Modulo 2 long division attempts

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Discussion Overview

The discussion revolves around the process of performing modulo 2 long division to find CRC (Cyclic Redundancy Check) code words for given information words using specified CRC polynomials. Participants are examining the correctness of calculations and the application of XOR operations in this context.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests confirmation on their modulo 2 division attempts for two CRC calculations using polynomials 1011 and 1101.
  • Another participant suggests checking the calculations by converting binary to decimal and provides a specific numerical example to illustrate a potential error in the first calculation.
  • A participant expresses confusion about their final operation in the first question, specifically regarding the XOR operation and the resulting remainder.
  • Another participant confirms that the use of XOR is correct in modulo 2 division and expresses that the original answers appear acceptable.

Areas of Agreement / Disagreement

There is no consensus on the correctness of the initial calculations, as one participant identifies a potential error while another believes the answers are correct. The discussion remains unresolved regarding the accuracy of the modulo 2 division results.

Contextual Notes

Participants reference specific binary operations and numerical conversions, but there are unresolved aspects regarding the calculations and the interpretation of the XOR operation in this context.

fran1942
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Hello, could someone please confirm if have done the modulo 2 division in order to find the CRC code word for these two correctly.

1) using the CRC polynominal 1011, for the information word 0101 1001
(attached image 1 is my attempt)

2) using the CRC polynominal 1101, for the information word 0100 1101
(attached image 2 is my attempt)

Thank you kindly for any confirmation.
 

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fran1942 said:
Hello, could someone please confirm if have done the modulo 2 division in order to find the CRC code word for these two correctly.

1) using the CRC polynominal 1011, for the information word 0101 1001
(attached image 1 is my attempt)

2) using the CRC polynominal 1101, for the information word 0100 1101
(attached image 2 is my attempt)

Thank you kindly for any confirmation.

You can check these by converting to decimal. For the first one, 1011001000 is 712, 1011 is 11. 712/11 is 64 remainder 8. You got 65 remainder 3. I'll give you a hint where you went wrong. 1000-1011 isn't 11. It's negative.
 
hello, thanks kindly for your help.
However, I just can't see what I have done wrong with that final operation on the first question.
I ended up with remainder 11 after I performed the XOR operation on 1000 and 1011.
How could I get another result. I thought the rule with modulo 2 division was to use XOR ?


Thanks for any clarification.
 
fran1942 said:
I thought the rule with modulo 2 division was to use XOR?
It is, and CRC's use the same type of math. Your answers look OK to me.
 

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