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Redundant Radix Representations of Rings
November 1999 (vol. 48 no. 11)
pp. 1153-1165

Abstract—This paper presents an analysis of radix representations of elements from general rings; in particular, we study the questions of redundancy and completeness in such representations. Mappings into radix representations, as well as conversions between such, are discussed, in particular where the target system is redundant. Results are shown valid for normed rings containing only a finite number of elements with a bounded distance from zero, essentially assuring that the ring is “discrete.” With only brief references to the more usual representations of integers, the emphasis is on various complex number systems, including the “classical” complex number systems for the Gaussian integers, as well as the Eisenstein integers, concluding with a summary on properties of some low-radix representations of such systems.

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Index Terms:
Radix representation of rings, integer and computer radix number systems, redundancy, number system conversion, computer arithmetic.
Citation:
Asger Munk Nielsen, Peter Kornerup, "Redundant Radix Representations of Rings," IEEE Transactions on Computers, vol. 48, no. 11, pp. 1153-1165, Nov. 1999, doi:10.1109/12.811100
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