Floating point

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In computing, floating point describes a system for representing numbers that would be too large or too small to be represented as integers. Numbers are in general represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16. The typical number that can be represented exactly is of the form:

The term floating point refers to the fact that the radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated separately in the internal representation, and floating-point representation can thus be thought of as a computer realization of scientific notation. Over the years, several different floating-point representations have been used in computers; however, for the last ten years the most commonly encountered representation is that defined by the IEEE 754 Standard.

The advantage of floating-point representation over fixed-point (and integer) representation is that it can support a much wider range of values. For example, a fixed-point representation that has seven decimal digits with two decimal places, can represent the numbers 12345.67, 123.45, 1.23 and so on, whereas a floating-point representation (such as the IEEE 754 decimal32 format) with seven decimal digits could in addition represent 1.234567, 123456.7, 0.00001234567, 1234567000000000, and so on. The floating-point format needs slightly more storage (to encode the position of the radix point), so when stored in the same space, floating-point numbers achieve their greater range at the expense of precision.

The speed of floating-point operations is an important measure of performance for computers in many application domains. It is measured in FLOPS.

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