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Error Detection Techniques in Computing

Explore different error detection methods including repetition, redundancy, Hamming code, checksums, and pinpoint techniques to ensure accurate data transmission and storage in computer systems. Understand how these techniques help in identifying and correcting errors in data.

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Error Detection Techniques in Computing

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  1. http://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.htmlhttp://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.html

  2. Error Detection and Correction Fixing 0101X011

  3. Computer Errors • RAM isn't perfect

  4. Computer Errors • Networks aren't either

  5. Computer Errors • How the heck do you read 1s and 0's off this?

  6. A message • 4 bit message:

  7. A message • 4 bit message: • An errror:

  8. Trick 1 : Repetition • To avoid misunderstanding, repeat yourself…

  9. Trick 1 : Repetition • An error:

  10. Trick 1 : Repetition • Most common message wins:

  11. Trick 1 : Repetition • What if every message is wrong:

  12. Trick 1 : Repetition • Most common bit wins: Corrected

  13. Trick 1 : Repetition • More errors: "Corrected"

  14. Trick 1 : Repetition • Best 3 out of 5? Corrected

  15. Overhead • Message size : 4 bits • Including repetition : 12 bits

  16. Overhead • Message size : 4 bits • Including repetition : 12 bits 200% overhead 10Mb download is now 30Mb!

  17. Trick 2 : Redundancy • Redundancy : more information than strictly required • Common linguistic trick: He took his seat She took her seat They took their seats

  18. Trick 2 : Redundancy • Redundancy : more information than strictly required • Common linguistic trick: He took his seat She took her seat They took theirseats

  19. Trick 2 : Redundancy • Repetion is redundancy • Can we be redundant more efficently?

  20. Hamming Distance • Hamming Distance : number of different bits

  21. Normal Binary • 4 bits : 16 possible values:

  22. Normal Binary • Using all patterns – any error looks like a different message • 1 bit errors for 1010

  23. Normal Binary • Only use half the patterns • All "good" patterns have a distance of 2 from each other

  24. Normal Binary • "Good" patterns have distance of 2:1 bit error is obviously an error • 1 bit errors for 1010

  25. Hamming Code • Use extra bits to "space out" messages • 4 bit message with 3 error correction bits:

  26. Hamming Code • 7 bits could be 27 = 128 codes • Only use 16 of them

  27. Hamming Code • Every good message has distance of 3+ from other good messages:

  28. Our Message • We get: 0110110 • Which message was it meant to be?

  29. Errors • Assuming • Started with valid code word • Only one error • Then • 1 bit from one valid word • 2+ bits from another valid code word Valid Code A Valid Code B Valid Code C Error

  30. Our Message • We get: 0110110 • Find the code with distance of 1

  31. Errors • Assuming 1 error bit, we can identify correct message:

  32. Hamming Code Overhead • Message size : 4 bits • Code word: 7 bits 75% overhead… 512bit message can be encoded with 522bits: 2% overhead!

  33. Trick 3 : Checksums • Parity • Odd or even number of 1's • 1 extra bit used to make odd num of 1's datacheckbit 1001100100 00001 11100

  34. Trick 3 : Checksums • Message: 00001 • All 1 bit errors: 10001 01001001010001100000

  35. Trick 3 : Checksums • Checksum for decimal number: • Add digits, mod by 10: Message: 46756 • 4 + 6 + 7 + 5 + 6 = 28 • 28 mod (clock size) 10 = 8 Coded message: 467568

  36. Trick 3 : Checksums Coded message: 467568 Error message: 461568 Check: 461568 • 4 + 6 + 1 + 5 + 6 = 22 • 22 mod (clock size) 10 = 2!!! we have a problem

  37. Two Errors Coded message: 467568 Error message: 421568 Check: 421568 • 4 + 2 + 1 + 5 + 6 = 18 • 18 mod (clock size) 10 = 8!!! we missed it

  38. Staircse Code • Multiply each digit by its place: 12345Message: 46756 • 4 x 1+ 6 x 2+ 7 x 3+ 5 x 4+ 6 x 5= 87 • 87 mod (clock size) 10 = 7 Coded message: 467567

  39. Two Errors w Stair Case Coded message: 467567 Error message: 421567 12345Check: 421567 • 4 x 1 + 2 x 2 + 1 x 3 + 5 x 4 + 6 x 5 = 61 • 61 mod (clock size) 10 = 1!!! we caught it

  40. Real Life Stair Case • ISBN – books: http://www-math.ucdenver.edu/~wcherowi/jcorner/isbn.html

  41. Trick 4: Pinpoint • How did I do it?

  42. Trick 4: Pinpoint • How did I do it? Every Row & Col should have odd # of black squares

  43. Trick 4: Pinpoint • How did I do it? Every Row & Col should have odd # of black squares

  44. Trick 4: Pinpoint • Message / Checksum

  45. Trick 4 : Pinpoint • With decimal values:

  46. Trick 4 : Pinpoint • With decimal values:

  47. Trick 4 : Pinpoint • With decimal values: 4 9

  48. Trick 4 : Pinpoint • With decimal values: 4 off by 2 9 off by 2

  49. Hamming Code • Hamming Codes as pinpoint parity checks: http://www.systems.caltech.edu/EE/Faculty/rjm/SAMPLE_20040708.html

  50. Real Life Checksum • Last digit of credit card number calculated to http://tywkiwdbi.blogspot.com/2012/06/checksum-number-on-credit-card.html

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