# Floating-point

**noun**

1.

a decimal point whose location is not fixed, used especially in computer operations.

floating-point

(flō’tĭng-point’)

Relating to a method of representing numerical quantities that uses two sets of integers, a mantissa and a characteristic, in which the value of the number is understood to be equal to the mantissa multiplied by a base (often 10) raised to the power of the characteristic. Scientific notation is one means of displaying floating-point numbers.

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)

Tagged: f

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- Floating-point representation
noun 1. (computing) the representation of numbers by two sets of digits (a, b), the set a indicating the significant digits, the set b giving the position of the radix point. The number is the product arb, where r is the base of the number system used Compare fixed-point representation

- Floating-point accelerator
hardware (FPA) Additional hardware to perform functions on floating point numbers such as addition, multiplication, logarithms, exponentials, trigonometric functions and various kinds of rounding and error detection. A floating point accelerator often functions as a co-processor to the CPU. The term “floating-point accelerator” suggests a physically larger system, often an extra circuit board, whereas a […]

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