IBM Hexadecimal Floating Point - Cleve Moler on Mathematics and Computing

[poster]

Our technical support group recently received a request for a tool that would convert IBM System/360 hexadecimal floating point numbers to the IEEE-754 format. I am probably the only one left at MathWorks that actually used IBM mainframe computers. I thought we had seen the last of hexadecimal arithmetic years ago. But, it turns out that the hexadecimal floating point format is alive and well.

Contents

• IBM System/360
• Formats
• Data
• Hex_ieee
• ieee2ibm
• ibm2ieee
• Examples
• Comparison
• Software

IBM System/360

The System/360 is a family of mainframe computers that IBM introduced in 1965 and that dominated the computer industry until PCs came along twenty years later. They range in size from desk-sized to systems that fill a large room.

Here is a photo of a mid-sized model.



System/360, Model 60. Photo from Ken Shirrif's blog, IBM 360/System Summary.

The System/360 architecture is byte-oriented, so it can handle business data processing as well as scientific and engineering computation. This leads to base-16, rather than base-2 or base-10, floating point arithmetic.

* Binary f*2^e 1/2