Search results
Results From The WOW.Com Content Network
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
The IEEE 754 floating-point standard defines the exponent field of a single-precision (32-bit) number as an 8-bit excess-127 field. The double-precision (64-bit) exponent field is an 11-bit excess-1023 field; see exponent bias. It also had use for binary-coded decimal numbers as excess-3.
IEEE 754-1985 [1] is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. [2] During its 23 years, it was the most widely used format for floating-point computation.
All integers with seven or fewer decimal digits, and any 2 n for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754 standard, the 32-bit base-2 format is officially referred to as binary32; it was called single in IEEE 754-1985.
Bounds on conversion between decimal and binary for the 80-bit format can be given as follows: If a decimal string with at most 18 significant digits is correctly rounded to an 80-bit IEEE 754 binary floating-point value (as on input) then converted back to the same number of significant decimal digits (as for output), then the final string ...
The IEEE 754-2008 standard includes decimal floating-point number formats in which the significand and the exponent (and the payloads of NaNs) can be encoded in two ways, referred to as binary encoding and decimal encoding.
Similar binary floating-point formats can be defined for computers. There is a number of such schemes, the most popular has been defined by Institute of Electrical and Electronics Engineers (IEEE). The IEEE 754-2008 standard specification defines a 64 bit floating-point format with: an 11-bit binary exponent, using "excess-1023" format.
A minifloat in 1 byte (8 bit) with 1 sign bit, 4 exponent bits and 3 significand bits (in short, a 1.4.3 minifloat) is demonstrated here. The exponent bias is defined as 7 to center the values around 1 to match other IEEE 754 floats [3] [4] so (for most values) the actual multiplier for exponent x is 2 x−7. All IEEE 754 principles should be ...