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Computation Of Cyclic Redundancy Checks
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive or operations replace subtractions. Division of this type is efficiently realised in hardware by a modified shift register, and in software by a series of equivalent algorithms, starting with simple code close to the mathematics and becoming faster (and arguably more obfuscated) through byte-wise parallelism and space–time tradeoffs. Various CRC standards extend the polynomial division algorithm by specifying an initial shift register value, a final Exclusive-Or step and, most critically, a bit ordering (endianness). As a result, the code seen in practice deviates confusingly from "pure" division, and the register may shift left or right. Example As an example of implementing polynomial divisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Redundancy Check
A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a short ''check value'' attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated and, in the event the check values do not match, corrective action can be taken against data corruption. CRCs can be used for error correction (see bitfilters). CRCs are so called because the ''check'' (data verification) value is a ''redundancy'' (it expands the message without adding information) and the algorithm is based on ''cyclic'' codes. CRCs are popular because they are simple to implement in binary hardware, easy to analyze mathematically, and particularly good at detecting common errors caused by noise in transmission channels. Because the check value has a fixed length, the function that generates it is occasionally used as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carry (arithmetic)
In elementary arithmetic, a carry is a Numerical digit, digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to addition, add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow. Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer. Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder (electronics), adder circuits. Manual arithmetic A typical example of carry is in the following pencil-and-paper addition: 1 27 + 59 ---- 86 7 + 9 = 16, and the digit 1 (number), 1 is the carry. The opposite is a borrow, as in − ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RS-232
In telecommunications, RS-232 or Recommended Standard 232 is a standard introduced in 1960 for serial communication transmission of data. It formally defines signals connecting between a ''DTE'' (''data terminal equipment'') such as a computer terminal or PC, and a ''DCE'' ('' data circuit-terminating equipment'' or '' data communication equipment''), such as a modem. The standard defines the electrical characteristics and timing of signals, the meaning of signals, and the physical size and pinout of connectors. The current version of the standard is ''TIA-232-F Interface Between Data Terminal Equipment and Data Circuit-Terminating Equipment Employing Serial Binary Data Interchange'', issued in 1997. The RS-232 standard had been commonly used with serial ports and serial cables. It is still widely used in industrial communication devices. A serial port complying with the RS-232 standard was once a standard feature of many types of computers. Personal computers used them ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8B/10B Encoding
In telecommunications, 8b/10b is a line code that maps 8-bit words to 10-bit symbols to achieve DC balance and bounded disparity, and at the same time provide enough state changes to allow reasonable clock recovery. This means that the difference between the counts of ones and zeros in a string of ''at least'' 20 bits is no more than two, and that there are not more than five ones or zeros in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal. An 8b/10b code can be implemented in various ways with focus on different performance parameters. One implementation was designed by K. Odaka for the DAT digital audio recorder. Kees Schouhamer Immink designed an 8b/10b code for the DCC audio recorder. The IBM implementation was described in 1983 by Al Widmer and Peter Franaszek. IBM implementation As the scheme name suggests, eight bits of data are transmitted as a 10-bit entity called a ''symbol'', or ''charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Transmission
In data transmission, parallel communication is a method of conveying multiple binary digits (bits) simultaneously using multiple conductors. This contrasts with serial communication, which conveys only a single bit at a time; this distinction is one way of characterizing a communications link. The basic difference between a parallel and a serial communication channel is the number of electrical conductors used at the physical layer to convey bits. Parallel communication implies more than one such conductor. For example, an 8-bit parallel channel will convey eight bits (or a byte) simultaneously, whereas a serial channel would convey those same bits sequentially, one at a time. If both channels operated at the same clock speed, the parallel channel would be eight times faster. A parallel channel may have additional conductors for other signals, such as a clock signal to pace the flow of data, a signal to control the direction of data flow, and handshaking signals. Parallel com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardware (computer)
Computer hardware includes the physical parts of a computer, such as the central processing unit (CPU), random-access memory (RAM), motherboard, computer data storage, graphics card, sound card, and computer case. It includes external devices such as a monitor, mouse, keyboard, and speakers. By contrast, software is a set of written instructions that can be stored and run by hardware. Hardware derived its name from the fact it is '' hard'' or rigid with respect to changes, whereas software is ''soft'' because it is easy to change. Hardware is typically directed by the software to execute any command or instruction. A combination of hardware and software forms a usable computing system, although other systems exist with only hardware. History Early computing devices were more complicated than the ancient abacus date to the seventeenth century. French mathematician Blaise Pascal designed a gear-based device that could add and subtract, selling around 50 models. The stepped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit-serial Architecture
In computer architecture, bit-serial architectures send data one bit at a time, along a single wire, in contrast to Parallel transmission, bit-parallel word (computer architecture), word architectures, in which data values are sent all bits or a word at once along a group of wires. All digital computers built before 1951, and most of the early massively parallel (computing), massive parallel processing machines used a bit-serial architecture—they were serial computers. Bit-serial architectures were developed for digital signal processing in the 1960s through 1980s, including efficient structures for bit-serial multiplication and accumulation. The HP Nut processor used in many Hewlett-Packard calculators operated bit-serially. Assuming N is an arbitrary integer number, N serial processors will often take less FPGA area and have a higher total performance than a single N-bit parallel processor. See also * Serial computer * 1-bit computing * Bit banging * Bit slicing * BKM a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microcontrollers
A microcontroller (MC, uC, or μC) or microcontroller unit (MCU) is a small computer on a single integrated circuit. A microcontroller contains one or more CPUs (processor cores) along with memory and programmable input/output peripherals. Program memory in the form of NOR flash, OTP ROM, or ferroelectric RAM is also often included on the chip, as well as a small amount of RAM. Microcontrollers are designed for embedded applications, in contrast to the microprocessors used in personal computers or other general-purpose applications consisting of various discrete chips. In modern terminology, a microcontroller is similar to, but less sophisticated than, a system on a chip (SoC). A SoC may include a microcontroller as one of its components but usually integrates it with advanced peripherals like a graphics processing unit (GPU), a Wi-Fi module, or one or more coprocessors. Microcontrollers are used in automatically controlled products and devices, such as automobile engi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associative
In mathematics, the associative property is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: \begin (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24 . \end Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division (mathematics), division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as noncommutative operations. The idea that simple operations, such as the multiplication (mathematics), multiplication and addition of numbers, are commutative was for many centuries implicitly assumed. Thus, this property was not named until the 19th century, when new algebraic structures started to be studied. Definition A binary operation * on a Set (mathematics), set ''S'' is ''commutative'' if x * y = y * x for all x,y \in S. An operat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exclusive OR
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, , \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduction Exclusive disjunction essentially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (computer Science)
In software development, an object is an entity that has state, behavior, and identity. An object can model some part of reality or can be an invention of the design process whose collaborations with other such objects serve as the mechanisms that provide some higher-level behavior. Put another way, an object represents an individual, identifiable item, unit, or entity, either real or abstract, with a well-defined role in the problem domain. A programming language can be classified based on its support for objects. A language that provides an encapsulation construct for state, behavior, and identity is classified as object-based. If the language also provides polymorphism and inheritance it is classified as object-oriented. A language that supports creating an object from a class is classified as class-based. A language that supports object creation via a template object is classified as prototype-based. The concept of object is used in many different software contexts, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
