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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 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.
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 .
Then, the fractional part can be formulated as a difference: frac ( x ) = x − ⌊ x ⌋ , x > 0 {\displaystyle \operatorname {frac} (x)=x-\lfloor x\rfloor ,\;x>0} . The fractional part of logarithms , [ 2 ] specifically, is also known as the mantissa ; by contrast with the mantissa, the integral part of a logarithm is called its ...
Mantissa (/ m æ n ˈ t ɪ s ə /) may refer to: Mantissa (logarithm) , the fractional part of the common (base-10) logarithm Significand (also commonly called mantissa), the significant digits of a floating-point number or a number in scientific notation
The significand (or mantissa) of an IEEE floating-point number is the part of a floating-point number that represents the significant digits. For a positive normalised number it can be represented as m 0 . m 1 m 2 m 3 ... m p −2 m p −1 (where m represents a significant digit, and p is the precision) with non-zero m 0 .
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]
A floating-point number is typically packed into a single bit-string, as the sign bit, the exponent field, and the significand or mantissa, from left to right. As an example, a IEEE 754 standard 32-bit float ("FP32", "float32", or "binary32") is packed as follows: The IEEE 754 binary floats are:
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