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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 standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and ...
[citation needed] Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. E.g., GW-BASIC's double-precision data type was the 64-bit MBF floating-point format.
The number 0.15625 represented as a single-precision IEEE 754-1985 floating-point number. See text for explanation. The three fields in a 64bit IEEE 754 float. Floating-point numbers in IEEE 754 format consist of three fields: a sign bit, a biased exponent, and a fraction. The following example illustrates the meaning of each.
The IEEE 754-2008 standard specification defines a 64 bit floating-point format with: an 11-bit binary exponent, using "excess-1023" format. Excess-1023 means the exponent appears as an unsigned binary integer from 0 to 2047; subtracting 1023 gives the actual signed value; a 52-bit significand, also an unsigned binary number, defining a ...
On a typical computer system, a double-precision (64-bit) binary floating-point number has a coefficient of 53 bits (including 1 implied bit), an exponent of 11 bits, and 1 sign bit. Since 2 10 = 1024, the complete range of the positive normal floating-point numbers in this format is from 2 −1022 ≈ 2 × 10 −308 to approximately 2 1024 ≈ ...
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 new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website [4] This standard replaces IEEE 754-1985. IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...