A simple parity-check bit, which is normally added at the end of the word (changing a 7-bit ASCII character to a byte), cannot detect even numbers of errors. For example, two, four, six, or eight errors cannot be detected in this way. A better solution is to organize the characters in a table and create row and column parities. The bit in the row parity is sent with the byte, the column parity is sent as an extra byte (Figure 10.23).

Show how the following errors can be detected:
a. An error at (R3, C3).
b. Two errors at (R3, C4) and (R3, C6).
c. Three errors at (R2, C4), (R2, C5), and (R3, C4).
d. Four errors at (R1, C2), (R1, C6), (R3, C2), and (R3, C6).

C2 4 5 6 7 R1 1 1 0 0 1 1 1 1 C2 4 5 6 7 R1 1 1 0 0 1 1 1. 1 R2 1 0 R2 1 0 1. 1. 1. R3 0 R3 0 1. 1. R4 0 1 R4 0 1. 1. 0 1 0 1 0 1 0 0 1 0 0 1 1 a. Detected and corrected b. Detected (2 4 3 6 7 R1 1 1 0 0 1 1 1|1 1 00 0 C2 4 5 6 7 R1 1 0 0 0 1 0 1 1. R2 1 0 R2 1 1. 1. 1. 1. R3 0 0 1 R3 0 1 1 0 0 1 0 1. R4 0 1 0 1 0 1 1 0 1 0 1 R4 0 0 1. 1. 1 0 1 0 1 0 1 c. Detected d. Not detected