In IEEE 754 floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias , also called a biased exponent . Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement , the usual representation for signed values, would make comparison harder.
20-466: (Redirected from Characteristics ) [REDACTED] Look up characteristic in Wiktionary, the free dictionary. A characteristic is a distinguishing feature of a person or thing. It may refer to: Computing [ edit ] Characteristic (biased exponent) , an ambiguous term formerly used by some authors to specify some type of exponent of
40-408: A floating point number Characteristic (significand) , an ambiguous term formerly used by some authors to specify the significand of a floating point number Science [ edit ] I–V or current–voltage characteristic , the current in a circuit as a function of the applied voltage Receiver operating characteristic Mathematics [ edit ] Characteristic (algebra) of
60-470: A lighted beacon Another name for ability score in Dungeons & Dragons See also [ edit ] All pages with titles containing Characteristic Characteristicks , a 1711 philosophical treatise by Anthony Ashley-Cooper, 3rd Earl of Shaftesbury Property (philosophy) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
80-467: A number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane . The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 power term, also called characteristics , where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: The same value can also be represented in scientific notation with
100-411: A ring, the smallest common cycle length of the ring's addition operation Characteristic (logarithm) , integer part of a common logarithm Characteristic function , usually the indicator function of a subset, though the term has other meanings in specific domains Characteristic polynomial , a polynomial associated with a square matrix in linear algebra Characteristic subgroup , a subgroup that
120-408: A significand ranging between 0.1 and 1.0 the true normalized form . For a normalized number , the most significant digit is always non-zero. When working in binary , this constraint uniquely determines this digit to always be 1. As such, it is not explicitly stored, being called the hidden bit . The significand is characterized by its width in (binary) digits , and depending on the context,
140-429: 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 . In 1914, Leonardo Torres Quevedo introduced floating-point arithmetic in his Essays on Automatics , where he proposed the format n ; m , showing the need for a fixed-sized significand as currently used for floating-point data. In 1946, Arthur Burks used
160-474: Is invariant under all automorphisms in group theory Characteristic value , another name for the eigenvalue of a matrix Characteristic vector (disambiguation) , another name for eigenvector of a matrix Characteristic word , a subclass of Sturmian word Euler characteristic , a topological invariant Method of characteristics , a technique for solving partial differential equations Other uses [ edit ] Light characteristic , pattern of
180-439: Is the case whether or not it is interpreted as a floating-point or integer value. The purpose of this is to enable high speed comparisons between floating-point numbers using fixed-point hardware. If there are e {\displaystyle e} bits in the exponent, the bias is typically set as b = 2 e − 1 − 1 {\displaystyle b=2^{e-1}-1} . Therefore,
200-480: Is the word used in the IEEE standard as the coefficient in front of a scientific notation number discussed above. The fractional part is called the fraction . To understand both terms, notice that in binary, 1 + mantissa ≈ significand, and the correspondence is exact when storing a power of two. This fact allows for a fast approximation of the base-2 logarithm, leading to algorithms e.g. for computing
220-452: The fast square-root and fast inverse-square-root . The implicit leading 1 is nothing but the hidden bit in IEEE 754 floating point, and the bitfield storing the remainder is thus the mantissa . However, whether or not the implicit 1 is included is a major point of confusion with both terms—and especially so with mantissa . In keeping with the original usage in the context of log tables, it should not be present. For those contexts where 1
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#1732772013692240-435: The exponent is stored as an unsigned value which is suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias. By arranging the fields such that the sign bit takes the most significant bit position, the biased exponent takes the middle position, then the significand will be the least significant bits and the resulting value will be ordered properly. This
260-431: The hidden bit may or may not be counted toward the width. 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. 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
280-436: The possible integer values that the biased exponent can express lie in the range [ 1 − b , b ] {\displaystyle [1-b,b]} . To understand this range, with e {\displaystyle e} bits in the exponent, the possible unsigned integers lie in the range [ 0 , 2 e − 1 ] {\displaystyle [0,2^{e}-1]} . However,
300-626: The significand 1.2345 as a fractional coefficient, and +2 as the exponent (and 10 as the base): Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form . For base 2, this 1.xxxx form is also called a normalized significand . Finally, 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 called this representation with
320-434: 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. Although the other names mentioned are common, significand is the word used by IEEE 754 , an important technical standard for floating-point arithmetic. In mathematics , the term "argument" may also be ambiguous, since "the argument of
340-455: The strings containing all zeros and all ones are reserved for special values, so the expressible integers lie in the range [ 1 , 2 e − 2 ] {\displaystyle [1,2^{e}-2]} . It follows that: When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. The floating-point format of the IBM 704 introduced
360-453: The terms mantissa and characteristic to describe the two parts of a floating-point number ( Burks 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 usage remains common among computer scientists today. The term significand was introduced by George Forsythe and Cleve Moler in 1967 and
380-501: The title Characteristic . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Characteristic&oldid=1249446922 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Characteristic (biased exponent) To solve this problem
400-407: The use of a biased exponent in 1954. Significand The significand (also coefficient , sometimes argument , or more ambiguously mantissa , fraction , or characteristic ) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits . Depending on the interpretation of the exponent ,
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