In the context of computing, a more common name for the mantissa is the significand.
IEEE Standard 754 defines the most commonly used representations for real numbers on computers. It defines 32-bit (single precision) and 64-bit (double precision) as follows.
The first bit is a sign bit, denoting the sign of the significand. This is followed by a fixed number of bits representing the exponent, which is in turn followed by another fixed number of bits representing the magnitude of the significand.
The exponent is often represented using excess-n notation. This means that a number, called the characteristic (or biased exponent), is stored instead of the exponent itself. To derive the characteristic for a floating-point number from its exponent, the bias (or excess factor) n is added to the exponent. For example, for an 8-bit characteristic, exponents in the range −128 to +127 are represented in excess-128 notation by characteristics in the range 0 to 255.
IEEE 754 specifies an 8-bit single-precision exponent, with a bias of 127, and an 11-bit double-precision exponent, with a bias of 1023. A nonzero floating-point number is normalized if the leading digit in its significand is nonzero. Since the only possible nonzero digit in base 2 is 1, the leading nonzero digit in the significand need not be explicitly represented. This means that the 23-bit significand in the IEEE 754 single-precision floating-point representation effectively provides 24 bits of resolution, and the 52-bit double-precision significand provides 53 bits of resolution.
Although normalized floating-point numbers are most frequently used, unnormalized representations are also needed to represent numbers close to zero.
"floating-point notation." A Dictionary of Computing. . Encyclopedia.com. (December 12, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/floating-point-notation
"floating-point notation." A Dictionary of Computing. . Retrieved December 12, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/floating-point-notation
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.