IEEE 754 Floating Point : Java Glossary

go to home page I words local find full screen, hide local find menu Google search web for more information on this topic jump to foot of page translate this page with Babelfish punctuation 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) ©1996-2009 Roedy Green, 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) 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 format, you can use Double.doubleToLongBits and Double.longBitsToDouble.

floating point
IEEE-754 background reading
IEEE-754 diagrams
Official IEEE-754 spec
Philosophy behind IEEE-754
primitives
Visualisation tool to understand IEEE encoding
Visualisation Tool to understand IEEE hex double format
Visualisation Tool to understand IEEE hex float format
CMP homejump to top You can get the freshest copy of this page from: or possibly from your local J: drive (Java virtual drive/mindprod.com website mirror)
http://mindprod.com/jgloss/ieee754.html J:\mindprod\jgloss\ieee754.html
CMP logofeedback Please email your feedback for publication, errors, omissions, typos, formatting errors, ambiguities, unclear wording, broken/redirected link reports, suggestions to improve this page or comments to Roedy Green : feedback email
mindprod.com IP:[65.110.21.43]
view BlogYour face IP:[38.107.191.106]
You are visitor number 14,320.