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Checksum
A checksum is a small-sized datum derived from a block of digital data for the purpose of detecting errors which may have been introduced during its transmission or storage. It is usually applied to an installation file after it is received from the download server. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authenticity. The actual procedure which yields the checksum from a data input is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm will usually output a significantly different value, even for small changes made to the input
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Two's Complement
Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation. For this reason, it is the most important example of a radix complement. The two's complement of an N-bit number is defined as its complement with respect to 2N
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Check Digit
A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits computed by an algorithm from the other digits (or letters) in the sequence input. With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits.Contents1 Design 2 Examples2.1 UPC 2.2 ISBN 10 2.3 ISBN 13 2.4 EAN (GLN, GTIN, EAN numbers administered by GS1) 2.5 Other examples of check digits2.5.1 International 2.5.2 In the USA 2.5.3 In Central America 2.5.4 In Eurasia 2.5.5 In Oceania3 Algorithms 4 See also 5 References 6 External linksDesign[edit]This section does not cite any sources
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Sha1sum
sha1sum is a computer program that calculates and verifies SHA-1 hashes. It is commonly used to verify the integrity of files. It (or a variant) is installed by default in most Unix-like operating systems.[citation needed] Variants include shasum (which permits SHA-1 through SHA-512 hash functions to be selected manually), sha224sum, sha256sum, sha384sum and sha512sum, which use a specific SHA-2 hash function, and sha3sum (which permits SHA-3 through SHA3-512, SHAKE, RawSHAKE and Keccak functions to be selected manually). Versions for Microsoft Windows also exist, and the ActivePerl distribution includes a perl implementation of shasum
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Md5sum
md5sum is a computer program that calculates and verifies 128-bit MD5 hashes, as described in RFC 1321. The MD5 hash functions as a compact digital fingerprint of a file. As with all such hashing algorithms, there is theoretically an unlimited number of files that will have any given MD5 hash. However, it is very unlikely that any two non-identical files in the real world will have the same MD5 hash, unless they have been specifically created to have the same hash. The underlying MD5 algorithm is no longer deemed secure. Thus, while md5sum is well-suited for identifying known files in situations that are not security related, it should not be relied on if there is a chance that files have been purposefully and maliciously tampered. In the latter case, the use of a newer hashing tool such as sha256sum is recommended. md5sum is used to verify the integrity of files, as virtually any change to a file will cause its MD5 hash to change
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Hamming Code
In telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.[1] Richard Hamming invented Hamming codes in 1950 as a way of automatically correcting errors introduced by punched card readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming(7,4)
Hamming(7,4)
code which adds three parity bits to four bits of data.[2] In mathematical terms, Hamming codes are a class of binary linear codes. For each integer r ≥ 2 there is a code with block length n = 2r − 1 and message length k = 2r − r − 1
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Analysis Of Algorithms
In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them. Usually, this involves determining a function that relates the length of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small
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Rolling Checksum
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input. A few hash functions allow a rolling hash to be computed very quickly—the new hash value is rapidly calculated given only the old hash value, the old value removed from the window, and the new value added to the window—similar to the way a moving average function can be computed much more quickly than other low-pass filters. One of the main applications is the Rabin–Karp string search algorithm, which uses the rolling hash described below. Another popular application is the rsync program, which uses a checksum based on Mark Adler's adler-32 as its rolling hash. Low Bandwidth Network Filesystem (LBFS) uses a Rabin fingerprint as its rolling hash. At best, rolling hash values are pairwise independent[1] or strongly universal
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Isopsephy
Isopsephy
Isopsephy
(/ˈaɪsəpˌsɛfi/; ἴσος isos meaning "equal" and ψῆφος psephos meaning "pebble") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number.[1] The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry. Isopsephy
Isopsephy
is related to gematria—the same practice using the Hebrew alphabet and the English alphabet—and the ancient number systems of many other peoples (for the Arabic alphabet
Arabic alphabet
version, see Abjad numerals)
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Datum
Data (/ˈdeɪtə/ DAY-tə, /ˈdætə/ DAT-ə, /ˈdɑːtə/ DAH-tə)[1] is a set of values of qualitative or quantitative variables. Data and information are often used interchangeably; however, the extent to which a set of data is informative to someone depends on the extent to which it is unexpected by that person. The amount of information content in a data stream may be characterized by its Shannon entropy. While the concept of data is commonly associated with scientific research, data is collected by a huge range of organizations and institutions, including businesses (e.g., sales data, revenue, profits, stock price), governments (e.g., crime rates, unemployment rates, literacy rates) and non-governmental organizations (e.g., censuses of the number of homeless people by non-profit organizations). Data is measured, collected and reported, and analyzed, whereupon it can be visualized using graphs, images or other analysis tools
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Exclusive Or
but not is Venn diagram
Venn diagram
of A ⊕ B ⊕ C displaystyle scriptstyle Aoplus Boplus C   ⊕   displaystyle ~oplus ~   ⇔   displaystyle ~Leftrightarrow ~ Exclusive or
Exclusive or
or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).[1] It is symbolized by the prefix operator J[2] and by the infix operators XOR (/ˌɛks ˈɔːr/), EOR, EXOR, ⊻, ⩒, ⩛, ⊕, ↮, and ≢. The negation of XOR is logical biconditional, which outputs true only when both inputs are the same. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator excludes that case. This is sometimes thought of as "one or the other but not both"
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Error-correcting Code
In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding[1] is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is the sender encodes the message in a redundant way by using an error-correcting code (ECC). The American mathematician Richard Hamming
Richard Hamming
pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code.[2] The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. FEC gives the receiver the ability to correct errors without needing a reverse channel to request retransmission of data, but at the cost of a fixed, higher forward channel bandwidth
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Byte
The byte (/baɪt/) is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer[1][2] and for this reason it is the smallest addressable unit of memory in many computer architectures. The size of the byte has historically been hardware dependent and no definitive standards existed that mandated the size – byte-sizes from 1[3] to 48 bits[4] are known to have been used in the past. Early character encoding systems often used six bits, and machines using six-bit and nine-bit bytes were common into the 1960s. These machines most commonly had memory words of 12, 24, 36, 48 or 60 bits, corresponding to two, four, six, eight or 10 six-bit bytes
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Word (data Type)
In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized piece of data handled as a unit by the instruction set or the hardware of the processor. The number of bits in a word (the word size, word width, or word length) is an important characteristic of any specific processor design or computer architecture. The size of a word is reflected in many aspects of a computer's structure and operation; the majority of the registers in a processor are usually word sized and the largest piece of data that can be transferred to and from the working memory in a single operation is a word in many (not all) architectures
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Bank Account
A bank account is a financial account maintained by a bank for a customer. A bank account can be a deposit account, a credit card account, a current account, or any other type of account offered by a financial institution, and represents the funds that a customer has entrusted to the financial institution and from which the customer can make withdrawals. Alternatively, accounts may be loan accounts in which case the customer owes money to the financial institution. The financial transactions which have occurred within a given period of time on a bank account are reported to the customer on a bank statement and the balance of the accounts at any point in time is the financial position of the customer with the institution. The laws of each country specify the manner in which accounts may be opened and operated
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Parity Bit
A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd. Parity bits are used as the simplest form of error detecting code. There are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the occurrences of bits whose value is 1 is counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0. In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number
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