Significand (original) (raw)

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

The original word for the significand appears to be mantissa, dating at least to the 1940's (see below). This usage of mantissa, while still popular, has been discouraged by the IEEE floating-point standard committee and professionals such as William Kahan. It conflicts with an older usage of mantissa for the fractional part of a logarithm (corresponding to the logarithm of the significand), although this older meaning has grown less common with the disappearance of logarithmic tables in favor of computers.

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."