The draft IEEE 754r standard proposed two encoding formats for decimal floating point numbers, the formats are referred to in the standard as binary encoding and decimal encoding.[1]. The binary encoding format is referred to by Intel[2] and others as Binary Integer Decimal (BID).
Format
A BID number has three fields, the sign the exponent and the magnitude.
The number has value v:
v = s × 10e × m
Where
s = +1 (positive numbers) when the sign bit is 0
s = −1 (negative numbers) when the sign bit is 1
e = exponent − bias
m = An integer in binary format.
The result can include +infinity, -infinity and NaN. If the top five bits of the exponent field have the encoding 11110 binary, the number represented is + or - infinity. Nan is represented by the tops five bits of the exponent field being set to 1.
Range
The range of numbers that can be represented by BID numbers is limited by the proposed IEEE754r standard to the smaller range of numbers that can be represented by the second encoding of the exponent and significand described by the standard, Densely Packed Decimal.
Comparing BID numbers
BID numbers are lexicographically ordered. If NaNs are excluded, the can be compared (>, <, or ==) as sign and magnitude integers.
References
- ^ "DRAFT Standard for Floating Point Arithmetic P754" (PDF). 2006-10-04. Retrieved 2007-07-01.
- ^ "IEEE 754R Decimal Floating-Point Arithmetic: Reliable and Efficient Implementation for Intel® Architecture Platforms". Intel. February 15, 2007. Retrieved 2007-07-01.