MATHM | Check Codes and Check Digits

• is mainly used in products sold in department stores and groceries.

  Universal Product Code (UPC)
• Check digit is the last digit
• The UPC consists of barcodes with 12 digits where the last one is the check digit.
• used on books where usually found at the last page of the book.

  International Standard Book Number (ISBN)
• ISBN can be ISBN-10 or ISBN-13 where they used 10 digits or 13 digits string of number respectively with the last digit as the check digit
• The United States Postal Services (USPS) is consist of 11 digits, while the Credit Card uses 16 digits where both of them uses their last digits as the check digits.
• Formula for: UPC

  
• Formula for: ISBN-10

  
• Formula for: ISBN-13

  
• Formula for: UPS

  
• Formula for: Credit Card