Check Digits | Computer for GCSE/IGCSE - Year 11 PDF Download

Check Digits

• Check Digits are used to determine if data has been corrupted without revealing where the corruption occurred.
• Data is transmitted in blocks with an additional check digit added at the end of each block.
• Check Digits are custom user-created algorithms designed to perform specific mathematical calculations on data.
• For example, consider the ISBN value found on books: 
  • Each book has a unique ISBN number that serves as an identifier. 
  • A standard ISBN number can consist of ten digits, such as 965-448-765-9. 
  • The final digit, known as the check digit (e.g., 9 in this case), is strategically chosen so that after applying the algorithm, the result is a whole number with no remainders. 
  • By performing a check digit algorithm on the ISBN number, its validity can be confirmed.

ISBN Check Digit Walkthrough

To verify the validity of an ISBN, a specific algorithm is applied. Let's take an example with the ISBN "965-448-765-9":

• Multiply each digit of the ISBN by numbers from 1 to 10 and sum them up:
• 9x1 + 6x2 + 5x3 + 4x4 + 4x5 + 8x6 + 7x7 + 6x8 + 5x9 + 9x10 = 352
• Divide the total sum by 11:
• 352 ÷ 11 = 32
• Since 32 is a whole number without any remainder, the ISBN is considered valid.

Another instance of a check digit application is in barcodes found on purchasable items:

• Barcodes are comprised of black and white lines, scannable by barcode scanners. These scanners emit a laser onto the lines, capturing the reflected light. By measuring the distances between these lines, the scanner deciphers numbers, thereby identifying the item.
• Additionally, barcodes employ a sequence of digits to uniquely distinguish each item, with the number of digits varying across codes. For instance, 9780201379624.
• Typically, the last digit in a barcode serves as the check digit, akin to an ISBN, which aids in validating and authenticating the item.

Barcode Check Digit Walkthrough

Understanding how to calculate a check digit for a barcode involves a specific algorithm that helps ensure the accuracy of the code. Let's break down the process step by step:

Basic Barcode Check Digit Calculation

• Take, for example, the barcode number 9780201379624. The last digit (4) is the check digit.
• Next, multiply each digit by 1 or 3, alternating between these two values, and then sum them up:
  • 9x1 + 7x3 + 8x1 + 0x3 + 2x1 + 0x3 + 1x1 + 3x3 + 7x1 + 9x3 + 6x1 + 2x3 = 96
• The check digit is calculated by finding the difference between the sum and the nearest multiple of 10 that is equal to or greater than the sum. In this case:
  • Rounded sum to the nearest 10: 100
  • Check digit calculation: 100 - 96 = 4
• Therefore, the check digit for the barcode number 9780201379624 is 4, which validates the original barcode.

Custom Check Digit Algorithm in Computer Science

• In computer science, a custom check digit algorithm may be implemented for data integrity verification:
• A check digit byte, ranging from 1 to 255 and stored in 8 bits, is used for this purpose.
• When the sum of all bytes in a data block is 255 or less, the check digit is simply the sum of all bytes.
• If the sum exceeds 255, an algorithm is applied:
  • Let X be the sum of all bytes.
  • Calculate Y: Y = X / 256 (round down to the nearest whole number).
  • Set Z: Z = Y * 256.
  • The check digit is then determined as: Check digit = X - Z.

Custom Check Digit Walkthrough

• For instance, if X equals 1496, Y would be 1496 divided by 256, resulting in 5.84. Rounded down, Y becomes 5.
  • Subsequently, Z is calculated as 5 multiplied by 256, which equals 1280.
  • The check digit is deduced by finding the difference between 1496 and 1280, yielding 216.
  • In this scenario, the check digit value is 216.
• When data is transmitted, the check digit is first computed and sent alongside the data block.
• Upon receiving the data, the check digit is recalculated based on the received information and matched against the transmitted check digit.
• If both values align, the data is error-free. However, in case of discrepancies, a resend request is initiated for data retransmission.