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The integer n is called the exponent and the real number m is called the significand or mantissa. [1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation.
In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number (Burks [11] et al.) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part.
The arithmetical difference between two consecutive representable floating-point numbers which have the same exponent is called a unit in the last place (ULP). For example, if there is no representable number lying between the representable numbers 1.45a70c22 hex and 1.45a70c24 hex , the ULP is 2×16 −8 , or 2 −31 .
The part of the representation that contains the significant figures (1.30 or 1.23) is known as the significand or mantissa. The digits in the base and exponent ( 10 3 or 10 −2 ) are considered exact numbers so for these digits, significant figures are irrelevant.
In single precision, the bias is 127, so in this example the biased exponent is 124; in double precision, the bias is 1023, so the biased exponent in this example is 1020. fraction = .01000… 2 . IEEE 754 adds a bias to the exponent so that numbers can in many cases be compared conveniently by the same hardware that compares signed 2's ...
In a normal floating-point value, there are no leading zeros in the significand (also commonly called mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as 1.23 × 10 −2). Conversely, a denormalized floating point value has a significand with a leading digit of zero.
Several earlier 16-bit floating point formats have existed including that of Hitachi's HD61810 DSP of 1982 (a 4-bit exponent and a 12-bit mantissa), [2] Thomas J. Scott's WIF of 1991 (5 exponent bits, 10 mantissa bits) [3] and the 3dfx Voodoo Graphics processor of 1995 (same as Hitachi).
When a real number like .007 is denoted alternatively by 7.0 × 10 —3 then it is said that the number is represented in scientific notation.More generally, to write a number in the form a × 10 b, where 1 <= a < 10 and b is an integer, is to express it in scientific notation, and a is called the significand or the mantissa, and b is its exponent. [3]