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Floating point - Wikipedia, the free encyclopedia
In computing, floating point describes a system for numerical representation in which a string of digits (or bits) represents a rational number. The term floating point refers to the fact that the...
en.wikipedia.org/wiki/Floating_point |
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Fixed-point arithmetic - Wikipedia, the free encyclopedia
In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point ( e.g. , after the decimal po...
en.wikipedia.org/wiki/Fixed-point_arithmetic |
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Floating point numbers are a numeric data type provided on most machines (hardware) and programming languages. Floating point provides a type to represent very large numbers and very small numbers at the expense of exactness, precision, or significant digits...
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The IEEE (Institute of Electrical and Electronics Engineers) has produced a standard for floating point arithmetic. This standard specifies how single precision (32 bit) and double precision (64 bit) floating point numbers are to be represented, as well as how arithmetic should be carried out on them.
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Of course one bit-pattern can't represent many numbers equally well, it will represent one of them exactly and the others will be misrepresented. We call numbers that can be represented exactly, FLOATING-POINT NUMBERS (FPN), the term 'real numbers' will be reserved for the mathematical constructs.
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Historically, different bases have been used for representing floating-point numbers, with base 2 (binary) being the most common, followed by base 10 (decimal), and other less common varieties such as base 16 (hexadecimal notation).
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However, fixed-point representations are unsatisfactory for most applications involving real numbers, for two reasons: (1) Real numbers that are very small are not ... By contrast with fixed-point representations, these computer analogues of scientific notation are described as floating-point representations.
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