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As an example of implementing polynomial division in hardware, suppose that we are trying to compute an 8-bit CRC of an 8-bit message made of the ASCII character "W", which is binary 01010111 2, decimal 87 10, or hexadecimal 57 16.
For example, some 16-bit CRC schemes swap the bytes of the check value. Omission of the high-order bit of the divisor polynomial: Since the high-order bit is always 1, and since an n -bit CRC must be defined by an ( n + 1 )-bit divisor which overflows an n -bit register , some writers assume that it is unnecessary to mention the divisor's high ...
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.
Catalyst 6500 Series Command Reference, 7.6, for example CPE: Customer premises equipment Telecom Telecom Glossary: CPU: Central processing Unit Microprocessor Wikipedia: CRC: Cyclic redundancy check Link and other layers 24 References here. CRC-16-CCITT: Cyclic redundancy check (X.25, HDLC) Link layers Reference on CRC page. CRT: Cathode Ray Tube
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.
It also defines the ITU-T standard CRC-32 polynomial as x 32 +x 26 +x 23 +x 22 +x 16 +x 12 +x 11 +x 10 +x 8 +x 7 +x 5 +x 4 +x 2 +x+1, and includes the LAPM framing protocol. V.42bis , also an adaptive data compression standard, is based on the Lempel Ziv dynamic dictionary approach, and may go to "transparent mode," in which data is transmitted ...
One example is the Linux kernel's EDAC subsystem (previously known as Bluesmoke), which collects the data from error-checking-enabled components inside a computer system; besides collecting and reporting back the events related to ECC memory, it also supports other checksumming errors, including those detected on the PCI bus.
X.25 is an ITU-T standard protocol suite for packet-switched data communication in wide area networks (WAN). It was originally defined by the International Telegraph and Telephone Consultative Committee (CCITT, now ITU-T) in a series of drafts and finalized in a publication known as The Orange Book in 1976.