Introduction to Computer Data Representation

Introduction to Computer Data Representation introduces readers to the representation of data within computers. Starting from basic principles of number representation in computers, the book covers ...
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Floating-Point Representations

Pp. 103-126 (24)

Peter Fenwick

Abstract

This chapter extends the earlier representations of integers to the equivalent of the real numbers of scientific calculation. It discusses the basic ideas, especially with reference to the IEEE 754 standard, and contrasting with descriptions of the IBM S/360 and Burroughs B6700 representations. There is extensive discussion of the requirements of ideal floating-point representations and the failings of practical implementations. Special mention is made of the requirements of range, precision and rounding. It concludes with examples of straight-forward calculations which can easily overwhelm many floating-point systems.

Keywords:

Floating-point basics, IEEE 754 standard, Floating-point precision, Floating-point range, Floating-point rounding, Not a Number (NaNs), examples of range problems.

Affiliation:

The University of Auckland (Retired) New Zealand