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Sign Bit
In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types have a sign bit, it is invariably located in the most significant bit position, so the term may be used interchangeably with "most significant bit" in some contexts. Almost always, if the sign bit is 0, the number is non-negative (positive or zero). If the sign bit is 1 then the number is negative. Formats other than two's complement integers allow a signed zero: distinct "positive zero" and "negative zero" representations, the latter of which does not correspond to the mathematical concept of a negative number. When using a complement representation, to convert a signed number to a wider format the additional bits must be filled with copies of the sign bit in order to preserve its numerical value, a process called '' sign extension'' or ''sign propagation''. Sign bit weight in Two's complement Two's complement is by far th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Zero
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the '' sign-magnitude'' and ''ones' complement'' signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can still be represented by +0, −0, or 0. The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that = −∞ and = +∞; division ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Arithmetic
A binary number is a number expressed in the Radix, base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computer, computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thoma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign And Magnitude
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 mainframe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z3 (computer)
The Z3 was a German electromechanical computer designed by Konrad Zuse in 1938, and completed in 1941. It was the world's first working Computer programming, programmable, fully automatic digital computer. The Z3 was built with 2,600 relays, implementing a 22-bit Word (data type), word length that operated at a clock frequency of about 5–10 Hertz, Hz. Program code was stored on punched celluloid, film. Initial values were entered manually. The Z3 was completed in Berlin in 1941. It was not considered vital, so it was never put into everyday operation. Based on the work of the German aerodynamics engineer Hans Georg Küssner (known for the Küssner effect), a "Program to Compute a Complex Matrix" was written and used to solve wing flutter problems. Zuse asked the German government for funding to replace the relays with fully electronic switches, but funding was denied during World War II since such development was deemed "not war-important". The original Z3 was destroyed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z1 (computer)
The Z1 was a motor-driven mechanical computer designed by German inventor Konrad Zuse from 1936 to 1937, which he built in his parents' home from 1936 to 1938. It was a binary, electrically driven, mechanical calculator, with limited programmability, reading instructions from punched celluloid film. The “Z1” was the first freely programmable computer in the world that used Boolean logic and binary floating-point numbers; however, it was unreliable in operation. It was completed in 1938 and financed completely by private funds. This computer was destroyed in the bombardment of Berlin in December 1943, during World War II, together with all construction plans. The Z1 was the first in a series of computers that Zuse designed. Its original name was "V1" for Versuchsmodell 1 (meaning Experimental Model 1). After WW2, it was renamed "Z1" to differentiate it from the flying bombs designed by Robert Lusser. The Z2 and Z3 were follow-ups based on many of the same ideas as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IBM Hexadecimal Floating-point
Hexadecimal floating-point arithmetic, floating point (now called HFP by IBM) is a format for encoding floating-point numbers first introduced on the IBM IBM System/360, System/360 computers, and supported on subsequent machines based on that architecture, as well as machines which were intended to be application-compatible with System/360. In comparison to IEEE 754 floating point, the HFP format has a longer significand, and a shorter Exponentiation, exponent. All HFP formats have 7 bits of exponent with a exponent bias, bias of 64. The normalized range of representable numbers is from 16−65 to 1663 (approx. 5.39761 × 10−79 to 7.237005 × 1075). The number is represented as the following formula: (−1)sign × 0.significand × 16exponent−64. Single-precision 32-bit A single-precision floating-point format, single-precision HFP number (called "short" by IBM) is stored in a 32-bit word: : In this format the initial bit is not suppressed, and the radix (hexadecimal) poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Floating Point
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinities, and special "not a number" values ( NaNs) * ''interchange formats:'' encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form * ''rounding rules:'' properties to be satisfied when rounding numbers during arithmetic and conversions * ''operations:'' arithmetic and other operations (such as trigonometric functions) on arithmetic for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign Magnitude
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 mainframe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ones' Complement
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the Binary number, binary representation of the number. The name "ones' complement" refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "Method of complements, 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' complement numeral system can only represent int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Number Representation
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 mainfra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
