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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 mainfr ... [...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] |
End-around Borrow
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the 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 " 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 integers in the range −(2N−1−1) t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative 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 is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base −2
A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base is equal to for some natural number (). Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the information normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent. The common names for negative-base positional numeral systems are formed by prefixing ''nega-'' to the name of the corresponding positive-base system; for example, negadecimal (base −10) corresponds to decim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CDC 160 Series
The CDC 160 series was a series of minicomputers built by Control Data Corporation. The CDC 160 and CDC 160-A were 12-bit minicomputers built from 1960 to 1965; the CDC 160G was a 13-bit minicomputer, with an extended version of the CDC 160-A instruction set, and a compatibility mode in which it did not use the 13th bit. The 160 was designed by Seymour Cray - reportedly over a long three-day weekend. It fit into the desk where its operator sat. The 160 architecture uses ones' complement arithmetic with end-around carry. NCR joint-marketed the 160-A under its own name for several years in the 1960s. Overview A publishing company that purchased a CDC 160-A described it as "a single user machine with no batch processing capability. Programmers and/or users would go to the computer room, sit at the console, load the paper tape bootstrap and start up a program." The CDC 160-A was a simple piece of hardware, and yet provided a variety of features which were scaled-down capabilitie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CDC 3000
The CDC 3000 series ("thirty-six hundred" or "thirty-one hundred") are a family of mainframe computers from Control Data Corporation (CDC). The first member, the CDC 3600, was a 48-bit system introduced in 1963. The same basic design led to the cut-down CDC 3400 of 1964, and then the 24-bit CDC 3300, 3200 and 3100 introduced between 1964 and 1965. The 3000 series replaced the earlier CDC 1604 and CDC 924 systems. The line was a great success and became CDC's cash cow through the 1960s. The series significantly outsold the much faster and more expensive machines in the CDC 6000 series, but the performance of the 3000's relative to other vendors quickly eroded. The line was phased out of production in the early 1970s in favour of new members of the 6000 series, and then the CDC Cyber series, initially based on the 6600 design but spanning a wide range of performance. Specifications Upper 3000 series The upper 3000 series uses a 48-bit word size. The first 3000 machine to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CDC 6000 Series
The CDC 6000 series is a discontinued family of mainframe computers manufactured by Control Data Corporation in the 1960s. It consisted of the CDC 6200, CDC 6300, #Versions, CDC 6400, #Versions, CDC 6500, CDC 6600 and #Versions, CDC 6700 computers, which were all extremely rapid and efficient for their time. Each is a large, Solid-state electronics, solid-state, general-purpose, digital computer that performs scientific and business data processing as well as multiprogramming, multiprocessing, Remote Job Entry, time-sharing, and data management tasks under the control of the operating system called CDC SCOPE, SCOPE (Supervisory Control Of Program Execution). By 1970 there also was a time-sharing oriented operating system named KRONOS. They were part of the first generation of supercomputers. The 6600 was the flagship of Control Data's 6000 series. Overview The CDC 6000 series computers are composed of four main functional devices: * the central memory * one or two high-speed cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UNIVAC 1100
The UNIVAC 1100/2200 series is a series of compatible 36-bit computer systems, beginning with the UNIVAC 1107 in 1962, initially made by UNIVAC, Sperry Rand. The series continues to be supported today by Unisys Corporation as the ClearPath Dorado Series. The solid-state electronics, solid-state 1107 model number was in the same sequence as the earlier vacuum-tube computers, but the early computers were not compatible with their Transistor computer, solid-state successors. Architecture Data formats *Fixed-point arithmetic, Fixed-point, either integer or fraction (mathematics), fraction **Whole word – 36-bit (ones' complement) **Half word – two 18-bit fields per word (unsigned or ones' complement) **Third word – three 12-bit fields per word (ones' complement) **Quarter word – four 9-bit fields per word (unsigned) **Sixth word – six 6-bit fields per word (unsigned) *Floating point **Single precision – 36 bits: sign bit, 8-bit characteristic, 27-bit mantissa **Double prec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both computer hardware, 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 calculation, calculating. In earlier times, it was used in reference to the action performed by Mechanical computer, mechanical computing machines, and before that, to Computer (occupation), 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LINC
The LINC (Laboratory INstrument Computer) is a 12-bit, 2048-word transistorized computer. The LINC is considered by some to be the first minicomputer and a forerunner to the personal computer. Originally named the Linc, suggesting the project's origins at MIT's Lincoln Laboratory, it was renamed LINC after the project moved from the Lincoln Laboratory. The LINC was designed by Wesley A. Clark and Charles Molnar. The LINC and other "MIT Group" machines were designed at MIT and eventually built by Digital Equipment Corporation (DEC) and Spear Inc. of Waltham, Massachusetts (later a division of Becton, Dickinson and Company). The LINC sold for more than $40,000 at the time. A typical configuration included an enclosed 6'X20" rack; four boxes holding (1) two tape drives, (2) display scope and input knobs, (3) control console and (4) data terminal interface; and a keyboard. The LINC interfaced well with laboratory experiments. Analog inputs and outputs were part of the basic de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
