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In fact, a few protocols use the CRC as the message delimiter, a technique called CRC-based framing. (This requires multiple frames to detect acquisition or loss of framing, so is limited to applications where the frames are a known length, and the frame contents are sufficiently random that valid CRCs in misaligned data are rare.)
To compute an n-bit binary CRC, line the bits representing the input in a row, and position the (n + 1)-bit pattern representing the CRC's divisor (called a "polynomial") underneath the left end of the row. In this example, we shall encode 14 bits of message with a 3-bit CRC, with a polynomial x 3 + x + 1.
Because a CRC is based on division, no polynomial can detect errors consisting of a string of zeroes prepended to the data, or of missing leading zeroes. However, see § Variations . All single bit errors will be detected by any polynomial with at least two terms with non-zero coefficients.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
The "chart" actually consists of a pair of charts: one, the individuals chart, displays the individual measured values; the other, the moving range chart, displays the difference from one point to the next.
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cksum is a command in Unix and Unix-like operating systems that generates a checksum value for a file or stream of data. The cksum command reads each file given in its arguments, or standard input if no arguments are provided, and outputs the file's 32-bit cyclic redundancy check (CRC) checksum and byte count. [1]
CRC Handbook of Chemistry and Physics, a science reference handbook published by CRC Press CRC Standard Mathematical Tables , a mathematics reference handbook published by CRC Press Cyclic redundancy check , a type of hash function used to produce a checksum in order to detect errors in data storage or transmission