Optimal number representations in negative base
نویسندگان
چکیده
منابع مشابه
On the Number of Optimal Base 2 Representations of Integers
We study representations of integers n in binary expansions using the digits 0,±1. We analyze the average number of such representations of minimal “weight” (= number of non-zero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in some detail. The main tool is the construction of a measure on [−1, 1], which encodes the number of r...
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The 2-dimensional logarithmic number system (2DLNS), a subset of the multi-DLNS (MDLNS), which has similar properties to the classical Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and has the ability to use multiple 2DLNS components, or digits. The second base in 2DLNS can be adjusted to improve the representation space ...
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We consider positional numeration systems with negative real base −β, where β > 1, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal (−β)-representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the p...
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In a multi-base representation of an integer (in contrast to, for example, the binary or decimal representation) the base (or radix) is replaced by products of powers of single bases. The resulting numeral system is usually redundant, which means that each integer can have multiple different digit expansions. We provide a general asymptotic formula for the number of such multi-base representati...
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We study representations of integers n in binary expansions using the digits 0,±1. We analyze the average number of such representations of minimal “weight” (= number of non-zero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in some detail. The main tool is the construction of a measure on [−1, 1], which encodes the number of r...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2013
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-013-0336-6