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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.
One of the most commonly encountered CRC polynomials is known as CRC-32, used by (among others) Ethernet, FDDI, ZIP and other archive formats, and PNG image format. Its polynomial can be written msbit-first as 0x04C11DB7, or lsbit-first as 0xEDB88320.
These inversions are extremely common but not universally performed, even in the case of the CRC-32 or CRC-16-CCITT polynomials. They are almost always included when sending variable-length messages, but often omitted when communicating fixed-length messages, as the problem of added zero bits is less likely to arise.
A CRC has properties that make it well suited for detecting burst errors. CRCs are particularly easy to implement in hardware and are therefore commonly used in computer networks and storage devices such as hard disk drives. The parity bit can be seen as a special-case 1-bit CRC.
Name Length Type Pearson hashing: 8 bits (or more) XOR/table Paul Hsieh's SuperFastHash [1]: 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function
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The TCP checksum is a weak check by modern standards and is normally paired with a CRC integrity check at layer 2, below both TCP and IP, such as is used in PPP or the Ethernet frame. However, introduction of errors in packets between CRC-protected hops is common and the 16-bit TCP checksum catches most of these.
A pregnant woman tested positive for opioids after eating an everything bagel, which had poppy seeds. (Getty Images) (Getty Images)
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