Error Detection Methods | Computer for GCSE/IGCSE - Year 11 PDF Download

Parity check

• Parity checking protocol verifies whether bits within a transmission have undergone corruption.
• Each transmitted byte designates one of its bits as a parity bit.
• Prior to transmission, the sender and receiver must decide whether to employ odd or even parity.
• In odd parity, the byte must contain an odd number of 1’s, inclusive of the parity bit.
• Conversely, for even parity, the byte should contain an even number of 1’s, including the parity bit.
• The parity bit's value is determined by tallying the number of 1’s within the byte, including the parity bit.
• If the actual number of 1’s contradicts the agreed parity, an error is flagged.
• Parity checks merely confirm that an error has arisen; they do not pinpoint the precise location of the error(s).

Even parity

• Below is an arbitrary binary string:

• When employing even parity, the sum of all bits in the byte, including the parity bit, should result in an even number.
  • For instance, if there are four 1’s in the byte, the parity bit must be 0; otherwise, the total, including the parity bit, would be five, an odd number.

Odd parity

• Below is an arbitrary binary string:
  
• When utilizing odd parity, the total of all bits in the byte, including the parity bit, should amount to an odd number.
  • For instance, if there are four 1’s in the byte, the parity bit must be 1; otherwise, the aggregate, including the parity bit, would equal four, an even number.
  • The table below displays various examples of the agreed parity between a sender and receiver and the corresponding parity bit utilized for each byte.

• Example #1: If the agreed parity is odd, all 1's in the main bit string are summed. If the total is already odd, the parity bit is set to 0 to maintain an odd total.
• Example #2: In the case of even parity, the sum of all 1's in the main bit string is calculated. If the total is odd, the parity bit is set to 1 to create an even total.
• Example #6: For even parity, the sum of all 1's in the main bit string is computed. If the total is already even, the parity bit remains 0 to preserve an even total.

How do errors occur?

• Errors can arise with parity bits when the total number of bits doesn't align with the agreed-upon parity.
• Interference, whether through wire disruptions or wireless disturbances like weather or other signals, can cause bits to be flipped or altered.

• Example #1: When the agreed parity is odd but the total number of ones is even (6), an error has occurred.
• Example #2: If the agreed parity is even and the total number of ones is also even (2), then no error is present.
• Example #3: In cases where the agreed parity is even but the total number of ones is odd (7), an error has occurred.
• Additional Information: Parity checks have limitations in detecting specific errors, like bit swaps preserving parity.
• Below is an arbitrary binary string with an odd agreed parity and a total of five ones (odd).

Parity Bytes and Parity Blocks

• Understanding Parity Checks: Parity checks do not identify the specific errors in the data. They simply indicate that an error has occurred during transmission.
• Utilizing Parity Blocks and Parity Bytes: Parity blocks and parity bytes play a crucial role in error detection and localization. 
  • A parity block comprises data where the count of '1's is calculated both horizontally and vertically. 
  • Additionally, a parity byte is transmitted alongside the data, containing parity bits determined through vertical parity calculations.
• The following is a parity block featuring a parity byte at the bottom and a parity bit column in the second column:
  
• The concept of odd parity is utilized in the provided table.
• In each byte row, the horizontal parity is calculated as a regular parity bit.
• For every row, each bit column computes the vertical parity, forming the parity byte. This byte is determined before transmission and is included with the parity block.
• Every parity bit monitors if a flip error has happened in a byte, while the parity byte identifies errors in bit columns.
• By comparing the horizontal and vertical parity values, errors can be pinpointed accurately.
• In a specific example, it's identified that the error lies in byte 3, bit 5 cell, where it ought to be 0 instead.
• Options for addressing the error include automatic correction or sending a retransmission request to the sender.

Checksums

• Checksums are utilized to ascertain if data has been corrupted without revealing the exact location of the corruption. Data is transmitted in blocks, with an additional checksum value appended at the block's conclusion.
• Checksums involve custom user-generated algorithms that execute mathematical operations on data.
• Understanding Checksum Byte:
  • A checksum byte is a value ranging from 1 to 255, stored in 8 bits, collectively known as a byte.
  • If the total of all transmitted data bytes is 255 or less, the checksum value equals the sum of all bytes.
  • If the sum of all bytes exceeds 255, a calculation algorithm is applied:
    • Calculate X as the sum of all bytes.
    • Find Y by dividing X by 256 and rounding down to the nearest whole number.
    • Calculate Z as Y multiplied by 256.
    • The checksum is derived as the difference between X and Z.

Custom Checksum Walkthrough

• When data is transmitted, a checksum is calculated and sent along with the data block. Upon reception, the checksum is recalculated. If the recalculated checksum matches the received checksum, the data is error-free. Otherwise, a resend request is triggered.
• Let's take an example to understand this process:
  • Consider X = 1496. When divided by 256, Y ≈ 5.84. Rounded down, Y equals 5.
  • Next, Z is determined as 5 * 256 = 1280.
  • The checksum is then calculated as 1496 - 1280 = 216.
  • Therefore, in this instance, the checksum value would be 216.
• Before data is sent, a checksum value is calculated.
• The calculated checksum value is then transmitted along with the data.
• Upon receiving the data, the receiver calculates the checksum value using the received data.
• The receiver compares the calculated checksum to the transmitted checksum.
• If the calculated and transmitted checksums match, no error is present; otherwise, an error has occurred.

Echo check

• Echo checks involve sending received data back to the original sender for verification. This process allows the sender to inspect the data for any potential errors that may have occurred during transmission.
• This verification method is not entirely dependable because errors could have arisen either when the sender dispatched the data or when the receiver forwarded it. In such cases, it becomes challenging to pinpoint exactly when the error occurred.
• In the event of an error, the sender will need to retransmit the data to ensure its accuracy and completeness.