|
Decimal64 Floating-point Format
In computing, decimal64 is a decimal floating-point computer numbering format that occupies 8 bytes (64 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal64 supports 16 decimal digits of significand and an exponent range of −383 to +384, i.e. to . (Equivalently, to .) In contrast, the corresponding binary format, which is the most commonly used type, has an approximate range of to . Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; , etc. Zero has 768 possible representations (1536 if both signed zeros are included). Decimal64 floating point is a relatively new decimal floating-point format, formally introduced in the 2008 version of IEEE 754 as well as with ISO/IEC/IEEE 60559:2011. Representation of decimal64 values IEEE 754 allows two alternative representation methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology and software engineering. The term "computing" is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the representation of numbers, though mathematical conc ... [...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] |
D Notation (scientific Notation)
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the ''significand'' or ''mantissa''. The term "mantissa" can be ambiguous where logarithms are involved, because it is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Data Type
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, "primitive data types" may refer to the standard data types built into a programming language. Data types which are not primitive are referred to as ''derived'' or ''composite''. Primitive types are almost always value types, but composite types may also be value types. Common primitive data types The Java virtual machine's set of primitive data types is: * Integer types with a variety of ranges and precisions (byte, short, int, long, char) * Floating-point number with single or double precisions; (float, double) * Boolean, logical values true and false. (boolean) * A value referring to an execu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 10967
ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with ISO/IEC/IEEE 60559:2011, more known as IEEE 754-2008, and much of the specifications are for IEEE 754 special values (though such values are not required by LIA itself, unless the parameter ''iec559'' is true). It was developed by the working group ISO/IEC JTC1/SC22/WG11, which was disbanded in 2011. LIA consists of three parts: * Part 1: ''Integer and floating point arithmetic'', second edition published 2012. * Part 2: ''Elementary numerical functions'', first edition published 2001. * Part 3: ''Complex integer and floating point arithmetic and complex elementary numerical functions'', first edition published 2006. Parts Part 1 Part 1 deals with the basic integer and floating point datatypes (for multiple radices, including 2 and 10), but unlike IEEE 754-2008 not the representation of the values. Part 1 also deals with basic arithmetic, including compari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don't Care
In digital logic, a don't-care term (abbreviated DC, historically also known as ''redundancies'', ''irrelevancies'', ''optional entries'', ''invalid combinations'', ''vacuous combinations'', ''forbidden combinations'', ''unused states'' or ''logical remainders'') for a function is an input-sequence (a series of bits) for which the function output does not matter. An input that is known never to occur is a can't-happen term. Both these types of conditions are treated the same way in logic design and may be referred to collectively as ''don't-care conditions'' for brevity. The designer of a logic circuit to implement the function need not care about such inputs, but can choose the circuit's output arbitrarily, usually such that the simplest circuit results ( minimization). Don't-care terms are important to consider in minimizing logic circuit design, including graphical methods like Karnaugh–Veitch maps and algebraic methods such as the Quine–McCluskey algorithm. In 1958, S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhäuser
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particularly: history of science, geosciences, computer science) and mathematics books and journals under the Birkhäuser imprint (with a leaf logo) sometimes called Birkhäuser Science. * Birkhäuser Verlag – an architecture and design publishing company was (re)created in 2010 when Springer sold its design and architecture segment to ACTAR. The resulting Spanish-Swiss company was then called ActarBirkhäuser. After a bankruptcy, in 2012 Birkhäuser Verlag was sold again, this time to De Gruyter. Additionally, the Reinach-based printer Birkhäuser+GBC operates independently of the above, being now owned by ''Basler Zeitung''. History The original Swiss publishers program focused on regional literature. In the 1920s the sons of Emil Birkhà ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Declet (computing)
In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure information contained in messages and the entropy of random variables. The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes). Primary units In 1928, Ralph Hartley observed a fundamental storage principle, which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of ''N'' possible states of that system, denoted . Changing the base of the logarithm from ''b'' to a diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subnormal Numbers
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest normal number is ''subnormal''. :: ''Usage note: in some older documents (especially standards documents such as the initial releases of IEEE 754 and 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.'' In a normal floating-point value, there are no leading zeros in the significand ( mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as ). Conversely, a denormalized floating point value has a significand with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary64
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754-2008 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 ''single precision'' and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
