1. Error Detection / Correction
Hamming code

2. Error Detection/Correction
Errors:
Hard Failure
Permanent defect
Soft Error
Random, non-destructive
No permanent damage to memory
Coding:
Coding can be used for
- Error detection
- Error correcting
Hamming code will be explored

3. Error Correcting Code Function
The output of the “Compare” to the “Corrector” is termed the “syndrome”, and is K bits long

4. Hamming Code Example Visualizing: With even parity: Word:
Identifying error:
With Error:

5. Increased word length for error correcting

6. Hamming Code Design – determining K
To store an M bit word with detection/correction takes M+K bit words
If K =1, we can detect single bit errors but not correct them
If 2K - 1 >= M + K , we can detect, identify, and correct all single bit errors,
i.e. the syndrome contains the information to correct any single bit error
Example: For M = 8:
and K = 3: 23 – 1 = 7 < (doesn’t work)
and K = 4: 24 – 1 = 15 > (works!)
Therefore, we must choose K =4,
i.e., the minimum size of the syndrome is 4

7. Hamming Code Syndrome
If we compare the read K bits compared with the write K bits,
using an exclusive or function, the result is called the “syndrome”.
If the syndrome is all zeros, there were no errors.
If there is a 1 bit somewhere, we know that represents an error.

8. Hamming Code Syndrome Design Criteria

9. A Layout of Data and Check Bits that Achieves Our Design Criteria:
C1 is a parity check on every data bit whose position is xxx1
C1 = D1 exor D exor D4 exor D exor D7
C2 is a parity check on every data bit whose position is xx1x
C2 = D exor D3 exor D exor D6 exor D7
C4 is a parity check on every data bit whose position is x1xx
C4 = D2 exor D3 exor D exor D8
C8 is a parity check on every data bit whose position is 1xxx
C8 = D5 exor D6 exor D7 exor D8
Why? Because we want the syndrome, the Hamming test word, to yield the address of the error.

10. Example:

11. Example:
Data stored =
Check bits:
Putting it together:

12. Example: Word fetched: Check bits: Putting it all together:
EXOR’ing:
0110 = 6  bit position 6 is wrong, i.e. bit D3 is wrong

13. SEC-DEC Example – Requires One Extra Check Bit
Single Error Correction, Double Error Detection:
Single Error Correction:
Word With Even Parity Word With Even Parity With Two Errors
With Errors Identifying Error SEC Attempt IS SEC Correct? Extra Bit Confirms DE

14. Lab Project 1 – 22x3 Memory Design (Due 10/25/07)
The bus signals are: D<0:2>, A<0:3>, AE (address enable), R/W#
Clearly show the master, decoders, muxes, and bus.
Data is transferred on the falling edge of the clock.
Use LED’s to display bus signals.
Use tristate buffers to drive the bus data lines (why?).
Part 1:
Clearly explain your design
Show the timing diagrams for the design implementation
Part 2:
Implement your design on the LogicWorks5 Simulator
Capture the timing diagrams from the Simulator for your report
Part 3: (with ONE partner)
Build a circuit(s) in the Laboratory
Capture the oscilloscope traces for your report
Part 4:
Document your project in a report written to a professional audience of your peers – Title Page, Abstract, Problem Description, Design, Data, Conclusions (include descriptions of problems and learning), and References)
Have fun, explore, and don’t be afraid to be creative !