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Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunication , ERROR DETECTION AND CORRECTION or ERROR CONTROL are techniques that enable reliable delivery of digital data over unreliable communication channels . Many communication channels are subject to channel noise , and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases
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Damm Algorithm
In error detection , the DAMM ALGORITHM is a check digit algorithm that detects all single-digit errors and all adjacent transposition errors . It was presented by H. Michael Damm in 2004. CONTENTS * 1 Strengths and weaknesses * 2 Design * 3 Algorithm
Algorithm
* 3.1 Validating a number against the included check digit * 3.2 Calculating the check digit * 4 Example * 4.1 Calculating the check digit * 4.2 Validating a number against the included check digit * 4.3 Graphical illustration * 5 References * 6 External links STRENGTHS AND WEAKNESSESThe Damm algorithm
Damm algorithm
is similar to the Verhoeff algorithm . It too will detect all occurrences of the two most frequently appearing types of transcription errors , namely altering one single digit, and transposing two adjacent digits (including the transposition of the trailing check digit and the preceding digit)
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Divisor
In mathematics , a DIVISOR of an integer n {displaystyle n} , also called a FACTOR of n {displaystyle n} , is an integer m {displaystyle m} that may be multiplied by some other integer to produce n {displaystyle n} . In this case one says also that n {displaystyle n} is a MULTIPLE of m . {displaystyle m.} An integer n {displaystyle n} is DIVISIBLE by another integer m {displaystyle m} if m {displaystyle m} is a divisor of n {displaystyle n} ; this implies dividing n {displaystyle n} by m {displaystyle m} leaves no remainder
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Polynomial Long Division
In algebra , POLYNOMIAL LONG DIVISION is an algorithm for dividing a polynomial by another polynomial of the same or lower degree , a generalised version of the familiar arithmetic technique called long division . It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. Sometimes using a shorthand version called synthetic division is faster, with less writing and fewer calculations. Polynomial
Polynomial
long division is an algorithm that implements the Euclidean division of polynomials , which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that A = BQ + R, and either R = 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R, which means that Q and R do not depend on the method used to compute them
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Ones' Complement
The ONES\' COMPLEMENT of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa). The ones' complement of the number then behaves like the negative of the original number in some arithmetic operations. To within a constant (of −1), the ones' complement behaves like the negative of the original number with binary addition . However, unlike two\'s complement , these numbers have not seen widespread use because of issues such as the offset of −1, that negating zero results in a distinct negative zero bit pattern, less simplicity with arithmetic borrowing , etc. 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
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Modular Arithmetic
In mathematics , MODULAR ARITHMETIC is a system of arithmetic for integers , where numbers "wrap around" upon reaching a certain value—the MODULUS (plural MODULI). The modern approach to modular arithmetic was developed by Carl Friedrich Gauss
Carl Friedrich Gauss
in his book Disquisitiones Arithmeticae , published in 1801. A familiar use of modular arithmetic is in the 12-hour clock
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. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours. Because the hour number starts over after it reaches 12, this is arithmetic modulo 12. According to the definition below, 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12
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Preimage Attack
In cryptography , a PREIMAGE ATTACK on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage . In the context of attack, there are two types of preimage resistance: * preimage resistance: for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output, i.e., given y, it is difficult to find an x such that h(x) = y. * second-preimage resistance: it is computationally infeasible to find any second input which has the same output as that of a specified input, i.e., given x, it is difficult to find a second preimage x′ ≠ x such that h(x) = h(x′). These can be compared with a collision resistance , in which it is computationally infeasible to find any two distinct inputs x, x′ that hash to the same output, i.e., such that h(x) = h(x′)
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Error Handling
EXCEPTION HANDLING is the process of responding to the occurrence, during computation , of exceptions – anomalous or exceptional conditions requiring special processing – often changing the normal flow of program execution . It is provided by specialized programming language constructs, computer hardware mechanisms like interrupts or operating system IPC facilities like signals . In general, an exception breaks the normal flow of execution and executes a pre-registered exception handler. The details of how this is done depends on whether it is a hardware or software exception and how the software exception is implemented. Some exceptions, especially hardware ones, may be handled so gracefully that execution can resume where it was interrupted
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Finite Field
In mathematics , a FINITE FIELD or GALOIS FIELD (so-named in honor of Évariste Galois ) is a field that contains a finite number of elements . As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number. The number of elements of a finite field is called its order. A finite field of order q exists if and only if the order q is a prime power pk (where p is a prime number and k is a positive integer). All fields of a given order are isomorphic . In a field of order pk, adding p copies of any element always results in zero; that is, the characteristic of the field is p. In a finite field of order q, the polynomial Xq − X has all q elements of the finite field as roots . The non-zero elements of a finite field form a multiplicative group
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Dividend
A DIVIDEND is a payment made by a corporation to its shareholders , usually as a distribution of profits . When a corporation earns a profit or surplus, the corporation is able to re-invest the profit in the business (called retained earnings ) and pay a proportion of the profit as a dividend to shareholders. Distribution to shareholders may be in cash (usually a deposit into a bank account) or, if the corporation has a dividend reinvestment plan , the amount can be paid by the issue of further shares or share repurchase
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Timeout (computing)
In telecommunications and related engineering (including computer networking and programming ), the term TIMEOUT or TIME-OUT has several meanings, including: * A network parameter related to an enforced event designed to occur at the conclusion of a predetermined elapsed time . * A specified period of time that will be allowed to elapse in a system before a specified event is to take place, unless another specified event occurs first; in either case, the period is terminated when either event takes place. Note: A timeout condition can be canceled by the receipt of an appropriate time-out cancellation signal . * An event that occurs at the end of a predetermined period of time that began at the occurrence of another specified event. The timeout can be prevented by an appropriate signal.Timeouts allow for more efficient usage of limited resources without requiring additional interaction from the agent interested in the goods that cause the consumption of these resources
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Frame (networking)
A FRAME is a digital data transmission unit in computer networking and telecommunication . A frame typically includes frame synchronization features consisting of a sequence of bits or symbols that indicate to the receiver, the beginning, and end of the payload data within the stream of symbols or bits it receives. If a receiver is connected to the system in the middle of a frame transmission, it ignores the data until it detects a new frame synchronization sequence. In the OSI model of computer networking, a frame is the protocol data unit at the data link layer . Frames are the result of the final layer of encapsulation before the data is transmitted over the physical layer. A frame is "the unit of transmission in a link layer protocol, and consists of a link layer header followed by a packet." Each frame is separated from the next by an interframe gap
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Data Integrity
DATA INTEGRITY is the maintenance of, and the assurance of the accuracy and consistency of, data over its entire life-cycle , and is a critical aspect to the design, implementation and usage of any system which stores, processes, or retrieves data. The term data integrity is broad in scope and may have widely different meanings depending on the specific context – even under the same general umbrella of computing . This article provides only a broad overview of some of the different types and concerns of data integrity. Data
Data
integrity is the opposite of data corruption , which is a form of data loss . The overall intent of any data integrity technique is the same: ensure data is recorded exactly as intended (such as a database correctly rejecting mutually exclusive possibilities,) and upon later retrieval, ensure the data is the same as it was when it was originally recorded
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Cryptographic Hash Function
A CRYPTOGRAPHIC HASH FUNCTION is a special class of hash function that has certain properties which make it suitable for use in cryptography . It is a mathematical algorithm that maps data of arbitrary size to a bit string of a fixed size (a hash function ) which is designed to also be a one-way function , that is, a function which is infeasible to invert. The only way to recreate the input data from an ideal cryptographic hash function's output is to attempt a brute-force search of possible inputs to see if they produce a match, or use a rainbow table of matched hashes. Bruce Schneier
Bruce Schneier
has called one-way hash functions "the workhorses of modern cryptography". The input data is often called the message, and the output (the hash value or hash) is often called the message digest or simply the digest
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Remainder
In mathematics, the REMAINDER is the amount "left over" after performing some computation. In arithmetic , the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra , the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor. Formally it is also true that a remainder is what is left after subtracting one number from another, although this is more precisely called the difference. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a function is approximated by a series expansion and the error expression ("the rest") is referred to as the remainder term
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Computer Network
A COMPUTER NETWORK or DATA NETWORK is a digital telecommunications network which allows nodes to share resources. In computer networks, networked computing devices exchange data with each other using a data link . The connections between nodes are established using either cable media or wireless media . Network computer devices that originate, route and terminate the data are called network nodes. Nodes can include hosts such as personal computers , phones , servers as well as networking hardware . Two such devices can be said to be networked together when one device is able to exchange information with the other device, whether or not they have a direct connection to each other. In most cases, application-specific communications protocols are layered (i.e. carried as payload ) over other more general communications protocols. This formidable collection of information technology requires skilled network management to keep it all running reliably
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