## Simple Parity Check

Â Â Â The simple party check method is based on parity. So, let me first tell you, how can we compute the parity of a given data unit. Suppose the data to be sent is 1100 001. To compute the parity of this data unit we have to count the number of 1â€™s in that data. Â As there are three 1â€™s in this data, we say the parity of this data unit is odd. It is because 3 is an odd number. If data is 1100 011, it contains 4 numbers of 1â€™s and as 4 is an even number, we say the parity of this data unit is even parity. Â

Â Â Â In the Simple Parity Check method, only one bit is sent with every data unit for error detection. This extra bit of redundant bit is called a **parity bit.** Suppose the data to be sent is 1010111; before transmitting this data unit, parity is computed, and it is made even (or odd parity in case odd parity is used for error detection). Â In this data, there are 5 1â€™s i.e., odd parity.

#### Example :

Â Â Â To make parity even one parity bit â€˜1â€™ is added to the data. Then the data will be 1010 1111 i.e., even parity data (as six is an even number). The parity bit helps the receiver to detect an error in the received data.

Â Â Â Let us take another example, suppose the data to be sent is 1010 011. Â In the data unit, there are four 1â€™s which means the parity of this data unit is already even. In this case, 0 will be added as a parity bit to let the parity be even.

Â Â Â So, In a simple parity check method sender will send every data unit as anÂ **even parity data unit**. When the receiver will see any data unit of odd parity receiver understand that at least one bit might have been changed in the transmission and therefore the data is corrupted or there is an error in the received data.Â

Â Â Â To help you understand better let me use a diagram given below and explain the concept better. In the simple parity check method, there is a **parity computer** at the sender side which computes the parity of every sent data and makes the parity even. Even parity data is transmitted. Â At the receiver side, there is a **parity checker**, which checks the parity of every received data unit. Â If the parity of the received data unit is even, then only the data is accepted otherwise the data is rejected. Â

Â Â Â Let us say the data to be sent is 1010 111. Â Before transmitting, this data unit it is given to a **party computer**. The parity computer will compute the parity of this data unit as there are 5 number of 1â€™s in the data. The parity bit is added as â€˜1â€™ to make the parity of this data unit even. Â Now there are six 1â€™s; the data now has even parity. Â This data unit i.e., original data (data word) with a parity bit is called a **code word.** The original data to be sent is called a **data word.**

Â Â Â So, the data to be sent is 10101111. Â If there is no error in the data transmission, the receiver will receive 10101111. When the receiver receives this data unit it is given to a parity checker and the parity checker will check whether the parity of received data isÂ odd or even. As in this case there are 6 number of 1â€™s the parity of this data unit is even. Â Therefore, this data passes the test, and is accepted by the receiver.

#### Error detection using Simple parity Check

Â Â Â Letâ€™s now understand how the receiver detects an error if the data is corrupted. Suppose the to send data is 1010 1111 and the received data is 1010 0111.

Â Â Â There is a one-bit error in the received data. When this data is given to the parity checker. The parity checker will check the parity of this data unit. As there are five 1â€™s in the data, the parity of this data unit is odd parity.Â Therefore, this data will be rejected by the receiver. (Because the receiver only accepts even parity data odd parity data will be assumed to be corrupted).

#### Limitations of Simple parity Check.

It is important to understand the limitations of the simple parity check method. Let us see how it behaves when two bits are in error. Let us say the sender sends 10101111. Â The receiver receives 1100111 which means two bits are in error. When the receiver receives this data, it is given to a parity checker. The parity checker will compute the parity, as there are 6 number of ones the party is even. As the party of this data unit is even the receiver will incorrectly accept the data. It is because in a simple parity check method, even parity data units are accepted. (Assuming there is no error). The drawbacks of the simple parity check method are:

- It detects only single-bit errors.
- If even the number of bits is corrupted, then it cannot detect errors.