A check digit is a way of verifying that a particular sequence of numbers has been entered correctly. They are found in many places; for example, bar codes, credit card account numbers, and Australian tax file numbers. In this question we will study the example of 13-digit ISBNS, which are used to identify books. 9788175 257665 EAN Group (a) (1) Publisher Example of 13-digit ISBN Source: https://en.wikipedia.org/wiki/SBN (ii) (e) Title Check digit The image on the left gives an example of a book with ISBN-13 number 9788175257665. You can see that each group of digits identifies a different characteristic of the book, with the check digit being the last number. Choose your favourite book published after 1 January 2007 and locate the ISBN-13 number, which is usually located under the barcode on the back of the book. Sum all the odd-valued digits and find the answer modulo 10, i.e. Y = x1 + x3 + x5 + x7 + x9 + x11+x13 (mod 10) [1] Sum all the even-valued digits, multiply by 3, and find the answer modulo 10, i.e. Z = 3(x + x4 + x6 + x + x10 + x12) (mod 10) (iii) Add your answers from a(i) and a(ii) together and find the answer modulo 10. (b) All ISBN-13 numbers have the property that the calculation in (a) gives the answer of zero. Use this fact to find the missing check digit in the ISBN-13 number 978-1-787-47730-?. (c) What would happen to the calculation of the check digit in (b) if you accidentally swapped the position of two (different) adjacent digits in the ISBN-13 number? [1] Research the concept of check digits and briefly give details of another example which uses a different function and modulus than ISBN-13. [1] [2] **(d) Describe and explain another type of error that could occur while typing in an ISBN-13 number, which would NOT be detected by the check digit. [2] [2] [1]