The EncodeDecode Application
The EncodeDecode application encodes and decodes all reasonable real number values, in single and double precision formats, using the IEEE 754 conversion standard.
Encoded single precision reals are specified with 8 hexadecimal digits while double precision reals are specified with 16 hexadecimal digits. Encoded values are entered in the data entry boxes on the left of the application.
Special encoded numbers such as 7F800000 or 7FF0000000000000 return +∞ while values such as FF800000 and FFF0000000000000 return -∞.
Some encoded combinations do not convert to actual numbers. The return value for these combinations will be NaN (Not a Number). A single precision decoding that produces NaN is 7F800010 and a double precision decoding that produces NaN is 7FF0000001000000.
Only hexadecimal characters from 0-f or 0-F are allowed as encoded characters.
Decoded real numbers are entered in the data entry boxes on the right of the application. When encoded, these values will be rounded to the 8 or 16 hexadecimal digits of precision.
The IEEE 754 standard establishes the means, whereby, real numbers (in their normal decoded form) can be encoded to appear as integer values. By encoding real numbers into an integer format, real numbers can also be passed across the bus.
This application is NOT a base change calculator or converter, but an application that actually encodes and decodes real numbers using the IEEE 754 standard.
If the details of this topic interest you, we invite you to view the “mechanics” of how this encoding and decoding process takes place by reading a portion of Chapter 18 (More Involved Coprocessor Programming) in our book “Core Assembly Language Programming for the PC” or “Core Assembly Language Programming for the Mac” available from iBooks in the iTunes store.
