# Inthiscase14313x11anexactmultipleofeleven

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Unformatted text preview: = 0 mod 10 After division by 10, the remainder is 0. 2 7/7/2009 CNT 3004 ‐ Polynomials Error Detection Method How ISBN Actually Works If a 'weighted sum' is constructed by multiplying each digit by a different constant, the problem of swapped digits going undetected can be eliminated. Furthermore, the final digit will be computed so that the weighted sum is an exact multiple of 11. In other words, the final digit is computed such that the sum "modulus 11" equals zero. In this case, 143 = 13 x 11, an exact multiple of eleven. ISBN 0 1 3 1 3 9 1 3 9 9 multiplier x10 x9 x8 x7 x6 x5 x4 x3 x2 x1 sum 0 + 9 + 24 + 7 + 18 + 45 + 4 + 9 + 18 + 9 = 143 143 = 0 mod 11 The ISBN is correct if a zero result is obtained. Note that the remainder of "division by eleven" could be any number from 0 to 10. If it works out that the value of the final digit must be 10, the letter 'X' is used instead to complete the ISBN. CNT 3004 ‐ Polynomials Forouzan: ISBN 0‐07‐296775‐7 3 7/7/2009 CNT 3004 ‐ Polynomials Polynomials • Binary values can be represented as polynomials with coefficients {0,1}. • For example, 110011 can be written as 1 x5 + 1 x4 + 0 x3 + 0 x2 + 1 x1 + 1 x0 and simplified as: x5 + x4 + x + 1 The order of a polynomial is the...
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