Rotating Binaries

07/18/2021

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by   Anant Gupta, et al.

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This paper investigates the behaviour of rotating binaries. A rotation by r digits to the left of a binary number B exhibits in particular cases the divisibility l| N_1(B)· r+1, where l is the bit-length of B and N_1(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.