Q 1.4 Checkbits and Checkblocks

1.Add in the checkbits to the front of each of these lines of binary

  1. 1011001

  2. 1000110

  3. 1011111

  4. 1011011

  5. 1101100

  6. 1100010

2. With error checking (ex. checkbits), we are introducing redundancy into the data (ie. the extra bits at the front) so that we can see if some data was messed up when it be transmitted. This error checking comes at a cost of wasted space.

  1. Assuming you have 8 bits, one of which is a checkbit; what percentage of the message is actual data and what percentage is error checking and redundant?

  2. Is the percentage of redundancy involved in using a checkbit acceptable? When would it be acceptable? When wouldn’t it be?

  3. How could we reduce the amount of redundant information (assuming 8 bits with one checkbit)?

3. Make these blocks into checkblocks.

(a) (b) (c)
1001001
1011010
1101010
0010101		 0110101
1011101
0101101
1010101		 1010010
1111101
0100011
1010111

4. Which bytes are in error? How do you know? (checkbit is at the front)

  1. 10111010

  2. 01011011

  3. 01111011

  4. 10000010

  5. 11110101

  6. 01101110

  7. 01010101

5. Which bit is incorrect? Use the checkbits at the left and bottom to help find them.

(a) (b) (c) (d) (e)
1010
0100
1111
0000		 0101
1001
0010
1010		 1111
1010
0110
0010		 1110
1010
0110
1100		 0110
1100
1001
1001

6. What is the difference between error detection and error correction?

7. If one bit is in error in a checkblock, we can both detect and correct it.

  1. If two bits are in error in a checkblock, can we detect the error? Consider a variety of positions for the bits that are in error. What if they are side by side in a row? Side by side in a column? Both in the checkbits? In completely different rows and columns?

  2. If two bits are in error in a checkblock, can we correct the error? Consider the same positions as before.

  3. If three bits are in error, can we (a) detect it (b) correct it? Consider a variety of positions for the bits that are in error; in an L shape, a rotated L, in a line horizontal, in a line vertical, in the checkbits.

  4. If four bits are in error, can you find a position that we cannot detect and cannot correct?