Parity Bit Calculator
Calculate parity bits for error detection. Determine even or odd parity bit to add to binary data for simple error checking.
Enter binary digits (0s and 1s only)
How to Use This Calculator
- Enter your binary data bits (only 0s and 1s).
- Select parity type: Even (total 1s must be even) or Odd (total 1s must be odd).
- The calculator displays the parity bit value and the complete data with parity bit.
- Use this to add error detection to binary data or understand parity checking.
Parity Bit Formula
Parity bit is calculated from the number of 1s in the data:
Odd Parity: Parity bit = 1 - (Number of 1s mod 2)
Example: Data "1010" has 2 ones. Even parity: Parity bit = 2 mod 2 = 0 (total 2 ones, even). Odd parity: Parity bit = 1 - 0 = 1 (total 3 ones, odd). Complete: "10100" (even) or "10101" (odd).
Full Description
Parity bits are a simple form of error detection used in digital communication and storage. A parity bit is an extra bit added to binary data to make the total number of 1s either even (even parity) or odd (odd parity). This allows detection of single-bit errors during transmission or storage, though it cannot correct errors or detect multiple errors.
Parity checking is simple and efficient, making it useful for basic error detection in serial communication, memory systems, and data storage. However, it has limitations: it can only detect odd numbers of bit errors (1, 3, 5, ...) and cannot detect even numbers of errors (2, 4, 6, ...) because they cancel out. For more robust error detection and correction, more advanced codes like Hamming codes or CRC are used.
This calculator helps you determine parity bits for binary data. Enter your data bits and select even or odd parity, and it calculates the parity bit and shows the complete data with parity. Use it to understand error detection, add parity to data, or learn about simple error checking methods. Parity bits are fundamental to reliable data transmission and storage.
Frequently Asked Questions
What is a parity bit?
A parity bit is an extra bit added to binary data for error detection. It ensures the total number of 1s (including the parity bit) is even (even parity) or odd (odd parity). This allows detection of single-bit errors during transmission or storage.
What's the difference between even and odd parity?
Even parity: Parity bit is set so total number of 1s (data + parity) is even. Odd parity: Parity bit is set so total number of 1s is odd. For example, data "1010" (2 ones): Even parity bit = 0 (2+0=2, even), Odd parity bit = 1 (2+1=3, odd).
How does parity detect errors?
After transmission, count the 1s in the received data (including parity bit). If the count doesn't match the expected parity (even or odd), an error occurred. Parity can detect single-bit errors but cannot correct them or detect multiple errors.
What are the limitations of parity?
Parity can only detect odd numbers of bit errors (1, 3, 5, ...). It cannot detect even numbers of errors (2, 4, 6, ...) because they cancel out. Parity also cannot correct errors—it only detects them. For error correction, use more advanced codes like Hamming codes.