Rotating Binaries

This paper investigates the behavior of rotating binaries. A rotation by r digits to the left of a binary number B exhibits in particular cases the divisibility l∣N1(B)·r+1, where l is the bit-length of B and N1(B) is the Hamming weight of B, that is the number of ones in B. The integer r is called...

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Bibliographic Details
Published in:AppliedMath 2022-03, Vol.2 (1), p.104-117
Main Authors: Gupta, Anant, Aberkane, Idriss J., Ghosh, Sourangshu, Abold, Adrian, Rahn, Alexander, Sultanow, Eldar
Format: Article
Language:English
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Summary:This paper investigates the behavior of rotating binaries. A rotation by r digits to the left of a binary number B exhibits in particular cases the divisibility l∣N1(B)·r+1, where l is the bit-length of B and N1(B) is the Hamming weight of B, that is the number of ones in B. The integer r is called the left-rotational distance. We investigate the connection between this rotational distance, the length, and the Hamming weight of binary numbers. Moreover, we follow the question under which circumstances the above-mentioned divisibility is true. We have found out and will demonstrate that this divisibility occurs for kn+c cycles.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath2010005