Explanation The test (7) is given below: A universal product number is a 12 digit number whose digits a 1 , a 2 , a 3 , a 4 , a 5 , ..... a 10 , a 11 , a 12 follow the test given below: 3 ( Sum of digits at odd positions ) + ( Sum of digits at even positions ) = 0 ( mod 10 ) No, the test will not always detect transposition errors. Let a 1 − a 2 a 3 a 4 a 5 a 6 − a 7 a 8 a 9 a 10 a 11 − x be a valid universal product code. Thus, A = 3 ( a 1 + a 3 + a 5 + a 7 + a 9 + a 11 ) + ( a 2 + a 4 + a 6 + a 8 + a 10 + x ) = 0 ( mod 10 ) If a 3 and a 4 are transposed the error will not be detected if B = 3 ( a 1 + a 4 + a 5 + a 7 + a 9 + a 11 ) + ( a 2 + a 3 + a 6 + <

3rd Edition

ISBN: 9780131679955

Author: Edgar G. Goodaire

Publisher: Prentice Hall

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Chapter 4.5, Problem 15E

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If the test in (7) detect transposition errors; that is, will it notice if two (different) adjacent digits have been interchanged.

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Chapter 4.5, Problem 14E

Chapter 4.5, Problem 16E

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If the test in (7) detect transposition errors; that is, will it notice if two (different) adjacent digits have been interchanged.

Solution Summary: The author explains that the test will not detect transposition errors if two adjacent digits have been interchanged.

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If the test in (7) detect transposition errors; that is, will it notice if two (different) adjacent digits have been interchanged.

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Chapter 4 Solutions