![]() However, in 1946 Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number ( Burks et al.) and that usage remains common among computer scientists today. The term significand was introduced by George Forsythe and Cleve Moler in 1967 and is the word used in the IEEE standard. IEEE 754 defines the precision p to be the number of digits in the significand, including any implicit leading bit (e.g., p = 53 for the double-precision format), thus in a way independent from the encoding, and the term to express what is encoded (that is, the significand without its leading bit) is trailing significand field. For example, the same IEEE 754 double-precision format is commonly described as having either a 53-bit significand, including the hidden bit, or a 52-bit significand, excluding the hidden bit. The significand is characterized by its width in (binary) digits, and depending on the context, the hidden bit may or may not be counted towards the width of the significand. ![]() When working in binary, this constraint uniquely determines this digit to always be 1 as such, it does not need to be explicitly stored, being called the hidden bit. Significands and the hidden bit įor a normalized number, the most significant digit is always non-zero. įor base 2, this 0.xxxx form is also called a normed significand. Schmid called this representation with a significand ranging between 0.1 and 1.0 the true normalized form. įor base 2, this 1.xxxx form is also called a normalized significand.įinally, the value can be represented in the format given by the Language Independent Arithmetic standard and several programming language standards, including Ada, C, Fortran and Modula-2, as Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form. The same value can also be represented in normalized form with 1.2345 as the fractional coefficient, and +2 as the exponent (and 10 as the base): Its value is given by the following arithmetic: ![]() ![]() The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 −2 power term, also called characteristics, where −2 is the exponent (and 10 is the base). Depending on the interpretation of the exponent, the significand may represent an integer or a fraction. The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic ) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. ![]()
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