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) 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 represenation details
primitives
Visualisation tool to understand IEEE encoding
Visualisation Tool to understand IEEE hex double format
Visualisation Tool to understand IEEE hex float format
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