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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.
(To be precise, the result is the CRC, with zero preset but with post-invert, of the inversion pattern.) Once this constant has been obtained (e.g. by performing a one-pass CRC generate/check on an arbitrary message), it can be used directly to verify the correctness of any other message checked using the same CRC algorithm.
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. [54]