Floating point operations

Data types and formats

Single-precision

Single-precision floating point numbers have the following format:

31 30 23 22 0

SIGN EXPONENT FRACTION

^

binary point

Field Position Full Name

sign 31 sign bit (0==positive, 1==negative)

exponent 30-23 exponent (biased by 127)

fraction 22-0 fraction (bits to right of binary point)

Field	Position	Full Name
sign	31	sign bit (0==positive, 1==negative)
exponent	30-23	exponent (biased by 127)
fraction	22-0	fraction (bits to right of binary point)

Double-precision

Double-precision floating point numbers have the following format:

63 62 52 51 0

SIGN EXPONENT FRACTION

^

binary point

Field Position Full Name

sign 63 sign bit (0==positive, 1==negative)

exponent 62-52 exponent (biased by 1023)

fraction 51-0 fraction (bits to right of binary point)

Field	Position	Full Name
sign	63	sign bit (0==positive, 1==negative)
exponent	62-52	exponent (biased by 1023)
fraction	51-0	fraction (bits to right of binary point)

NOTE: For big-endian machines, the high-order word is at the low address; for little-endian machines, the high-order word is at the high address:

Extended-precision

Extended-precision floating point numbers have the following format on the Intel386 (TM) microprocessor:

79 78 64 63 0

SIGN EXPONENT FRACTION

^

binary point

For extended precision, bit 63 is always a 1, and the decimal point comes after this bit. The other formats have an implicit bit 1 before the fraction, as explained in ``Normalized numbers''.

Field Position Full Name

sign 79 sign bit (0==positive, 1==negative)

exponent 78-64 exponent (biased by 16,383)

fraction 63-0 fraction (bit 63=1, followed by the

decimal point. Bits 62-0 are the fraction.