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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.
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By far the most popular FCS algorithm is a cyclic redundancy check (CRC), used in Ethernet and other IEEE 802 protocols with 32 bits, in X.25 with 16 or 32 bits, in HDLC with 16 or 32 bits, in Frame Relay with 16 bits, [3] in Point-to-Point Protocol (PPP) with 16 or 32 bits, and in other data link layer protocols.
The first word identifies whether the sector is on the upper or lower side of the platter, followed by the track number (1 to 256 or 1 to 512) and finally the sector number (1 to 40). The second word is all zeros. The third word contains a cyclic redundancy check (CRC) of the header. This is checked during a read operation.