Gupta, AnantAnantGuptaAberkane, Idriss J.Idriss J.AberkaneGhosh, SourangshuSourangshuGhoshAbold, AdrianAdrianAboldRahn, AlexanderAlexanderRahnSultanow, EldarEldarSultanow2024-10-232024-10-2320222673-9909https://fis.uni-bamberg.de/handle/uniba/104000This 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.engbinary rotationcircular left shiftcollatz cyclerandomnessarticle10.3390/appliedmath2010005https://www.mdpi.com/2673-9909/2/1/5/pdf