Significand

From Academic Kids

The significand (also coefficient or, more informally, mantissa) is the part of a floating-point number that contains its significant digits. Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction.

For example, the number 123.45 can be represented as a decimal floating-point number with integer significand 12345 and exponent −2. Its value is given by the formula:

12345 × 10−2

This same value could also be represented with the fractional coefficient 1.2345 and exponent +2:

1.2345 × 10+2

Use of "mantissa"

In some circles, the word used to describe the significand or coefficient is often mantissa (see Burks et al., below). This usage of "mantissa" is discouraged by the IEEE floating-point standard committee and by computer science professionals such as William Kahan and Donald Knuth because it conflicts with a pre-existing usage of mantissa for the fractional part of a logarithm (17th century, from the Latin word for makeweight); see common logarithm for more on this older meaning.

(The older and newer meanings are related, in that the fractional part of a logarithm is the logarithm of the significand for the same base, plus a constant depending on the normalization.)

References

  • Burks, Arthur W.; Goldstine, Herman H.; Von Neumann, John (1946). Preliminary discussion of the logical design of an electronic computing instrument. Technical Report, Institute for Advanced Study, Princeton, NJ. In Von Neumann, Collected Works Vol. 5, A. H. Taub, ed., MacMillan, New York, 1963, p.42:

    5.3. "Several of the digital computers being built or planned in this country and England are to contain a so-called "floating decimal point". This is a mechanism for expressing each word as a characteristic and a mantissa—e.g. 123.45 would be carried in the machine as (0.12345,03), where the 3 is the exponent of 10 associated with the number."
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