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Logarithmic Number System
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. Overview A number, X, is represented in an LNS by two components: the logarithm (x) of its absolute value (as a binary word usually in two's complement), and its sign bit (s): :X \rightarrow \begin x = \log_b\big, X\big, , \\ s = \begin 0\text X > 0, \\ 1\text X A VHDL library for LNS hardware generation Computer arithmetic Digital signal processing [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonardo Torres Quevedo
Leonardo Torres Quevedo (; 28 December 1852 – 18 December 1936) was a Spanish civil engineer, mathematician and inventor, known for his numerous engineering innovations, including Aerial tramway, aerial trams, airships, catamarans, and remote control. He was also a pioneer in the field of Computer science, computing and robotics. Torres was a member of several scientific and cultural institutions and held such important positions as the seat ''N'' of the Royal Spanish Academy, Real Academia Española (1920–1936) and the presidency of the Spanish Royal Academy of Sciences (1928–1934). In 1927 he became a foreign associate of the French Academy of Sciences. His first groundbreaking invention was a cable car system patented in 1887 for the safe transportation of people, an activity that culminated in 1916 when the Whirlpool Aero Car was opened in Niagara Falls. In the 1890s, Torres focused his efforts on Analog computer, analog computation. He published ''Sur les machines alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A-law Algorithm
An A-law algorithm is a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, i.e. modify, the dynamic range of an analog signal for digitizing. It is one of the two companding algorithms in the G.711 standard from ITU-T, the other being the similar μ-law, used in North America and Japan. For a given input x, the equation for A-law encoding is as follows: F(x) = \sgn(x) \begin \dfrac, & , x, < \dfrac, \\ ex \dfrac, & \dfrac \leq , x, \leq 1, \end where is the compression parameter. In Europe, . A-law expansion is given by the inverse function: The reason for this encoding is that the wide |
ITU-T G
The International Telecommunication Union Telecommunication Standardization Sector (ITU-T) is one of the three Sectors (branches) of the International Telecommunication Union (ITU). It is responsible for coordinating standards for telecommunications and Information Communication Technology, such as X.509 for cybersecurity, Y.3172 and Y.3173 for machine learning, and H.264/MPEG-4 AVC for video compression, between its Member States, Private Sector Members, and Academia Members. The World Telecommunication Standardization Assembly (WTSA), the sector's governing conference, convenes every four years. ITU-T has a permanent secretariat called the Telecommunication Standardization Bureau (TSB), which is based at the ITU headquarters in Geneva, Switzerland. The current director of the TSB is Seizo Onoe (of Japan), whose 4-year term commenced on 1 January 2023. Seizo Onoe succeeded Chaesub Lee of South Korea, who was director from 1 January 2015 until 31 December 2022. Primary fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zech's Logarithm
Zech logarithms are used to implement addition in finite fields when elements are represented as powers of a generator \alpha. Zech logarithms are named after Julius Zech, and are also called Jacobi logarithms, after Carl G. J. Jacobi who used them for number theoretic investigations. Definition Given a primitive element \alpha of a finite field, the Zech logarithm relative to the base \alpha is defined by the equation :\alpha^ = 1 + \alpha^n, which is often rewritten as :Z_\alpha(n) = \log_\alpha(1 + \alpha^n). The choice of base \alpha is usually dropped from the notation when it is clear from the context. To be more precise, Z_\alpha is a function on the integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...s modular arithmetic, modulo the multiplicative order of \alph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Level-index Arithmetic
The level-index (LI) representation of numbers, and its algorithms for arithmetic operations, were introduced by Charles Clenshaw and Frank Olver in 1984. The symmetric form of the LI system and its arithmetic operations were presented by Clenshaw and Peter Turner in 1987. Michael Anuta, Daniel Lozier, Nicolas Schabanel and Turner developed the algorithm for symmetric level-index (SLI) arithmetic, and a parallel implementation of it. There has been extensive work on developing the SLI arithmetic algorithms and extending them to complex and vector arithmetic operations. Definition The idea of the level-index system is to represent a non-negative real number as : X = e^, where 0 \leq f < 1, and the process of exponentiation is performed times, with . and are the level and index of respectively. is the LI image of . For example, : so its LI image is : The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tapered Floating Point
In computing, tapered floating point (TFP) is a format similar to floating point, but with variable-sized entries for the significand and exponent instead of the fixed-length entries found in normal floating-point formats. In addition to this, tapered floating-point formats provide a fixed-size pointer entry indicating the number of digits in the exponent entry. The number of digits of the significand entry (including the sign) results from the difference of the fixed total length minus the length of the exponent and pointer entries. Thus numbers with a small exponent, i.e. whose order of magnitude is close to the one of 1, have a higher relative precision than those with a large exponent. History The tapered floating-point scheme was first proposed by Robert Morris of Bell Laboratories in 1971, and refined with ''leveling'' by Masao Iri and Shouichi Matsui of University of Tokyo in 1981, and by Hozumi Hamada of Hitachi, Ltd. Alan Feldstein of Arizona State University and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subnormal Number
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the arithmetic underflow, underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest positive normal number (computing), normal number is ''subnormal'', while ''denormal'' can also refer to numbers outside that range. Terminology In some older documents (especially standards documents such as the initial releases of IEEE 754-1985, IEEE 754 and ISO_9899, the C language), "denormal" is used to refer exclusively to subnormal numbers. This usage persists in various standards documents, especially when discussing hardware that is incapable of representing any other denormalized numbers, but the discussion here uses the term "subnormal" in line with the 2008 revision of IEEE 754-2008, IEEE 754. In casual discussions the terms ''subnormal'' and ''denormal'' are often used interchangeably, in part because there ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whose level (logarithmic quantity), levels differ by one decibel have a power ratio of 101/10 (approximately ) or root-power ratio of 101/20 (approximately ). The strict original usage above only expresses a relative change. However, the word decibel has since also been used for expressing an Absolute scale, absolute value that is relative to some fixed reference value, in which case the dB symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "#Voltage, V" (e.g., "20 dBV"). As it originated from a need to express power ratios, two principal types of scaling of the decibel are used to provide consistency depending on whether the scaling refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field-programmable Gate Array
A field-programmable gate array (FPGA) is a type of configurable integrated circuit that can be repeatedly programmed after manufacturing. FPGAs are a subset of logic devices referred to as programmable logic devices (PLDs). They consist of an array of programmable logic device, programmable logic block, logic blocks with a connecting grid, that can be configured "in the field" to interconnect with other logic blocks to perform various digital functions. FPGAs are often used in limited (low) quantity production of custom-made products, and in research and development, where the higher cost of individual FPGAs is not as important, and where creating and manufacturing a custom circuit would not be feasible. Other applications for FPGAs include the telecommunications, automotive, aerospace, and industrial sectors, which benefit from their flexibility, high signal processing speed, and parallel processing abilities. A FPGA configuration is generally written using a hardware descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Logic Unit
In computing, an arithmetic logic unit (ALU) is a Combinational logic, 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 (opcode); 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 net (electronics), nets, which are the electrical conductors used to convey Digital signal (electroni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
