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# Floating-Point Exponent

The exponent is the component of a finite floating-point representation that signifies the integer power to which the radix is raised in determining the value of that floating-point representation.

Within the IEEE 754-2008 framework, separate notation is used to specify the exponent in the case that the significand is considered as a single integer digit and/or a fraction field versus the case that the significand is viewed as an integer. In the prior case, the exponent is denoted ; in the latter, it is denoted . These two notions are connected by the identity for the precision (IEEE Computer Society 2008).

In floating-point arithmetic, special distinction is made with regards to the so-called "biased exponents." A biased exponent is the result of adding to the exponent some constant (called the bias) chosen to make the range of the exponent nonnegative. Similarly, one often distinguishes preferred exponents as well.

Arithmetic, Biased Exponent, Floating-Point Algebra, Floating-Point Arithmetic, Floating-Point Normal Number, Floating-Point Number, Floating-Point Preferred Exponent, Floating-Point Quantum, Floating-Point Representation, IEEE 754-2008, Interval Arithmetic, NaN, Quiet NaN, Signaling NaN, Significand, Subnormal Number

This entry contributed by Christopher Stover

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## References

IEEE Computer Society. "IEEE Standard for Floating-Point Arithmetic: IEEE Std 754-2008 (Revision of IEEE Std 754-1985)." 2008. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4610935.

## Cite this as:

Stover, Christopher. "Floating-Point Exponent." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Floating-PointExponent.html