Design 3 Bit Parity generator using logic gates
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There are two main types of parity generators: even and odd. They both achieve the same goal of detecting single-bit errors during data transmission, but in slightly different ways. Here’s how to design a 3-bit parity generator for both even and odd parity:
Even Parity Generator:
Truth Table:
Create a truth table with four columns for the three data bits (A, B, C) and one column for the parity bit (P).
Fill the data bit columns with all eight possible combinations (000, 001, 010, etc.).
In the parity bit column, set P to 0 for cases where there are an even number of 1s in the data bits, and set P to 1 for cases with an odd number of 1s.
Logic Gates:
Analyze the truth table to identify a logical expression for the parity bit. You’ll find that P is the XOR (exclusive OR) of all three data bits (P = A XOR B XOR C).
Use two XOR gates to implement this logic. Connect each data bit (A, B, C) to one input of the first XOR gate. Connect the output of the first XOR gate and another data bit (let’s say B) to the inputs of the second XOR gate. The final output of the second XOR gate is the parity bit (P).
Odd Parity Generator:
Truth Table:
Similar to even parity, create a truth table with data bits (A, B, C) and a parity bit (P).
This time, set P to 1 for even numbers of 1s in the data bits and set P to 0 for odd numbers of 1s.
Logic Gates:
Analyze the truth table. You’ll find that P is the complement (NOT) of the even parity expression (P = NOT(A XOR B XOR C)).
There are two ways to implement this:
Option 1: Use the same circuit as the even parity generator but add an inverter (NOT gate) before the final output. This inverter flips the even parity bit to achieve odd parity.
Option 2: Use two XOR gates. Connect A and B to the first XOR gate. Connect the output of the first XOR gate and C to the second XOR gate. The final output of the second XOR gate is the parity bit (P).
Choosing the Right Parity:
Even or odd parity is a system-specific choice. Both methods can detect single-bit errors, but they cannot detect multiple-bit errors.
Make sure the sender and receiver agree on the chosen parity scheme (even or odd) to ensure proper error detection.