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Floating-Point Representation

Floating-point representation is based on the observation that every nonzero rational number $ x$ admits a representation of the form

$\displaystyle x = \pm m \cdot 2^e,$

where $ e$ is an integer, called the exponent of $ x$ , and $ m$ is a rational in the range $ 1 \leq m < 2$ , called the significand of $ x$ . A floating-point format is a scheme for representing a rational number as a bit vector consisting of three fields corresponding to its sign, exponent, and significand. In this chapter, we present several such formats, including those prescribed by IEEE Standard 754 [IEEE85], and examine the characteristics of the numbers that they represent.


Subsections
David Russinoff 2007-01-02