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Signed Digit Representations of Minimal Hamming Weight
August 1993 (vol. 42 no. 8)
pp. 1007-1010

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.

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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.
S. Arno, F.S. Wheeler, "Signed Digit Representations of Minimal Hamming Weight," IEEE Transactions on Computers, vol. 42, no. 8, pp. 1007-1010, Aug. 1993, doi:10.1109/12.238495
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