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- W2051270653 abstract "Lexicographic continued fraction binary (LCF) representation provides an order preserving bitstring representation of the non negative real numbers where every rational number has a finite length bitstring representation. We investigate the precision of k-bit LCF approximation. The maximum gap size over [0,1] for (k+1)-bit LCF representation is shown to be less than 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>−.81k</sup> , comparable to binary coded decimal in worst case representation efficiency. The distribution of gap sizes for (k+1)-bit LCF representation over [0,1] is shown on a logarithmic scale to be bell shaped between 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>−.81k</sup> and 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>−1.39k</sup> , becoming more peaked near the value corresponding to uniform spacing, 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>−k</sup> , with increasing k." @default.
- W2051270653 created "2016-06-24" @default.
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- W2051270653 date "1985-06-01" @default.
- W2051270653 modified "2023-09-26" @default.
- W2051270653 title "Finite precision lexicographic continued fraction number systems" @default.
- W2051270653 doi "https://doi.org/10.1109/arith.1985.6158959" @default.
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