Issue No. 08 - August (1993 vol. 42)

ISSN: 0018-9340

pp: 1007-1010

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.238495

ABSTRACT

<p> The authors give an online algorithm for computing a canonical signed digit representation of minimal Hamming weight for any integer n. Using combinatorial techniques, the probability distributions Pr(K/sub r/=h), where K/sub r/ is taken to be a random variable on the uniform probability space of k-digit integers is computed. Also, using a Markov chain analysis, it is shown that E(K/sub r/) approximately (r-1)k/(r+1) as k to infinity.</p>

INDEX TERMS

signed digit representations; minimal Hamming weight; online algorithm; combinatorial techniques; probability distributions; random variable; uniform probability space; k-digit integers; Markov chain analysis; digital arithmetic.

CITATION

S. Arno, F.S. Wheeler, "Signed Digit Representations of Minimal Hamming Weight",

*IEEE Transactions on Computers*, vol. 42, no. , pp. 1007-1010, August 1993, doi:10.1109/12.238495