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. Pinpoint
How did I do it?

7. Pinpoint
Message / Check Bit Every Row & Col should have odd # of black squares

8. Pinpoint
How did I do it?
Every Row & Col should have odd # of black squares

9. Real Life Checksum Last digit of credit card number calculated to

10. Real Life Stair Case
ISBN – books:

11. Hamming Codes

12. Hamming Code Message Coded Message 0000  0001  0010  0011  0000000
Use extra bits to "space out" messages
4 bit message with 3 error correction bits:
Message
Coded Message
0000 
0001 
0010 
0011 

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

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

15. Our Message We get: 0110110 Which message was it meant to be? 0000000

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

17. Our Message We get: 0110110 Find the closest match:
The message was supposed to be

18. Hamming Code Hamming Codes as pinpoint parity checks:
/SAMPLE_ html

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