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Balanced Ternary
Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a non-standard positional numeral system. It was used in some early computers and also in some solutions of balance puzzles. Different sources use different glyphs used to represent the three digits in balanced ternary. In this article, T (which resembles a ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+' to represent −1 and 1 respectively, or using Greek letter theta (Θ), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Numeral System
A ternary numeral system (also called base 3 or trinary) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log2 3 (about 1.58496) bits of information. Although ''ternary'' most often refers to a system in which the three digits are all non–negative numbers; specifically , , and , the adjective also lends its name to the balanced ternary system; comprising the digits −1, 0 and +1, used in comparison logic and ternary computers. Comparison to other bases Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary. For example, decimal 365 or senary 1405 corresponds to binary 101101101 (nine digits) and to ternary 111112 (six digits). However, they are still far less compact than the corresponding representations in bases such as decimalsee below for a compact way to codify ternary using nonary (base 9) and septemvigesimal (base 27). As for rational numbers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra. A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific writer; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics. B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rounding
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". He is the author of the multi-volume work ''The Art of Computer Programming'' and contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems designed to encou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix Point
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping. Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to an (either baseline or middle) dot and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, with the aforementioned generic terms reserved for abstract usage. In many contexts, when a number is spoken, the function of the separator is assumed by the spoken name of the symbol: ''comma'' or ''point'' in most cases. In some specialized contexts, the word ''decimal'' is instead used for this purpose (such as in International Civil Aviation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surjective Map
In mathematics, a surjective function (also known as surjection, or onto function) is a function that every element can be mapped from element so that . In other words, every element of the function's codomain is the image of one element of its Domain of a function, domain. It is not required that be unique (mathematics), unique; the function may map one or more elements of to the same element of . The term ''surjective'' and the related terms ''injective function, injective'' and ''bijective function, bijective'' were introduced by Nicolas Bourbaki, a group of mainly France, French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word ''wikt:sur#French, sur'' means ''over'' or ''above'', and relates to the fact that the image (mathematics), image of the domain of a surjective function completely covers the function's codomain. Any function induces a surject ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language, formal language theory and computer programming, string concatenation is the operation of joining character string (computer science), character strings wikt:end-to-end, end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary operation, binary infix operator. The + (plus) operator is often operator overloading, overloaded to denote concatenation for string arguments: "Hello, " + "World" has the value "Hello, World". In other languages there is a separate operator, particularly to specify implicit type conversion to string, as opposed to more complicated behavior for generic plus. Examples include . in Edinburgh IMP, Perl, and PHP, .. in Lua (programming language), Lua, and & in Ada, AppleScript, and Visual Basic. Other syntax exists, like ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleene Plus
In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics, it is more commonly known as the free monoid construction. The application of the Kleene star to a set V is written as ''V^*''. It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". # If V is a set of strings, then ''V^*'' is defined as the smallest superset of V that contains the empty string \varepsilon and is closed under the string concatenation operation. # If V is a set of symbols or characters, then ''V^*'' is the set of all strings over symbols in V, including the empty string \varepsilon. The set ''V^*'' can also be described as the set containing the empty string and all finite-length strings that can be generated by concatenating arbitrary e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
