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Question Suppose you are given a 7 digit number which is a UPC. Prove that if a...

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Advance Math

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Suppose you are given a 7 digit number which is a UPC. Provethat if a mistake is made when scanning the number, causing onedigit to be read incorrectly, then you will be able to tell that anerror has been made.

Extra information.

A number is a Universal Product Code (UPC) if its last digitagrees with the following computations:

• The sum of the odd position digits (not including the last) isM. That is we add the first digit to the third digit to the fifthdigit etc.

• The sum of the even position digits (not including the last)is N. •

c = (3M + N)%10.

• If c = 0 then the check digit is 0.

• If c 6= 0, then the check digit is 10 ? c.

An example with number 1231242.

1) you add all odd-positioned digits except the last one:

M=1+3+2=6

2) add all even positioned digits, not including the lastone:

N=2+1+4=7

3) c=(3M+N)%10=(6*3+7)%10=5

4) the check digit is 10-5=5

So 1231242 is not a UPC.

However, if we change the last digit to be 5, then it will beUPC. That is 1231245 is a UPC

Answer & Explanation Solved by verified expert
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The UPC includes a check digit to detect common data    See Answer
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