Title :
Closed-form expression for the average weight of signed-digit representations
Author :
Wu, Huapeng ; Hasan, M. Anwar
Author_Institution :
Dept. of Electr. & Comput. Eng., Illinois Inst. of Technol., Chicago, IL, USA
fDate :
8/1/1999 12:00:00 AM
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 {±1, ±2, ..., ±(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 n, n⩾1
Keywords :
digital arithmetic; average weight; canonical SD representation; closed form expressions; closed-form expression; minimal weight SD representation; minimal weight signed-digit representation; nonzero digits; nonzero signed-digits; positive integer; radix-r form; radix-r number system; signed-digit representations; Arithmetic; Closed-form solution; Elliptic curves; Probability distribution;
Journal_Title :
Computers, IEEE Transactions on
