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Nines' Complement
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (hardware) for addition throughout the whole range. For a given number of Positional notation, places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called ''complements''. Thus subtraction of any number is implemented by adding its complement. Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the ''radix complement'' (as described below) is also valuable in number theory, such as in Midy's theorem. The ''nines' complement'' of a number given in decimal repr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complement Numbering Gnangarra
A complement is something that completes something else. Complement may refer specifically to: The arts * Complement (music), an interval that, when added to another, spans an octave ** Aggregate complementation, the separation of pitch-class collections into complementary sets * Complementary color, in the visual arts Biology and medicine *Complement system (immunology), a cascade of proteins in the blood that form part of innate immunity *Complementary DNA, DNA reverse transcribed from a mature mRNA template *Complementarity (molecular biology), a property whereby double stranded nucleic acids pair with each other *Complementation (genetics), a test to determine if independent recessive mutant phenotypes are caused by mutations in the same gene or in different genes Grammar and linguistics * Complement (linguistics), a word or phrase having a particular syntactic role ** Subject complement, a word or phrase adding to a clause's subject after a linking verb * Phonetic com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Series
In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series :\frac \,+\, \frac \,+\, \frac \,+\, \frac \,+\, \cdots is geometric, because each successive term can be obtained by multiplying the previous term by 1/2. In general, a geometric series is written as a + ar + ar^2 + ar^3 + ..., where a is the coefficient of each term and r is the common ratio between adjacent terms. The geometric series had an important role in the early development of calculus, is used throughout mathematics, and can serve as an introduction to frequently used mathematical tools such as the Taylor series, the complex Fourier series, and the matrix exponential. The name geometric series indicates each term is the geometric mean of its two neighboring terms, similar to how the name arithmetic series indicates each term is the arithmetic mean of its two neighboring terms. The sequence of geometric series term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian numbers, rightmost bit in little-endian numbers) to indicate whether the binary number is positive or negative (the sign). It is used in computer science as the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. When the most significant bit is a one, the number is signed as negative. . Two's complement is executed by 1) inverting (i.e. flipping) all bits, then 2) adding a place value of 1 to the inverted number. For example, say the number −6 is of interest. +6 in binary is 0110 (the leftmost most significant bit is needed for the sign; positive 6 is not 110 because it would be interpreted as -2). Step one is to flip all bits, yielding 1001. St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mental Arithmetic
Mental calculation consists of arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator. People may use mental calculation when computing tools are not available, when it is faster than other means of calculation (such as conventional educational institution methods), or even in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems. People with unusually high ability to perform mental calculations are called mental calculators or ''lightning calculator''s. Many of these techniques take advantage of or rely on the decimal numeral system. Usually, the choice of radix is what determines which method or methods to use. Methods and techniques Casting out nines After applying an arithmetic operation to two operands and getting a result, the following procedure can be used to improve confidence in the correctness of result: # ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curta Calculator
The Curta is a hand-held mechanical calculator designed by Curt Herzstark. It is known for its extremely compact design: a small cylinder that fits in the palm of the hand. It was affectionately known as the "pepper grinder" or "peppermill" due to its shape and means of operation; its superficial resemblance to a certain type of hand grenade also earned it the nickname "math grenade". Curtas were considered the best portable calculators available until they were displaced by electronic calculators in the 1970s. History The Curta was conceived by Curt Herzstark in the 1930s in Vienna, Austria. By 1938, he had filed a key patent, covering his complemented stepped drum. This single drum replaced the multiple drums, typically around 10 or so, of contemporary calculators, and it enabled not only addition, but subtraction through nines complement math, essentially subtracting by adding. The nines' complement math breakthrough eliminated the significant mechanical complexity c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comptometer
The Comptometer was the first commercially successful key-driven mechanical calculator, patented in the United States by Dorr Felt in 1887. A key-driven calculator is extremely fast because each key adds or subtracts its value to the accumulator as soon as it is pressed and a skilled operator can enter all of the digits of a number simultaneously, using as many fingers as required, making them sometimes faster to use than electronic calculators. Consequently, in specialized applications, comptometers remained in use in limited numbers into the early 1990s, but with the exception of museum pieces, they have all now been superseded by electronic calculators and computers. Manufactured without interruption from 1887 to the mid-1970s, it was constantly improved. The mechanical versions were made faster and more reliable, then a line of electro-mechanical models was added in the 1930s. It was the first mechanical calculator to receive an all-electronic calculator engine in 1961, with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End-around Carry
In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols. The four best-known methods of extending the binary numeral system to represent signed numbers are: sign–magnitude, ones' complement, two's complement, and offset binary. Some of the alternative methods use implicit instead of explicit signs, such as negative binary, using the base −2. Corresponding methods can be devised for other bases, whether positive, negative, fractional, or other elaborations on such themes. There is no definitive criterion by which any of the representations is universally superior. For integers, the representation used in most current computing devices is two's complement, although the Unisys ClearPath Dorado series mainframes u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Circuit
In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce. For example, the values in a Boolean circuit are boolean values, and the circuit includes conjunction, disjunction, and negation gates. The values in an integer circuit are sets of integers and the gates compute set union, set intersection, and set complement, as well as the arithmetic operations addition and multiplication. Formal definition A circuit is a triple (M, L, G), where * M is a set of values, * L is a set of gate labels, each of which is a function from M^ to M for some non-negative integer i (where i represents the number of inputs to the gate), and * G is a labelled directed acyclic graph with labels fr ... [...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] |
Ones' Complement
The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (''note this is possessive of the plural "ones", not of a singular "one"'') refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number (the term "complement" refers to such pairs of mutually additive inverse numbers, here in respect to a non-0 base number). This mathematical operation is primarily of interest in computer science, where it has varying effects depending on how a specific computer represents numbers. A ones' complement system or ones' complement arithmetic is a system in which negative numbers are represented by the inverse of the binary representations of their corresponding positive numbers. In such a system, a number is negated (converted from positive to negative or vice versa) by computing its ones' complement. An N-bit ones ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
