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Asger Munk Nielsen, Peter Kornerup, "Redundant Radix Representations of Rings," IEEE Transactions on Computers, vol. 48, no. 11, pp. 11531165, November, 1999.  
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@article{ 10.1109/12.811100, author = {Asger Munk Nielsen and Peter Kornerup}, title = {Redundant Radix Representations of Rings}, journal ={IEEE Transactions on Computers}, volume = {48}, number = {11}, issn = {00189340}, year = {1999}, pages = {11531165}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.811100}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Redundant Radix Representations of Rings IS  11 SN  00189340 SP1153 EP1165 EPD  11531165 A1  Asger Munk Nielsen, A1  Peter Kornerup, PY  1999 KW  Radix representation of rings KW  integer and computer radix number systems KW  redundancy KW  number system conversion KW  computer arithmetic. VL  48 JA  IEEE Transactions on Computers ER   
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 lowradix representations of such systems.
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