Computers represent information using bits. A bit string is a sequence of zero or more bits. This information is encoded by the sender and will be transmitted. The receiver then decodes the information.

Data sent may be corrupted along the way because noise may interfere every time an information is transmitted to any channel. A channel is the physical medium through which information is transmitted. Examples of channels include telephone lines, internet cables, fiber optic lines, hard drives, disks, CD-ROMs, DVDs, etc. These channels are subject to noise disturbances. Noise refers to interference caused by sunspots, lightning, meteor showers, poor typing, and poor hearing, among others.

Oftentimes, data are transferred in the form

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Lesson 6. 6 Error Detecting Codes

When a message is transmitted, the inevitable noise disturbance usually degrades the quality of communication. Whenever repetition is possible, it is sufficient to detect the occurrence of an error. When an error is detected, we simply retransmit the message, and it may be correct the second time or even possibly the third time.

Error detection is a great aid in high-quality maintenance. Without error detection, a large digital system becomes unmaintainable.

It is not possible to detect an error if every possible symbol, or set of symbols, that can be received is a legitimate message. It is only possible to catch errors if there are some restrictions on what a proper message is. The problem is to keep these restrictions on the possible messages down to ones that are simple. In practice, “simple” means “easily computable.”

Single-Parity Check

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Odd

Example 6 – 22. Determine the number of bits transmitted in the bit string 11010011.

Solution. There are 9 bits transmitted. 8 information bits and 1 parity bit. Parity bit is an extra bit that is attached to the data bits. Parity bit is chosen so that the number of 1 bits in the code word is even or odd.

Parity checking is a means of checking if the communication of a sequence of bits has been correctly received. The two types of most commonly used parity checking are simple parity and two-dimensional parity. Simple parity is used to check single-bit errors while two-dimensional parity check is used to check burst errors. Burst errors mean two or more bits in the data has changed.

Single Parity Check

An even parity bit is generated by counting the number of 1s. If the number of 1s is odd, then the even parity bit will have a value of 1, otherwise the parity bit will be 0. In the same manner, an odd parity bit is generated by counting the number of 1s. However, if the number of 1s is even, then the odd parity bit will have a value of 1, otherwise the parity bit will be 0

Example 6 – 23. Generate an even parity bit of the bit string 10101101.

Solution: Since there are 5 1s, then the even parity bit will have a value of