Problem Set: Error Detection and Correction

1. Given the following codewords, created for a memory with 7-bit words stored with one parity bit. Does this system use even or odd parity?

       1110 0110
       0000 1000
       1010 1011
       1111 1110
   

2. Show how the following 7 bit words would be stored with a parity bit using even parity:
   1. 010 1100
   2. 101 0101
   3. 000 0100
   4. 111 0010
3. Using the SED/SEC Hamming code discussed in class, and the info above, show the 7 bit word that will be stored for the following 4 bit words:
   1. 0100
   2. 0101
   3. 1111
4. Use the same code as in the previous problem. Determine whether there is an error, and if so, in which bit, for each of the following words fetched from memory:
   1. 0001011
   2. 0110011
   3. 0110101
5. Using the DED/SEC Hamming code discussed in class, and the info above, show the 8 bit word that will be stored for the following 4 bit words:
   1. 0010
   2. 1011
   3. 1100
6. Use the same code as in the previous problem. For each of the following words fetched from memory, determine whether there is no error, an error in one bit, or an error in two bits. If there is an error in one bit, which bit is in error?
   1. 11100011
   2. 10111101
   3. 10100100
7. In the Hamming code for 8 data bits which was discussed in class, how can you tell whether there was an error in a check bit as opposed to an error in a data bit?
8. Using the SED/SEC Hamming code given in class, show the 12 bit word that will be stored for the following 8 bit words:
   1. 1010 0110
   2. 0111 0011
   3. 1010 1101
9. Using the Hamming code given in class, determine whether there is an error, and if so, in which bit, for each of the following words fetched from memory:
   1. 1010 0101 0001
   2. 0011 0100 0111
   3. 1010 0100 0001
10. Suppose we want an error correcting code that will allows all single bit errors to be corrected for memory words of length 10.
    1. How many check bits are needed?
    2. Assuming we use the technique presented in class to create our Hamming code, what will be the code word for the 10 bit word 10 0110 0110?

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