Chapter 1.10, Problem 3QE

a.

Explanation of Solution

Determine whether the pattern $100101101$ has encountered error or not:

• In an even parity, each pattern is designed to contain an even number of $1\text{'}\text{s}$. Therefore, an error is signaled by the occurrence of a pattern with an odd number of $1\text{'}\text{s}$.
• Calculate the number of $1\text{'}\text{s}$ in pattern $100101101$

b.

Explanation of Solution

Determine whether the pattern $100000001$ has encountered error or not:

• In an even parity, each pattern is designed to contain an even number of $1\text{'}\text{s}$. Therefore, an error is signaled by the occurrence of a pattern with an odd number of $1\text{'}\text{s}$.
• Calculate the number of $1\text{'}\text{s}$ in pattern $100000001$

c.

Explanation of Solution

Determine whether the pattern $000000000$ has encountered error or not:

• In an even parity, each pattern is designed to contain an even number of $1\text{'}\text{s}$. Therefore, an error is signaled by the occurrence of a pattern with an odd number of $1\text{'}\text{s}$.
• Calculate the number of $1\text{'}\text{s}$ in pattern $000000000$

d.

Explanation of Solution

Determine whether the pattern $111000000$ has encountered error or not.

• In an even parity, each pattern is designed to contain an even number of $1\text{'}\text{s}$. Therefore, an error is signaled by the occurrence of a pattern with an odd number of $1\text{'}\text{s}$.
• Calculate the number of $1\text{'}\text{s}$ in pattern $111000000$

e.

Explanation of Solution

Determine whether the pattern $011111111$ has encountered error or not.

• In an even parity, each pattern is designed to contain an even number of $1\text{'}\text{s}$. Therefore, an error is signaled by the occurrence of a pattern with an odd number of $1\text{'}\text{s}$.
• Calculate the number of one’s in pattern $011111111$.

  $\text{Number of }1\text{'}\text{s}\text{in}\text{total}$

Explanation of Solution

Error detection by parity check:

• In case of an odd parity, if a pattern originally has an odd number of $1\text{'}\text{s}$ and suffers two errors, it still has an odd number of $1\text{'}\text{s}$. The parity system will not detect the errors