Four rows of 4-bit data were sent with an even parity bit for each row at its right end and a final row of even parity bits for each column (vertical and horizontal parity). The received bits were row 1: 1011 1, row 2: 0100 0, row 3: 1100 0, row 4: 0101 0 and parity row: 0100 (the rightmost bit of each row is its row parity). If exactly one bit is wrong, which of the following is its position?

Answer: B. Row 2 and column 3

Counting the 1s in each row, including the parity bit, gives 4 for row 1, 1 for row 2, 2 for row 3 and 2 for row 4, so only row 2 is odd. Counting the 1s in each column, including the parity row, gives 2 for column 1, 4 for column 2, 1 for column 3 and 2 for column 4, so only column 3 is odd. Therefore the bit where row 2 and column 3 cross is wrong, and flipping it corrects the error.

• A. Row 1 has four 1s, an even number, so row 1 contains no error.
• B. Correct. Exactly one row and one column are odd, and the bit at their intersection is the wrong one.
• C. This mixes up rows and columns. Row 3 has two 1s, an even number, so it contains no error.