19.1 Floating-Point Format

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Floating-point numbers consist of three parts : a sign, a fraction, and an exponent. Our fraction is expressed as a four-digit decimal. The exponent is a single-decimal digit. So our format is:

± f.fff x 10 ^{± e}

where:

±

is the sign (plus or minus).

f.fff

is the four-digit fraction.

±e

is the single-digit exponent.

Zero is +0.000 x 10 ⁺⁰ . We represent these numbers in "E" format: ± f.fff E ± e . This format is similar to the floating-point format used in many computers. The IEEE has defined a floating-point standard (#742), but not all machines use it.

Table 19-1 shows some typical floating-point numbers.

Table 19-1. Floating-point examples

Notation	Number
+1.000E+0	1.0
+3.300E+5	330000.0
-8.223E-3	-0.008223
+0.000E+0	0.0

The floating-point operations defined in this chapter follow a rigid set of rules. To minimize errors we make use of a guard digit . That is an extra digit added to the end of the fraction during computation. Many computers use a guard digit in their floating-point units.

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