Parity Checking and Parity Generation

Introduction:
Parity checking is a technique used in digital systems to detect errors in data transmission. It involves adding an extra bit, known as a parity bit, to a group of data bits. Parity generation, on the other hand, refers to the process of generating the parity bit based on the data bits.

Options:
a) AND, OR, NOT gates
b) XOR, Exclusive NOR gate
c) NAND gates
d) NOR gates

Explanation:

XOR, Exclusive NOR Gate:
XOR (Exclusive OR) and XNOR (Exclusive NOR) gates are best suited for parity checking and parity generation. These gates produce an output that is true when the number of inputs that are true is odd. This property makes them ideal for generating and checking parity bits.

- XOR Gate: The XOR gate outputs a high (logic 1) when the number of inputs that are high is odd, and outputs a low (logic 0) when the number of inputs that are high is even. This behavior is suitable for generating and checking parity bits.

- XNOR Gate: The XNOR gate outputs a high (logic 1) when the number of inputs that are high is even, and outputs a low (logic 0) when the number of inputs that are high is odd. By complementing the output of the XNOR gate, we can obtain the parity bit. Therefore, XNOR gates are also suitable for generating and checking parity bits.

Other Options:

a) AND, OR, NOT gates: These gates are not suitable for parity checking and generation because they do not have the property of producing an odd or even output based on the number of inputs that are true.

c) NAND gates: NAND gates can be used for parity checking and generation, but they require additional logic to invert the output to obtain the parity bit. This makes them less suitable compared to XOR and XNOR gates.

d) NOR gates: NOR gates can also be used for parity checking and generation, but like NAND gates, they require additional logic to invert the output to obtain the parity bit.

Conclusion:

XOR and XNOR gates are the best suited for parity checking and parity generation. They have the inherent property of producing an odd or even output based on the number of inputs that are true, making them ideal for generating and checking parity bits.

Parity check : EXOR

parity generation : EXNOR

Explanation

Parity generation

The XNOR gate will emit 1 only when there is not exactly one 1 input.

This feature can be used for parity generation.

Suppose A wants to send 1001. XNOR gate will give parity as 0.

But if A sends 1000 XNOR gate gives 1 as parity

Parity check

B receives: 10010

B computes parity: 1+0+0+1+0 (mod 2) = 0 //this can be achieved by EXOR