IEEE 754 Floating Point : Java Glossary

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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.


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