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Closed-Form Expression for the Average Weight of Signed-Digit Representations
August 1999 (vol. 48 no. 8)
pp. 848-851

Abstract—In radix-$r$ number system, the minimal weight signed-digit (SD) representation has minimal number of nonzero signed-digits which belong to the set $\{\pm{1},\pm{2},\ldots,\pm{(r-1)}\}$. In this article, we derive closed form expressions for the average number of nonzero digits in the minimal weight SD representation and for the average length of the canonical SD representation, a special case of the minimal weight SD form, of a positive integer whose radix-$r$ form is of length $\schmi{n}$, $\schmi{n}\geq 1$.

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Index Terms:
Radix-$r$ number system, minimal weight signed-digit representation, canonical signed-digit representation.
Citation:
Huapeng Wu, M. Anwar Hasan, "Closed-Form Expression for the Average Weight of Signed-Digit Representations," IEEE Transactions on Computers, vol. 48, no. 8, pp. 848-851, Aug. 1999, doi:10.1109/12.795126
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