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Math Help - Codes

  1. #1
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    Codes

    *Barcodes - introduce an 11 digit code for each item, with the fist 10 digits x1,x2....x10 being information digits and x11 being the check digit. Each digit is a decimal digit (one of 0,1,.......8,9). The check digit is calculated so that:
    x1-x2+x3-x4+x5-x6+x7-x8+x9-x10+x11 =0 (mod 10)

    - calculate the check digit if the information digits are 0987654321.

    -explain why the code is not able to detect the
    interchange of two adjacent digits for certain values of the digit!!!!! help

    Any help is greatly appreciated!!!
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  2. #2
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    Quote Originally Posted by Jacko View Post
    -explain why the code is not able to detect the
    interchange of two adjacent digits for certain values of the digit!!!!! help
    If the two adjacent digits x and y are interchanged then x-y will become y-x. Suppose that x-y=5. This will become -5, which cannot be distinguished from +5 (mod 10). So if two adjacent digits differ by 5 then the check digit will stay the same when they are interchanged.
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