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Dadda Tree
The Dadda multiplier is a hardware binary multiplier design invented by computer scientist Luigi Dadda in 1965. It uses a selection of full and half adders to sum the partial products in stages (the Dadda tree or Dadda reduction) until two numbers are left. The design is similar to the Wallace multiplier, but the different reduction tree reduces the required number of gates (for all but the smallest operand sizes) and makes it slightly faster (for all operand sizes). Dadda and Wallace multipliers have the same three steps for two bit strings w_1 and w_2 of lengths \ell_1 and \ell_2 respectively: # Multiply (logical AND) each bit of w_1, by each bit of w_2, yielding \ell_1\cdot\ell_2 results, grouped by weight in columns # Reduce the number of partial products by stages of full and half adders until we are left with at most two bits of each weight. # Add the final result with a conventional adder. As with the Wallace multiplier, the multiplication products of the first step c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Multiplier
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve computing the set of ''partial products,'' which are then summed together using binary adders. This process is similar to long multiplication, except that it uses a base-2 (binary) numeral system. History Between 1947 and 1949 Arthur Alec Robinson worked for English Electric Ltd, as a student apprentice, and then as a development engineer. Crucially during this period he studied for a PhD degree at the University of Manchester, where he worked on the design of the hardware multiplier for the early Mark 1 computer. However, until the late 1970s, most minicomputers did not have a multiply instruction, and so programmers used a "multiply routine" which repeatedly shifts and accumulates partial results, often written using loop unwinding. Mainfr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallace Tree
A Wallace multiplier is a hardware implementation of a binary multiplier, a digital circuit that multiplies two integers. It uses a selection of full and half adders (the Wallace tree or Wallace reduction) to sum partial products in stages until two numbers are left. Wallace multipliers reduce as much as possible on each layer, whereas Dadda multipliers try to minimize the required number of gates by postponing the reduction to the upper layers. Wallace multipliers were devised by the Australian computer scientist Chris Wallace in 1964. The Wallace tree has three steps: # Multiply each bit of one of the arguments, by each bit of the other. # Reduce the number of partial products to two by layers of full and half adders. # Group the wires in two numbers, and add them with a conventional adder. Compared to naively adding partial products with regular adders, the benefit of the Wallace tree is its faster speed. It has O(\log n) reduction layers, but each layer has only O(1) pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) 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''. 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''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Arithmetic
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs). The inputs to an ALU are the data to be operated on, called operands, and a code indicating the operation to be performed; the ALU's output is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers. Signals An ALU has a variety of input and output nets, which are the electrical conductors used to convey digital signals between the ALU and external circuitry. When an ALU is o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Logic Circuits
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The International Society
The International Society of Sculptors, Painters and Gravers was a union of professional artists that existed from 1898 to 1925, "To promote the study, practice, and knowledge of sculpture, painting, etching, lithographing, engraving, and kindred arts in England or elsewhere...". It came to be known simply as The International. Philip Athill (January 1985)The International Society of Sculptors, Painters and Gravers ''The Burlington Magazine'' 127(982): 21-29+33. The society organised exhibitions, some for members only and some open to others, and social events such as musical evenings and soirées. The exhibitions were held in a number of London venues, and in other cities around England, including Nottingham and Manchester. Its founder and first president was James McNeill Whistler. On his death, the presidency was taken up by Auguste Rodin, with John Lavery as vice-president. The society contributed £500 towards the cost of Whistler's memorial. Formation The society was initial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ''Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modulo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kochanski Multiplication
Kochanski multiplication is an algorithm that allows modular arithmetic (multiplication or operations based on it, such as exponentiation) to be performed efficiently when the modulus is large (typically several hundred bits). This has particular application in number theory and in cryptography: for example, in the RSA cryptosystem and Diffie–Hellman key exchange Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include: * Diffie–Hellman–Merkle key exchange * Diffie–Hellman key agreement * Diffie–Hellman key establishment * Diffie–Hellman key negotiation * Exponential key exc .... The most common way of implementing large-integer multiplication in hardware is to express the multiplier in binary numeral system, binary and enumerate its bits, one bit at a time, starting with the most significant bit, perform the following operations on an accumulator (computing), accumulator: #Double the contents of the accumulator (if the accumulator stores numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BKM Algorithm
The BKM algorithm is a shift-and-add algorithm for computing elementary functions, first published in 1994 by Jean-Claude Bajard, Sylvanus Kla, and Jean-Michel Muller. BKM is based on computing complex logarithms (''L-mode'') and exponentials (''E-mode'') using a method similar to the algorithm Henry Briggs used to compute logarithms. By using a precomputed table of logarithms of negative powers of two, the BKM algorithm computes elementary functions using only integer add, shift, and compare operations. BKM is similar to CORDIC, but uses a table of logarithms rather than a table of arctangents. On each iteration, a choice of coefficient is made from a set of nine complex numbers, 1, 0, −1, i, −i, 1+i, 1−i, −1+i, −1−i, rather than only −1 or +1 as used by CORDIC. BKM provides a simpler method of computing some elementary functions, and unlike CORDIC, BKM needs no result scaling factor. The convergence rate of BKM is approximately one bit per iteration, like CORDIC, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fused Multiply–add
Fuse or FUSE may refer to: Devices * Fuse (electrical), a device used in electrical systems to protect against excessive current ** Fuse (automotive), a class of fuses for vehicles * Fuse (hydraulic), a device used in hydraulic systems to protect against sudden loss of fluid pressure * Fuse (explosives) or fuze, the part of the device that initiates function * Fuze or fuse, a mechanism for exploding military munitions such as bombs, shells, and mines Computing * Fuse ESB, an open-source integration platform based on Apache Camel * Filesystem in Userspace, a virtual file system interface for Unix-like operating systems * Fuse (emulator), the Free Unix Spectrum Emulator of the ZX Spectrum * Fuse Internet Service, a former Cincinnati Bell Internet service provider based in Cincinnati, Ohio, United States * Fuse Universal, a learning platform Science * Far Ultraviolet Spectroscopic Explorer, a space-based ultraviolet telescope and spectroscope * Intramembranous ossification, the fus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luigi Dadda
Luigi Dadda (April 29, 1923 – October 26, 2012) was an Italian computer engineer, best known for the design of the Dadda multiplier and as one of the first researchers on modern computers in Italy. He was rector at the Politecnico di Milano technical university from 1972 to 1984, collaborating on research at the same university until 2012. He was a Life Fellow of the IEEE. He studied electrical engineering at the Politecnico di Milano and graduated in 1947 with a thesis on signal transmission, a microwave radio bridge between the cities of Turin and Trieste. His research interests then turned to models and analog computers as an assistant professor, and in 1953 he received a grant from the National Science Foundation in order to study at the California Institute of Technology in Pasadena. In the interim, the Politecnico di Milano requested funding for a digital computer under the Marshall Plan; the request was granted in the sum of US$120,000, and the rector of the time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Booth's Multiplication Algorithm
Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation. The algorithm was invented by Andrew Donald Booth in 1950 while doing research on crystallography at Birkbeck College in Bloomsbury, London. Booth's algorithm is of interest in the study of computer architecture. The algorithm Booth's algorithm examines adjacent pairs of bits of the 'N'-bit multiplier ''Y'' in signed two's complement representation, including an implicit bit below the least significant bit, ''y''−1 = 0. For each bit ''y''''i'', for ''i'' running from 0 to ''N'' − 1, the bits ''y''''i'' and ''y''''i''−1 are considered. Where these two bits are equal, the product accumulator ''P'' is left unchanged. Where ''y''''i'' = 0 and ''y''''i''−1 = 1, the multiplicand times 2''i'' is added to ''P''; and where ''y''i = 1 and ''y''i−1 = 0, the multiplicand times 2''i'' is subtracted from ''P''. The final value of ''P'' is the signe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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