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<p><b>Abstract</b>—In radix-<tmath>$r$</tmath> number system, the minimal weight signed-digit (SD) representation has minimal number of nonzero signed-digits which belong to the set <tmath>$\{\pm{1},\pm{2},\ldots,\pm{(r-1)}\}$</tmath>. 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-<tmath>$r$</tmath> form is of length <tmath>$\schmi{n}$</tmath>, <tmath>$\schmi{n}\geq 1$</tmath>.</p>
Radix-$r$ number system, minimal weight signed-digit representation, canonical signed-digit representation.

H. Wu and M. A. Hasan, "Closed-Form Expression for the Average Weight of Signed-Digit Representations," in IEEE Transactions on Computers, vol. 48, no. , pp. 848-851, 1999.
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