# floating-point

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## floating-point

(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.

Opposite: fixed-point.
References in periodicals archive ?
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[6.] Nachtigal, M., Thapliyal, H., Ranganathan, N.: Design of a reversible floating-point adder architecture.
(trillions of floating-point operations per second).
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Many applications, particularly commercial and financial applications, require decimal floating-point operations to avoid errors from conversions between binary and decimal formats.

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