### Convergence Estimates for the Distribution of Trailing DigitsConvergence Estimates for the Distribution of Trailing Digits

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 Author Feldstein, Alan ♦ Goodman, Richard Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1976 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract This paper analyzes the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $\textit{β}$ and randomly chosen from a logarithmic distribution. The analysis shows that the $\textit{n}th$ digit for $\textit{n}$ ≥ 2 is actually approximately uniformly distributed. The approximation depends upon both $\textit{n}$ and the $base\textit{β}.$ It becomes better as $\textit{n}$ increases, and it is exact in the limit as $\textit{n}$ ⇒ ∞. A table of this distribution is presented for various β and $\textit{n},$ along with a table of the maximum digit by digit deviation Δ of the logarithmic distribution from the uniform distribution. Various asymptotic results for Δ are included. These results have application in resolving open questions of Henrici, of Kaneko and Liu, and of Tsao. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1976-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 23 Issue Number 2 Page Count 11 Starting Page 287 Ending Page 297

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Source: ACM Digital Library