Error Detection Methods (Cambridge (CIE) O Level Computer Science): Revision Note
Exam code: 2210
Parity Check
What is a parity check?
A parity check determines whether bits in a transmission have been corrupted
Every byte transmitted has one of its bits allocated as a parity bit
The sender and receiver must agree before transmission whether they are using odd or even parity
If odd parity is used then there must be an odd number of 1’s in the byte, including the parity bit
If even parity is used then there must be an even number of 1’s in the byte, including the parity bit
The value of the parity bit is determined by counting the number of 1’s in the byte, including the parity bit
If the number of 1’s does not match the agreed parity then an error has occurred
Parity checks only check that an error has occurred, they do not reveal where the error(s) occurred
Even parity
Below is an arbitrary binary string
EVEN | Byte | ||||||
|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
If an even parity bit is used then all bits in the byte, including the parity bit, must add up to an even number
There are four 1’s in the byte
This means the parity bit must be 0 otherwise the whole byte, including the parity bit, would add up to five which is an odd number
Odd parity
Below is an arbitrary binary string
ODD | Byte | ||||||
|---|---|---|---|---|---|---|---|
1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
If an odd parity bit is used then all bits in the byte, including the parity bit, must add up to an odd number
There are four 1’s in the byte. This means the parity bit must be a 1 otherwise the whole byte, including the parity bit, would add up to four which is an even number
The table below shows a number of examples of the agreed parity between a sender and receiver and the parity bit used for each byte
Example # | Agreed parity | Parity bit | Main bit string | Total number of 1’s | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
#1 | ODD | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 5 |
#2 | EVEN | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 2 |
#3 | EVEN | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 6 |
#4 | ODD | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 5 |
#5 | ODD | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 5 |
#6 | EVEN | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 4 |
Example #1: The agreed parity is odd. All of the 1’s in the main bit string are added (5). As this number is odd already the parity bit is set to 0 so the whole byte stays odd
Example #2: The agreed parity is even. All of the 1’s in the main bit string are added (1). As this number is odd the parity bit is set to 1 to make the total number of 1’s even (2)
Example #6: The agreed parity is even. All of the 1’s in the main bit string are added (4). As this number is even already the parity bit is set to 0 so the whole byte stays even
How do errors occur?
When using parity bits, an error occurs when the number of total bits does not match the agreed parity
Bits can be flipped or changed due to interference on a wire or wirelessly due to weather or other signals
Example # | Agreed parity | Parity bit | Main bit string | Total number of 1’s | Error | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
#1 | ODD | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 6 | Error |
#2 | EVEN | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 2 | No error |
#3 | EVEN | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 7 | Error |
#4 | ODD | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 5 | No error |
#5 | ODD | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 6 | Error |
#6 | EVEN | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 3 | Error |
Parity checks are quick and easy to implement but fail to detect bit swaps that cause the parity to remain the same
Parity Byte & Block Check
What are parity byte & block checks?
Parity blocks and parity bytes can be used to check an error has occurred and where the error is located
Parity checks on their own do not pinpoint where errors in data exist, only that an error has occurred
A parity block consists of a block of data with the number of 1’s totalled horizontally and vertically
A parity byte is also sent with the data which contains the parity bits from the vertical parity calculation
Below is a parity block with a parity byte at the bottom and a parity bit column in the second column
ODD | Parity bit | Bit 2 | Bit 3 | Bit 4 | Bit 5 | Bit 6 | Bit 7 | Bit 8 |
|---|---|---|---|---|---|---|---|---|
Byte 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
Byte 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Byte 3 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
Byte 4 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
Byte 5 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
Byte 6 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
Byte 7 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
Byte 8 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
Parity byte | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
The above table uses odd parity
Each byte row calculates the horizontal parity as a parity bit as normal
Each bit column calculates the vertical parity for each row, the parity byte
It is calculated before transmission and sent with the parity block
Each parity bit tracks if a flip error occurred in a byte while the parity byte calculates if an error occurred in a bit column
By cross referencing both horizontal and vertical parity values the error can be pinpointed
In the above example the byte 3 / bit 5 cell is the error and should be a 0 instead
The error could be fixed automatically or a retransmission request could be sent to the sender
Checksum
What is a checksum?
A checksum is a value that can be used to determine if data has been corrupted or altered
It indicates whether data differs from its original form but does not specify where
Checksums are calculated using an algorithm and the value is added to the transmission
The receiving device re-calculates the checksum and compares to the original
If the checksums do not match, it is assumed an error has occurred
Worked Example
Describe the process a checksum algorithm uses to determine if an error has occurred
[5]
Answer
Before data is transmitted a checksum value is calculated [1]
The checksum value is transmitted with the data [1]
The receiver calculates the checksum value using the received data [1]
The calculated checksum is compared to the transmitted checksum [1]
If they are the same then there is no error otherwise an error has occurred [1]
Echo Check
What is an echo check?
An echo checks involve transmitting the received data back to the sender
The sender then checks the data to see if any errors occurred during transmission
This method isn’t reliable as an error could have occurred when the sender transmits the data or when the receiver transmits the data
If an error does occur the sender will retransmit the data
Worked Example
Four 7-bit binary values are transmitted from one computer to another.
A parity bit is added to each binary value creating 8-bit binary values. All the binary values are transmitted and received correctly.
(a) Identify whether each 8-bit binary value has been sent using odd or even parity by writing odd or even in the type of parity column.
8-bit binary value | Type of parity |
|---|---|
01100100 |
|
10010001 |
|
00000011 |
|
10110010 |
|
[4]
(b) An error may not be detected when using a parity check.
Identify why an error may not be detected.
[1]
Answers
(a)
8-bit binary value | Type of parity |
|---|---|
01100100 | Odd [1] |
10010001 | Odd [1] |
00000011 | Even [1] |
10110010 | Even [1] |
(b)
Any one from:
there is a transposition of bits [1]
it does not check the order of the bits (just the sum of 1s/0s) [1]
even number of bits change [1]
incorrect bits still add up to correct parity [1]
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