Pls. Answer correctly

Topic : Application of Modular Arithmetic * International Standard Book Number (ISBN)

4.1.5. Application of Modular Arithmetic * International Standard Book Number (ISBN) a. Formula for the ISBN - 13 Check Digit x = 10 - (di+3d2+d3+3d4+ds+3d6+d7+3ds+do+3d10+di1+3d12) Mod 10 If x = 10, then the check digit is 0 Example: 1. Determine the ISBN check digit for the book. How Mathematicians Think by Byers, William (2002). The first 12 digits of the ISBN are 978-0-691-12738-x Solution: Using the formula, we have: x = 10 - [9+3(7)+8+3(0)+6+3(9)+1+3(1)+2+3(7)+3+3(8)] Mod 10 x = 10 - 125 Mod 10 x = 10-5 x = 5, the check digit 2. There is a purchase order for the book The Mathematical Tourist by Ivars Peterson with ISBN 978-0-760-73261-6. Verify if the ISBN is valid. Solution: Using the formula, we have x = 10 - [9+3(7)+8+3(0)+7+3(6)+0+3(7)+3+3(2)+6+3(1)] Mod 10 x = 10 - 102 Mod 10 x = 10 - 2 x=8 . The ISBN is not valid since the check digit is 8 and not 6. * b. Formula for the ISBN - 10 check digits x = 11 - [ (10d1 + 9d2 + 8d3 + 7d4 + 6ds + 5d6 + 4d7 + 3ds + 2do) Mod 11] Example: The ISBN-10 for the "Math Word" is 0-8493-9640-9. Verify if the ISBN is valid Solution: Using the formula: x = 11 - [ (10(0) + 9(8) + 8(4) + 7(9) + 6(3) +5(9) + 4(6) + 3(4) + 2(0)) Mod 11] x= 11 - 266 Mod 11 x = 11 - 2 : The ISBN is valid since the computed check digit is 9, which conforms with last digit of the ISBN Universal Product Code (UPC) Formula: x = 10 - [ (3d1 + d2 + 3d3 + d4 + 3ds + d6 + 3d7 + de + 3d + d10 + 3d11) Mod 10] If x = 10, then check digit is 0. Example: The first 11 digits of the UPC of the film "Alice in Wonderland" are 7-86936-79798-X. Find its check digit. Solution: using the formula, we have x = 10 - [ 3(7) +8+ 3(6) +9+3(3) +6+3(7) +9 +3(7)+9+3(8)] Mod 10 x = 10 - 155 Mod 10 x = 10 - 5 x= 5 : The check digit is 5. Example: Is 1-32342-65933-9 a valid UPC? Solution: Using the formula we have x = 10 - [ 3(1) +3+ 3(2) +3+3(4) +2+3(6)+5+ 3(9)+ 3 + 3(3)] Mod 10 x = 10 - 91 Mod 10 1= 9 The UPC is valid since 9 conforms with the last digit of the UPC. Note: Common error . Transposition errors - occur when two adjacent digits are interchanged. 2. If la-bl = 5, the UPC coding method will not catch the transposition order.