Editing IBM hexadecimal floating-point (section)

{{Short description|Number representation}}
{{Floating-point}}
'''[[Hexadecimal]] [[floating-point arithmetic|floating point]]''' (now called '''HFP''' by '''IBM''') is a format for encoding floating-point numbers first introduced on the [[IBM]] [[IBM System/360|System/360]] computers, and supported on subsequent machines based on that architecture,<ref>[http://www.bitsavers.org/pdf/ibm/360/princOps/A22-6821-6_360PrincOpsJan67.pdf ''IBM System/360 Principles of Operation''], IBM Publication A22-6821-6, Seventh Edition (January 13, 1967), pp.41-50</ref><ref>[http://www.bitsavers.org/pdf/ibm/370/princOps/GA22-7000-4_370_Principles_Of_Operation_Sep75.pdf ''IBM System/370 Principles of Operation''], IBM Publication GA22-7000-4, Fifth Edition (September 1, 1975), pp.157-170</ref><ref>[http://publibz.boulder.ibm.com/epubs/pdf/dz9zr001.pdf ''z/Architecture Principles of Operation''], IBM Publication SA22-7832-01, Second Edition (October, 2001), chapter 9 ff.</ref> as well as machines which were intended to be application-compatible with System/360.<ref>{{cite book |last1=Xerox Data Systems |title=Xerox SIGMA 7 Computer Reference Manyal |date=Oct 1973 |page=48 |url=https://catalog.hathitrust.org/Record/000429866 |accessdate=Nov 13, 2020}}</ref><ref>{{cite book |last1=RCA |title=Spectra 70 processors: 35 45 55 |date=Mar 1966 |page=184 |url=http://bitsavers.org/pdf/rca/spectra70/model35_45_55/70-35-601_spectra70_35-55_Mar66.pdf |accessdate=Nov 13, 2020}}</ref>

In comparison to [[IEEE 754]] floating point, the HFP format has a longer [[significand]], and a shorter [[Exponentiation|exponent]]. All HFP formats have 7 bits of exponent with a [[exponent bias|bias]] of 64. The normalized range of representable numbers is from 16<sup>−65</sup> to 16<sup>63</sup> (approx. 5.39761 × 10<sup>−79</sup> to 7.237005 × 10<sup>75</sup>).

The number is represented as the following formula: (−1)<sup>sign</sup> × 0.<small>significand</small> × 16<sup>exponent−64</sup>.