A 3-bit redundancy-check code (odd parity for columns, even parity for rows) has been used to transmit data. This means that the original data had words of 2 bits each. The following sequence is received (notice that one error occured):
0 0 0 1 0 1 0 1 0 0 0 0 1 0 1
Remember that the very last bit should check for even parity on the last word (row), not for odd parity on the last column; you do not need to worry about the check for odd parity on the last column. For example, if you have the two 3-bit words 000 and 110, you know that the first word is correct (even parity), the second word is correct (even parity), the first column is correct (odd parity), the second column is correct (odd parity). Checking the last column would tell you something is not correct (it is of even parity), when obviously everything is fine! Checking the last column is useless and could even be misleading. The parity of the last column also depends, by construction, on the number of words in the data.
a) How many of the bits in the above sequence are redundant bits (i.e. they were added as part of the redundancy-check code before transmission), and how many bits are for the data only?
Redundant Bits:
Data Bits:
b) State in which word the error occured (1 for leftmost - 5 for rightmost)
1
2
3
4
5
c) State in which bit position (1 for left, 2 for middle, 3 for right) in that word:
1
2
3 (parity bit)
d) Give the original data sequence that was sent (correct the error, and eliminate the added bits used for error detection/correction)