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Sixteen-bit messages are transmitted using a Hamming code How many check bits are needed to ensure that the receiver can detect and correct single bit errors Show the bit pattern transmitted for the?

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2009-06-26 19:59:55
2009-06-26 19:59:55

BY USING FORMULA (M+R+1)<=2r 011110110011001110101 ----

The formula

d + p + 1 <= 2^p

(where d is the number of data bits and p is the number of check bits)

indicates that we need at least 5 check bits in order to correct single-bit errors in blocks of 16 data bits -- a (21,16) code. SECDED requires 6 check bits for blocks of 16 data bits.

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Hamming code is a linear error-correcting code named after its inventor, Richard Hamming. Hamming codes can detect and correct single-bit errors, and can detect (but not correct) double-bit errors. In other words, the Hamming distance between the transmitted and received code-words must be zero or one for reliable communication.


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Hamming Codes are used for detecting multiple errors in a transmitted code. It can trace missing parts of a code that may have been lost through transmission and it can also tell you if an error has occurred in any bit of the code using Modulo Tow Arithmetic.Read more: http://wiki.answers.com/What_are_hamming_codes_used_for#ixzz21gh0KNMn


Hamming Code for A: 010010000100 (The strike numbers are the check bits) Hamming Code for 3: 001100011101


hamming code between 1000110 and 1110100 can be calculated by just exoring both codes with each other as follow: 1000110 1110100 ------------ 0110010 now by counting the ones in the result that gives 3 then hamming dictance = 3


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Hamming Code is a system involving multiple parity bits per word such that not only can errors be detected but certain types of errors can be corrected. The first Hamming Code was called (7,4) because it added 3 parity bits to 4 data bits, creating a 7 bit code. See link for example.


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It depends on what you are doing. The cyclic redundancy check will only detect an error, while the hamming code can also correct many types of errors. However to perform this correction the extra error detection parity bits required in hamming code are many more than the bits needed for cyclic redundancy check, per data byte being checked. Normally cyclic redundancy check is done on large block of data that can be resent or retried to get the correct block of data (e.g. telecommunication channels, disk sectors). Normally hamming code is done on individual bytes or words of computer memory.


When the data link transfer time is long, hamming allows corrections to be applied as data is received, whereas feedback would be needed to request repeating the data this could result in very long delays in data reception!When data is being read from RAM, hamming allows corrections, whereas there might be no good copy of the data in RAM to attempt rereading in response to feedback.


A special system of multiple parity bits (e.g. Hamming parity) that allows not only error detection but limited error correction.Ordinary single bit parity can detect reliably single bit errors.Hamming parity can correct single bit errors and detect reliably double bit errors.


In comparing two bit patterns, the Hamming distance is the count of bits different in the two patterns. More generally, if two ordered lists of items are compared, the Hamming distance is the number of items that do not identically agree. This distance is applicable to encoded information, and is a particularly simple metric of comparison, often more useful than the city-block distance (the sum of absolute values of distances along the coordinate axes) or Euclidean distance (the square root of the sum of squares of the distances along the coordinate axes). also Metric.



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