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What (who) is floating point underflow - definition
NUMBER REPRESENTATION
IBM Floating Point Standard; IBM floating point architecture; IBM floating-point architecture; IBM Floating Point Architecture; Hexadecimal floating point (IBM); IBM Hexadecimal Floating Point; IBM hexadecimal floating point
floating point underflow
floating-point
![Single-precision floating-point numbers on a [[number line]]: the green lines mark representable values.](https://commons.wikimedia.org/wiki/Special:FilePath/A number line representing single-precision floating point's numbers and numbers that it cannot display.png?width=200 "Single-precision floating-point numbers on a [[number line]]: the green lines mark representable values.")
![signs]] of representable values](https://commons.wikimedia.org/wiki/Special:FilePath/FloatingPointPrecisionAugmented.png?width=200 "signs]] of representable values")
![Z3]] computer, which uses a 22-bit binary floating-point representation](https://commons.wikimedia.org/wiki/Special:FilePath/Konrad Zuse (1992).jpg?width=200 "Z3]] computer, which uses a 22-bit binary floating-point representation")
![[[Leonardo Torres y Quevedo]], who proposed a form of floating point in 1914](https://commons.wikimedia.org/wiki/Special:FilePath/Quevedo 1917.jpg?width=200 "[[Leonardo Torres y Quevedo]], who proposed a form of floating point in 1914")
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
<programming, mathematics> A number representation consisting
of a mantissa, M, an exponent, E, and a radix (or
"base"). The number represented is M*R^E where R is the
radix.
In science and engineering, exponential notation or
scientific notation uses a radix of ten so, for example, the
number 93,000,000 might be written 9.3 x 10^7 (where ^7 is
superscript 7).
In computer hardware, floating point numbers are usually
represented with a radix of two since the mantissa and
exponent are stored in binary, though many different
representations could be used. The IEEE specify a
standard representation which is used by many hardware
floating-point systems. Non-zero numbers are normalised so
that the binary point is immediately before the most
significant bit of the mantissa. Since the number is
non-zero, this bit must be a one so it need not be stored. A
fixed "bias" is added to the exponent so that positive and
negative exponents can be represented without a sign bit.
Finally, extreme values of exponent (all zeros and all ones)
are used to represent special numbers like zero and positive
and negative infinity.
In programming languages with explicit typing,
floating-point types are introduced with the keyword "float"
or sometimes "double" for a higher precision type.
See also floating-point accelerator, floating-point unit.
Opposite: fixed-point.
(2008-06-13)
floating-point
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
¦ noun [as modifier] Computing denoting a mode of representing numbers as two sequences of bits, one representing the digits in the number and the other an exponent which determines the position of the radix point.
Wikipedia
IBM hexadecimal floating-point
Hexadecimal floating point (now called HFP by IBM) is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent machines based on that architecture, as well as machines which were intended to be application-compatible with System/360.
In comparison to IEEE 754 floating point, the HFP format has a longer significand, and a shorter exponent. All HFP formats have 7 bits of exponent with a bias of 64. The normalized range of representable numbers is from 16−65 to 1663 (approx. 5.39761 × 10−79 to 7.237005 × 1075).
The number is represented as the following formula: (−1)sign × 0.significand × 16exponent−64.
