A Formalization of Floating Point Numeric Base Conversion

Abstract

The process of converting arbitrary real numbers into a floating point format is formalized as a mapping of the reals into a specified subset of real numbers. The structure of this subset, the set of a significant digit base beta floating point numbers, is analyzed and properties of conversion mappings are determined. For a restricted conversion mapping of the n significant digit base beta numbers to the m significant digit base delta numbers the one-to-one, onto, and order preserving properties of the mapping are summarized. Multiple conversions consisting of a composition of individual conversion mappings are investigated and some results on the invariant points of such compound conversions are presented. The hardware and software implications of these results with regards to establishing goals and standards for floating point formats and conversion procedures are considered.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1970
Accession Number
AD0771746

Entities

People

  • David W. Matula

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Computations
  • Computer Networks
  • Computers
  • Conversion
  • Digital Computers
  • Environment
  • Errors
  • Health Services
  • Identities
  • Information Processing
  • Intervals
  • Irrational Numbers
  • Numbers
  • Public Health
  • Real Numbers
  • Standards

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  • Brain and Cognitive Science; Experimental Psychology; Cognitive Neuroscience
  • Computer Science.
  • Mathematical Modeling and Probability Theory.