110 0101 0000 

 100 0100 1 



10 0001 1000 

 10 0010 01 



REMAINDER 11 1100 



step 3, pad with leading zero's 



0011 1100 



Using hexadecimal notation, the above calculation would be: 



AE 32 BO 61 / 89 = ? with a remainder of 3C. 



A table of some sample 32 bit data streams and their remainders 

 when divided by the primitive 1000 1001 (89 Hex) (all values are in 

 hexadecimal) : 



data stream remainder 



00 00 00 01 12 



00 00 00 10 32 



00 00 01 00 16 



00 00 10 00 72 



01 Dl E3 96 53 

 17 24 CD 9E 39 

 27 48 87 Al 73 

 2A 3E BE 71 5A 

 69 53 D9 Fl 56 

 8D 4E 9F 9A 5D 

 AE 32 BO 61 . 3C 

 CI 58 F8 8C 00 

 C9 4C IF 55 69 

 FA F4 17 F9 46 



Upon receipt of a transmission, the data stream is once again 

 divided by the primitive. The remainder is compared with the 

 transmitted remainder. If the remainders match, no errors 

 occurred. 



References: 



Lin, S., An Introduction to Error-Correcting Codes, Prentice-Hall, 

 New Jersey, 1970. 



Wakerly, J., Error Detecting Codes, Self-Checking Circuits and 

 Applications, North-Holland, New York, 1978. 



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