Thread: 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!!!

Originally Posted by Jacko

-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.