 Technologies and Management received data '124354 239', performs the division by the same prime number '241' and checks to see if the remainder is the same as that contained in the received block. Should the remainder of the division be different from '239' then an error must have occurred in transmission. As discussed above, CRC codes use binary modulo-2 arithmetic and can operate on a binary data block of indefinite length. This sequence of binary data is divided by a modulo-2 binary prime number,2 to produce a remainder between zero and the prime number, which is then appended to the binary sequence to produce a CRC codeword. This operation results in the added sequence becoming modulo-2 divisible by the prime number. To ensure that the original data are transmitted, the data block is appended by a number of zeros before division. The error detection decoder performs the modulo-2 division by the same prime number and if the remainder is zero it checks that no error has occurred. If the remainder is non-zero it follows that an error has occurred. Example 6.4 The binary sequence '11010101' is to be transmitted. Use '1011', a module-2 prime number, as a divisor and calculate the remainder. Form the CRC codeword sequence and verify that it is divisible by the prime number. Answer '11010101' is appended by '000' to produce '11010101000' 11010101000:1011=11110110 and remainder '010' CRC codeword is then formed as 11010101010 which consists of the original data sequence '11010101', and parity bits '010'. You can check that '11010101010' is indeed divisible by '1011'. The CRC divisor is usually written as a modulo-2 polynomial and characterised by the largest degree polynomial. For example four CRC polynomials are used in the 3G standards as shown in Figure 6.6. The polynomial lengths (prime number size) are 24, 16, 12 and 8. The length of a CRC polynomial is generally selected to yield a desired level of undetected error probability. This is the probability that a codeword may be corrupted during transmission into a