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Significand - Wikipedia

Significand

The significand1 (also coefficient,1 sometimes argument,2 or more ambiguously mantissa,3 fraction,456 or characteristic73) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign.

Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term “mantissa” to be misleading, since the mantissa of a logarithm is always its fractional part.89 Although the other names mentioned are common, significand is the word used by IEEE 754, an important technical standard for floating-point arithmetic.10 In mathematics, the term “argument” may also be ambiguous, since “the argument of a number” sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane.11

Printed 2026-06-28.

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Footnotes

  1. Kahan, William Morton (2002-04-19). “Names for Standardized Floating-Point Formats” (PDF). Archived (PDF) from the original on 2023-12-27. Retrieved 2023-12-27. […] m is the significand or coefficient or (wrongly) mantissa […] (8 pages) ↩ ↩2

  2. Clements, Alan (2006-02-09). Principles of Computer Hardware. OUP Oxford. ISBN 978-0-19-927313-3. ↩

  3. Gosling, John B. (1980). “6.1 Floating-Point Notation/6.8.5 Exponent Representation”. In Sumner, Frank H. (ed.). Design of Arithmetic Units for Digital Computers. Macmillan Computer Science Series (1 ed.). Department of Computer Science, University of Manchester, Manchester, UK: The Macmillan Press Ltd. pp. 74, 91, 137–138. ISBN 0-333-26397-9. […] In floating-point representation, a number x is represented by two signed numbers m and e such that x = m · b where m is the mantissa, e the exponent and b the base. […] The mantissa is sometimes termed the characteristic and a version of the exponent also has this title from some authors. It is hoped that the terms here will be unambiguous. […] [w]e use a[n exponent] value which is shifted by half the binary range of the number. […] This special form is sometimes referred to as a biased exponent, since it is the conventional value plus a constant. Some authors have called it a characteristic, but this term should not be used, since CDC and others use this term for the mantissa. It is also referred to as an ‘excess -’ representation, where, for example, - is 64 for a 7-bit exponent (2 = 64). […] (NB. Gosling does not mention the term significand at all.) ↩ ↩2

  4. English Electric KDF9: Very high speed data processing system for Commerce, Industry, Science (PDF) (Product flyer). English Electric. c. 1961. Publication No. DP/103. 096320WP/RP0961. Archived (PDF) from the original on 2020-07-27. Retrieved 2020-07-27. ↩

  5. Savard, John J. G. (2018) [2005]. “Floating-Point Formats”. quadibloc. A Note on Field Designations. Archived from the original on 2018-07-03. Retrieved 2018-07-16. ↩

  6. The term fraction is used in IEEE 754-1985 with a different meaning: it is the fractional part of the significand, i.e. the significand without its explicit or implicit leading bit. ↩

  7. Knuth, Donald E. (1997). The Art of Computer Programming. Vol. 2. Addison-Wesley. p. 214. ISBN 0-201-89684-2. […] Other names are occasionally used for this purpose, notably ‘characteristic’ and ‘mantissa’; but it is an abuse of terminology to call the fraction part a mantissa, since that term has quite a different meaning in connection with logarithms. Furthermore the English word mantissa means’a worthless addition.’ […] ↩

  8. Magazines, Hearst (February 1913). Popular Mechanics. Hearst Magazines. p. 291. ↩

  9. Gupta, Dr Alok (2020-07-04). Business Mathematics by Alok Gupta: SBPD Publications. SBPD publications. p. 140. ISBN 978-93-86908-16-2. ↩

  10. 754-1985 - IEEE Standard for Binary Floating-Point Arithmetic. IEEE. doi:10.1109/IEEESTD.1985.82928. ISBN 0-7381-1165-1. ↩

  11. Gowers, Timothy; Barrow-Green, June; Leader, Imre (2010-07-18). The Princeton Companion to Mathematics. Princeton University Press. p. 201. ISBN 978-1-4008-3039-8. ↩

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