Error checking and correction

Parity bits

• Parity checking can only detect an odd number of errors and can not correct them
• Types of Parity:
• Even: The number of 1s is counted and if the number of 1s is odd then the parity bit is set to 1.
• Odd: The number of 1s is counted and if the number of 1s is even then the parity bit is set to 1.​​​​​​​
• In short:
• Even parity: odd # of 1's is made even
• Odd parity: even # of 1's is made odd

Examples of parity

• I have the sequence: 0100010
• Even parity(8 bits) : 01000100
• Odd parity(8 bits) : 01000101
• I have the sequence: 1000000
• Even parity(8 bits) : 10000001
• Odd parity(8 bits) : 10000000

Majority voting

• Interference can occur which can cause 1's to be received as 0's and vice versa. Therefore, a system called majority voting is used.
• Majority voting is where each bit is represented by 3 bits to try and curb damage from interference.
• This works but is not completely secure.
• It works because it is unlikely that 2 bits of the 3-bit representation change.

Check digits

• To detect a human error by checking whether a sequence of numbers has been added correctly, check digits can be added to the end of the sequence.
• An example can be, multiply the 2nd and 4th entry, this answer is the check digits.
• The computer knows what this answer should be, if the 2nd and 4th entry are incorrect, the computer can now tell that it is either the 2nd or 4th. It can even work out which of the two it is if there are a range of check digits involving the 2nd and 4th digit.