IEEE 754 Floating Point : Java Glossary

home page go to the Java Glossary Home go to the Computer Buyer’s Glossary up jump to foot of page Google search web for more information on this topic Pinterest pin button
* 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (all)
©1996-2017 Roedy Green of Canadian Mind Products

IEEE 754 Floating Point
the internal binary format used for floating point and double numbers. The format assigns a meaning to every possible combination of bits. There are also representation for NaN (Not A Number) (Not a Number) and plus and minus infinity.
Floating Point Bit Representation
Type Size in Bytes Size in Bits Accuracy Range Fields Integers
double 8 bytes 64 bits
14 to 15 significant digits		 ±4.94065645841246544e-324d to
±1.79769313486231570e+308d		 is formed of 3 fields:
1-bit sign
11-bit base 2 exponent biased+1023
52-bit fraction, lead 1 implied
e.g. 3. = 0x4008000000000000
-3. = 0xC008000000000000		 a double can exactly represent integers
in the range -253 to +253.
float 4 bytes 32 bits 6 to 7 significant digits ±1.40129846432481707e-45 to
±3.40282346638528860e+38		 is formed of 3 fields:
1-bit sign
8-bit base 2 exponent biased+127
23-bit fraction, lead 1 implied
e.g. 3. = 0x404000
-3. = 0xC04000		 a float can exactly represent integers
in the range -224 to +224.
A side effect of this signed-magnitude format is you can have both +0 and -0.

To study the IEEE (Institute of Electrical & Electronics Engineers) format, you can use Double.doubleToLongBits and Double.longBitsToDouble.

This page is posted
on the web at:

 http://mindprod.com/jgloss/ieee754.html

Optional Replicator mirror
of mindprod.com
on local hard disk J:

 J:\mindprod\jgloss\ieee754.html
Canadian Mind Products
Please the feedback from other visitors, or your own feedback about the site.
Contact Roedy. Please feel free to link to this page without explicit permission.

IP:[65.110.21.43]
Your face IP:[18.118.140.78]
You are visitor number