Hello. I need help answering a few questions. These questions revolve around the

ID: 3121080 • Letter: H

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Hello. I need help answering a few questions. These questions revolve around the Numberphile video on Youtube 11.11.11. This is the link attached. If it does not work, type in Numberphile 11.11.11 and it should pop up. https://www.youtube.com/watch?v=sPFWfAxIiwg

a.) In the video, he talks about the 13-digit ISBN and how it has a different error-correcting code, Search and provide information about this alternate scheme.

b.) What does it take for an error to "slip past"? That is, can you find any schemes that allow you to start with a valid ISBN, make some type of mistake, and still have a valid ISBN?

c.) Provide information on an error-checking code that can be applied to numbers of arbitrary length

d.) Learn and provide information about an error correcting code. This is a code that allows you to not only detect an error, but also figure out where the error is located an fix it.

e.) Describe other real-life apllications of error checking/ and or error correcting codes besides how it is applied to books.

***Please provide any links to websites to find any information!***

Explanation / Answer

Ans(a):

in 13 digit code , first three digits are uniqe (978)

that's why he is explaining only 10 digits in the video.

you can find more info on

http://mathworld.wolfram.com/ISBN.html

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ans(b):

As the rule says , sum must be multiple of 11, so the missing number can be adjusted to get sum of all digits as a multiple of 11.

that is how they find and correct the invalid ISBN.

ans(c, d, e):

read folowing link to know more about error detection and correction codes and its uses for arbitrary length

http://circuit.ucsd.edu/~yhk/ece154c-spr16/pdfs/ErrorCorrectionI.pdf

you can see the following links too:

https://en.wikipedia.org/wiki/Error_detection_and_correction

http://mathworld.wolfram.com/Error-CorrectingCode.html

http://www.i-programmer.info/babbages-bag/214-error-correcting-codes.html

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