Why $H(A)=H(C)$ where $C$ is $A$ with an additional parity bit?

1. What is the purpose of adding parity bit?
2. Why would you expect a CRC to detect more errors than a parity bit?
3. Where is the parity bit added?
4. How to add parity bit in C?

What is the purpose of adding parity bit?

The parity bit, unlike the start and stop bits, is an optional parameter, used in serial communications to determine if the data character being transmitted is correctly received by the remote device.

Why would you expect a CRC to detect more errors than a parity bit?

Because it is used mostly in data transmission and is used to check errors in digital data. The CRC has more bits and therefore provides more redundancy. That is, it provides more information that can be used to detect errors.

Where is the parity bit added?

The parity bit is added to the transmitted data by inserting it into the shift register at the correct bit position. A single parity bit can only detect an odd number of errors, that is, 1, 3, 5, and so on. If there is an even number of bits in error then the parity bit will be correct and no error will be detected.

How to add parity bit in C?

Assuming the parity bit must make the byte have an even number of 1 bits: keep a count of the number of 1-bits printed and when the total is BITS-1, check if the count is odd. If yes, emit a '1', else emit a zero. This appends the parity bit, where normally the parity bit is prepended.