considered using a cyclic redundancy checking circuit in the manner described here.

51 citations

Journal ArticleDOI
TL;DR: In this paper, three methods of guaranteeing division safe calculations in 0-totalised fields are proposed, where division is defined as a total operation with 0−1=0, where 0 is the number of operations in the total operation.
Abstract: A 0-totalised field is a field in which division is a total operation with 0−1=0. Equational reasoning in such fields is greatly simplified but in deriving a term one still wishes to know whether or not the calculation has invoked 0−1. If it has not then we call the derivation division safe. We propose three methods of guaranteeing division safe calculations in 0-totalised fields.

51 citations

Proceedings ArticleDOI
26 Jun 1991
TL;DR: The author describes the design decisions made when designing integer division for a new 64-b machine, and proposes a fast and economical scheme for computing both unsigned and signed integer quotients which guarantees an exact answer without any correction.
Abstract: By using a reciprocal approximation, integer division can be synthesized from a multiply followed by a shift. Without carefully selecting the reciprocal, however, the quotient obtained often suffers from off-by-one errors, requiring a correction step. The author describes the design decisions made when designing integer division for a new 64-b machine. The result is a fast and economical scheme for computing both unsigned and signed integer quotients which guarantees an exact answer without any correction. The reciprocal computation is fast enough, with one table lookup and five multiplies, so that this scheme is competitive with a dedicated divider, while requiring much less hardware specific to division. The real strength of the proposed method is division by a constant, which takes only a single multiply and shift, one operation on the machine considered. The analysis shows that the computed quotient is always exact: no adjustment or correction is necessary. >

51 citations

Journal ArticleDOI
TL;DR: In this article, the dense wavelength division multiplexing of fiber Bragg grating sensors is demonstrated by combining code division and wavelength division MIMO schemes, which allows close spectral spacing among Bragg sensors without sensor spectral dynamic range limitation.
Abstract: The dense wavelength division multiplexing of fibre Bragg grating sensors is demonstrated by combining code division and wavelength division multiplexing schemes. This approach allows close spectral spacing among Bragg grating sensors without sensor spectral dynamic range limitation.

50 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20242
2023739
20221,583
2021239
2020416
2019465