






Transmitted data (unprotected): 1111000 1010101 1111111 Even parity: 11110000 10101010 11111111 Odd parity: 11110001 10101011 11111110 



Transmitted data (unprotected): 1111000 1010101 1111111 Two dimensional (even) parity: 11110000 10101010 11111111 10100101 





From the discussion above:
we know that the sender will transmit: 1011010000
Case 1: no error in message
Decode:
Case 2: one error in message
Decode:
Case 3: detectable two bits error in message
Decode:
Case 4: undetectable two bits error in message
Decode:



Generator polynomial: 1101 (Math. notation: 1×x^{3} + 1×x^{2} + 0×x^{1} + + 1×x^{0}) N = 4 (Generator polynomial has 4 terms, or bits in "1001")



Generator polynomial: 1101 (Math. notation: 1×x^{3} + 1×x^{2} + 0×x^{1} + + 1×x^{0}) N = 4 (Generator polynomial has 4 terms, or bits in "1001") 
Generator polynomial: 1101 (Math. notation: 1×x^{3} + 1×x^{2} + 0×x^{1} + + 1×x^{0}) N = 4 (Generator polynomial has 4 terms, or bits in "1001") 

Name  Generator polynomial 

CRCCCITT  10001000000100001 
CRC16  11000000000000101 
CRC32  100000100110000010001110110110111 



Quick example: generator polynomial = 1101
Circuit:

How to use it:

This is a logicsim program from my CS355 class...