IEEE 754 Floating Point Binary Interchange Formats

IEEE 754 Floating Point Binary Interchange Format
MSB S sign (1 bit)
E biased exponent (w bits)
T trailing significand (t bits)

IEEE 754 Floating Point Binary Interchange Format Characteristics
float32 float64 Parameter
32 64 k, storage width in bits
24 53 p, precision in bits
127 1023 emax, maximum exponent e
127 1023 bias, E - e
1 1 sign bit
8 11 w, exponent field width in bits
23 52 t, trailing significand field width in bits
32 64 k, storage width in bits

IEEE 754 Floating Point Binary Interchange Format Values
S E T Meaning
0 0 0 +0
1 0 0 -0
0 0 y>0 +subnormal
1 0 y>0 -subnormal
0 ~0 0 +Inf
1 ~0 0 -Inf
* ~0 0b1... qNaN
* ~0 0b0... sNaN (T != 0)
0 0<x<~0 y +normal
1 0<x<~0 y -normal

The trailing significand field, T, encodes the $ p - 1 $ least significant bits of the precision. The most significant bit is implicitly encoded in the value of the exponent field, E. (This bit is sometimes referred to as the "hidden" bit.) When E is zero, the hidden bit is implicitly zero; when E is non-zero, the hidden bit is implicitly one.

Note:
The terms "denormal" and "subnormal" are equivalent.
See also:
http://en.wikipedia.org/wiki/Floating_point

http://en.wikipedia.org/wiki/Single_precision

http://en.wikipedia.org/wiki/Double_precision

http://en.wikipedia.org/wiki/Q_(number_format)


Generated on Fri Nov 13 15:38:37 2009 for fpassist for PPC SPE by  doxygen 1.5.9