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Floating point - Note | A Wisdom Archive on Floating point - Note | | Floating point - Note A selection of articles related to Floating point - Note | |
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More material related to Floating Point can be found here:
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Floating point, Floating point - Examples, Floating point - Hidden bit, Floating point - IEEE standard, Floating point - Note, Floating point - Problems with floating-point, Floating point - Properties of floating point arithmetic, Floating point - Usage in computing, Significant digits, Fixed-point arithmetic, Computable number, IEEE Floating Point Standard, IBM Floating Point Architecture, FLOPS, -0, half precision – single precision – double precision – quad precision
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ARTICLES RELATED TO Floating point - Note | | | |  Floating point - Note: Encyclopedia II - Floating point - Examples
Floating point - Hidden bit.
When using binary (b = 2), one bit, called the hidden bit or the implied bit, can be omitted if all numbers are required to be normalized. The leading digit (most significant bit) of the significand of a normalized binary floating-point number is always non-zero; in particular it is always 1. This means that this bit does not need to be stored explicitly, since for a normalized number it can be understood to be 1.
The IEEE 754 standard exploits this fact. R ...
See also:Floating point, Floating point - Usage in computing, Floating point - Problems with floating-point, Floating point - Properties of floating point arithmetic, Floating point - IEEE standard, Floating point - Examples, Floating point - Hidden bit, Floating point - Note Read more here: » Floating point: Encyclopedia II - Floating point - Examples |
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| | | | Floating point - Note: Encyclopedia II - Floating point - IEEE standard The IEEE has standardized the computer representation for binary floating-point numbers in IEEE 754. This standard is followed by almost all modern machines. Notable exceptions include IBM Mainframes, which have both hexadecimal and IEEE 754 data types, and Cray vector machines, where the T90 series had an IEEE version, but the SV1 still uses Cray floating-point format.
As of 2000, the IEEE 754 stan ...
See also:Floating point, Floating point - Usage in computing, Floating point - Problems with floating-point, Floating point - Properties of floating point arithmetic, Floating point - IEEE standard, Floating point - Examples, Floating point - Hidden bit, Floating point - Note Read more here: » Floating point: Encyclopedia II - Floating point - IEEE standard |
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| | | | Floating point - Note: Encyclopedia II - Floating point - Properties of floating point arithmetic Arithmetic using the floating point number system has two important properties that differ from those of arithmetic using real numbers.
Floating point arithmetic is not associative. This means that in general for floating point numbers x, y, and z:
Floating point arithmetic is also not distributive. This means that in general:
In short, the order in which operations are carried out can change the output of a floating point calculation. This is important in numerical ana ...
See also:Floating point, Floating point - Usage in computing, Floating point - Problems with floating-point, Floating point - Properties of floating point arithmetic, Floating point - IEEE standard, Floating point - Examples, Floating point - Hidden bit, Floating point - Note Read more here: » Floating point: Encyclopedia II - Floating point - Properties of floating point arithmetic |
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| | | | Floating point - Note: Encyclopedia II - Floating point - Problems with floating-point Floating-point numbers usually behave very similarly to the real numbers they are used to approximate. However, this can easily lead programmers into over-confidently ignoring the need for numerical analysis. There are many cases where floating-point numbers do not model real numbers well, even in simple cases such as representing the decimal fraction 0.1, which cannot be exactly represented in any binary floating-point format. For this reason, financial software tends not to use a binary floating-point n ...
See also:Floating point, Floating point - Usage in computing, Floating point - Problems with floating-point, Floating point - Properties of floating point arithmetic, Floating point - IEEE standard, Floating point - Examples, Floating point - Hidden bit, Floating point - Note Read more here: » Floating point: Encyclopedia II - Floating point - Problems with floating-point |
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