Significand Guide, Meaning , Facts, Information and Description

The significand (also the coefficient or, more informally, the 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

Note

The word initially used, in computing, for the significand was often mantissa (see Burks et al., below). This usage of mantissa, while still common, is discouraged by the IEEE floating-point standard committee and professionals such as William Kahan and Don Knuth. It conflicts with the established usage of mantissa for the fractional part of a number or logarithm (17^thC, from the Latin for makeweight), although this older meaning has grown less common with the disappearance of logarithmic tables in favor of computers (see common logarithm for more on the older meaning).

Reference

• Arthur W. Burks, Herman H. Goldstine, and John von Neumann, Preliminary discussion of the logical design of an electronic computing instrument, Technical Report, Institute for Advanced Study, Princeton NJ (1946). In J. 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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