On the Distribution of the Most Significant Hexadecimal Digit.
ResearchPublished 1968
An investigation of the distribution of the most significant hexadecimal digit of numbers produced through scientific computing with the IBM-360 computer. Theoretical results are derived for the operations of multiplication, division, and addition (subtraction); these are compared, in some cases, with experimental results. It is shown that after certain sequences of operations, the distributions tend to be stable in the most significant hexadecimal digit and uniform in the number of leading zero binary bits in that digit. This leads to the uniform binary distribution, a very simple formula for obtaining the distribution of the leading hexadecimal digit d. Applications of the results of the study to truncation error analysis and function approximation are given. 51 pp. Refs.
Document Details
- Copyright: RAND Corporation
- Availability: Web Only
- Year: 1968
- DOI: https://doi.org/10.7249/pubs
- Document Number: RM-5496-PR
Citation
RAND Style Manual
Chicago Manual of Style
This publication is part of the RAND research memorandum series. The research memorandum series, a product of RAND from 1948 to 1973, included working papers meant to report current results of RAND research to appropriate audiences.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.