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Multiplication Algorithm
A multiplication algorithm is an algorithm (or method) to multiplication, multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic. The oldest and simplest method, known since Ancient history, antiquity as long multiplication or grade-school multiplication, consists of multiplying every digit in the first number by every digit in the second and adding the results. This has a time complexity of O(n^2), where ''n'' is the number of digits. When done by hand, this may also be reframed as grid method multiplication or lattice multiplication. In software, this may be called "shift and add" due to bitshifts and addition being the only two operations needed. In 1960, Anatoly Karatsuba discovered Karatsuba multiplication, unleashing a flood of research into fast multiplication algorithms. This method uses three multiplications rather than four to multiply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implicit Constant
Implicit may refer to: Mathematics * Implicit function * Implicit function theorem * Implicit curve * Implicit surface * Implicit differential equation Other uses * Implicit assumption, in logic * Implicit-association test, in social psychology * Implicit bit, in floating-point arithmetic * Implicit learning, in learning psychology * Implicit memory, in long-term human memory * Implicit solvation, in computational chemistry * Implicit stereotype (implicit bias), in social identity theory * Implicit type conversion, in computing See also * Implicit and explicit atheism, types of atheism coined by George H. Smith * Implication (other) * Implicature {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbitrary-precision Arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microcode
In processor design, microcode serves as an intermediary layer situated between the central processing unit (CPU) hardware and the programmer-visible instruction set architecture of a computer. It consists of a set of hardware-level instructions that implement the higher-level machine code instructions or control internal finite-state machine sequencing in many digital processing components. While microcode is utilized in Intel and AMD general-purpose CPUs in contemporary desktops and laptops, it functions only as a fallback path for scenarios that the faster hardwired control unit is unable to manage. Housed in special high-speed memory, microcode translates machine instructions, state machine data, or other input into sequences of detailed circuit-level operations. It separates the machine instructions from the underlying electronics, thereby enabling greater flexibility in designing and altering instructions. Moreover, it facilitates the construction of complex multi-step inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Hardware
Computer hardware includes the physical parts of a computer, such as the central processing unit (CPU), random-access memory (RAM), motherboard, computer data storage, graphics card, sound card, and computer case. It includes external devices such as a Computer monitor, monitor, Computer mouse, mouse, Computer keyboard, keyboard, and Computer speakers, speakers. By contrast, software is a set of written instructions that can be stored and run by hardware. Hardware derived its name from the fact it is ''Hardness, hard'' or rigid with respect to changes, whereas software is ''soft'' because it is easy to change. Hardware is typically directed by the software to execute any command or Instruction (computing), instruction. A combination of hardware and software forms a usable computing system, although Digital electronics, other systems exist with only hardware. History Early computing devices were more complicated than the ancient abacus date to the seventeenth century. French ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrated Circuit
An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components are etched onto a small, flat piece ("chip") of semiconductor material, usually silicon. Integrated circuits are used in a wide range of electronic devices, including computers, smartphones, and televisions, to perform various functions such as processing and storing information. They have greatly impacted the field of electronics by enabling device miniaturization and enhanced functionality. Integrated circuits are orders of magnitude smaller, faster, and less expensive than those constructed of discrete components, allowing a large transistor count. The IC's mass production capability, reliability, and building-block approach to integrated circuit design have ensured the rapid adoption of standardized ICs in place of designs using discre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total population of over 84 million in an area of , making it the most populous member state of the European Union. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The Capital of Germany, nation's capital and List of cities in Germany by population, most populous city is Berlin and its main financial centre is Frankfurt; the largest urban area is the Ruhr. Settlement in the territory of modern Germany began in the Lower Paleolithic, with various tribes inhabiting it from the Neolithic onward, chiefly the Celts. Various Germanic peoples, Germanic tribes have inhabited the northern parts of modern Germany since classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abacus
An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. An abacus consists of a two-dimensional array of Sliding (motion), slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one Numerical digit, digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases). Roman Empire, Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication Table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication binary operation, operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. History Pre-modern times The oldest known multiplication tables were used by the Babylonian mathematics, Babylonians about 4000 years ago. However, they used a base of 60. The oldest known tables using a base of 10 are the Chinese mathematics, Chinese Tsinghua Bamboo Slips#Decimal multiplication table, decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplier
Multiplier may refer to: Mathematics * Multiplier (arithmetic), the number of multiples being computed in multiplication * Constant multiplier, a constant factor with units of measurement * Lagrange multiplier, a scalar variable used in mathematics to solve an optimisation problem for a given constraint * Multiplier (Fourier analysis), an operator that multiplies the Fourier coefficients of a function by a specified function (known as the symbol) * Multiplier of orbit, a formula for computing a value of a variable based on its own previous value or values; see Periodic points of complex quadratic mappings * Characteristic multiplier, an eigenvalue of a monodromy matrix * Multiplier algebra, a construction on C*-Algebras and similar structures Electrical engineering * Binary multiplier, a digital circuit to perform rapid multiplication of two numbers in binary representation * Analog multiplier, a device that multiplies two analog signals * Frequency multiplier, a device that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicand
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a '' product''. Multiplication is often denoted by the cross symbol, , by the mid-line dot operator, , by juxtaposition, or, in programming languages, by an asterisk, . The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''; both numbers can be referred to as ''factors''. This is to be distinguished from ''terms'', which are added. :a\times b = \underbrace_ . Whether the first factor is the multiplier or the multiplicand may be ambiguous or depend upon context. For example, the expression 3 \times 4 , can be phrased as "3 times 4" and evaluated as 4+4+4, where 3 is the multiplier, but a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral System
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal or base-10 numeral system (today, the most common system globally), the number ''three'' in the binary or base-2 numeral system (used in modern computers), and the number ''two'' in the unary numeral system (used in tallying scores). The number the numeral represents is called its ''value''. Additionally, not all number systems can represent the same set of numbers; for example, Roman, Greek, and Egyptian numerals don't have a representation of the number zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
