# Modular Arithmetic - Thinking Mathematically

1) The definition of length, weight, and modulus of a check digit scheme.

2) Choose one of the schemes discussed in the worksheets and describe it in terms of length weight and modulus. Then illustrate the check digit computation on an ID number valid for that scheme (for example on a book or some product you have handy).

3) Subject the ID number you chose in 2) to a single digit error to demonstrate how that error is detected. Then subject it to a transposition error and explain why the error is detected (if it is) or why it isn't (if it isn't).

4) Create a length 4 check digit scheme (you pick the weights and modulus) and analyze its ability to detect single digit errors and transposition errors.

Please see attachments to view worksheets.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1). The definition of length, weight, and modulus of a check digit scheme.

Check digit schemes are numbers appended to an identification number that allow the accuracy of information stored to be checked by an algorithm.

Error detecting codes are algorithms that utilize check digits to detect, but not to correct, errors in entering identification numbers.

A code is a n-tuple, i.e., as

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Please see attachment for the rest of the solution.

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