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Minimal Weight Digit Set Conversions
June 2004 (vol. 53 no. 6)
pp. 666-677

Abstract—This paper considers the problem of recoding a number to minimize the number of nonzero digits in its representation, that is, to minimize the weight of the representation. A general sliding window scheme is described that extends minimal binary sliding window conversion to arbitrary radix and to encompass signed digit sets. This new conversion expresses a number of known recoding techniques as special cases. Proof that this scheme achieves minimal weight for a given digit set is provided and results concerning the theoretical average and worst-case weight are derived.

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Index Terms:
Digital arithmetic, redundant number systems, digit set conversion.
Braden Phillips, Neil Burgess, "Minimal Weight Digit Set Conversions," IEEE Transactions on Computers, vol. 53, no. 6, pp. 666-677, June 2004, doi:10.1109/TC.2004.14
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