Error Flagging in Odd-Parity System

Which of the following data would be flagged as having an error in an odd-parity system?

1) 1111 1001 1011 1000

2) 1111 1001 1011 1001

3) 1111 1001 1011 1010

4) 1111 1001 1011 1011

Answer:

Data 3) 1111 1001 1011 1010 would be flagged as having an error in an odd-parity system checking 16 bits at a time because it contains an even number of 1s (10), violating the odd-parity rule.

In an odd-parity system that checks parity 16 bits at a time, the data that would be flagged as having an error is the one that does not have an odd number of 1s. To determine which data would be flagged, we need to count the numbers of 1s in each of the options:

1111 1001 1011 1000 = 10 1s (Even number, correct parity)

1111 1001 1011 1001 = 11 1s (Odd number, correct parity)

1111 1001 1011 1010 = 10 1s (Even number, correct parity)

1111 1001 1011 1011 = 11 1s (Odd number, correct parity)

Since an odd-parity system requires that each set of 16 bits have an odd number of 1s, options 1, 2, and 4 are correct. The data that would be flagged as having an error is option 3) 1111 1001 1011 1010 because it has an even number of 1s (10), which violates the odd-parity rule.