Editing IEEE 754-1985 (section)

=== Denormalized numbers ===

The number representations described above are called ''normalized,'' meaning that the implicit leading binary digit is a 1. To reduce the loss of precision when an [[Arithmetic underflow|underflow]] occurs, IEEE&nbsp;754 includes the ability to represent fractions smaller than are possible in the normalized representation, by making the implicit leading digit a 0. Such numbers are called [[denormal numbers|denormal]]. They don't include as many [[significant digits]] as a normalized number, but they enable a gradual loss of precision when the result of an [[Floating-point arithmetic#Floating-point operations|operation]] is not exactly zero but is too close to zero to be represented by a normalized number.

A denormal number is represented with a biased exponent of all 0 bits, which represents an exponent of −126 in single precision (not −127), or −1022 in double precision (not −1023).<ref>{{cite book|last=Hennessy|title=Computer Organization and Design|year=2009|url=https://archive.org/details/computerorganiza00patt_779|url-access=limited|publisher=Morgan Kaufmann|page=[https://archive.org/details/computerorganiza00patt_779/page/n291 270]|isbn=9780123744937 }}</ref> In contrast, the smallest biased exponent representing a normal number is 1 (see [[#Examples|examples]] below).