Access Restriction

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

Open content in new tab

   Open content in new tab
Source: ACM Digital Library