Parity Bit Calculator
Generate parity bits for error detection or check binary messages for transmission errors
Parity Bit Operations
Enter the original data message without parity bit
Quick Examples
Even Parity Example:
Message: 1101 (3 ones)
Parity bit: 1 (makes 4 ones = even)
Result: 11011
Odd Parity Example:
Message: 1101 (3 ones)
Parity bit: 0 (keeps 3 ones = odd)
Result: 11010
Parity Types
Even Parity
- • Total number of 1s must be even
- • Add 0 if message has even 1s
- • Add 1 if message has odd 1s
- • Formula: (sum of 1s) mod 2
Odd Parity
- • Total number of 1s must be odd
- • Add 1 if message has even 1s
- • Add 0 if message has odd 1s
- • Formula: NOT((sum of 1s) mod 2)
Error Detection Limits
Detects single-bit errors
Detects odd number of bit errors
Cannot detect even number of bit errors
Cannot locate error position
Cannot correct errors
Usage Tips
Parity bits are typically added at the end
Choose parity type before transmission
Use for simple error detection in noisy channels
Consider Hamming codes for error correction
Understanding Parity Bits
What are Parity Bits?
A parity bit is an extra bit added to a binary message to enable error detection during data transmission. It provides a simple method to detect single-bit errors in digital communication systems.
How They Work
- •Count the number of 1s in the original message
- •Add a parity bit to make the total count even or odd
- •Receiver checks if parity matches expectations
- •Mismatch indicates transmission error
Mathematical Foundation
Parity = (∑ bits) mod 2
Sum of all 1s in message, modulo 2
Applications
- •Serial communication protocols
- •Memory systems (RAM error detection)
- •Network packet transmission
- •Storage devices and file systems
Step-by-Step Example
Even Parity Calculation
Step 1: Original message = 1101
Step 2: Count 1s = 3 (odd)
Step 3: Add 1 to make total even = 4
Step 4: Result = 11011
Check: Total 1s = 4 (even) ✓
Error Detection Process
Transmission Check
Sent: 11011 (even parity)
Received: 11001 (bit flip)
Count 1s: 3 (odd)
Expected: Even count
Result: Error detected! ⚠️