Binary Parity Calculator
Check whether a binary string has even or odd parity. The calculator counts all set bits, determines the current parity, and shows which parity bit would be required for even-parity or odd-parity transmission.
What Is Binary Parity?
Binary parity describes whether the number of 1 bits in a binary
string is even or odd.
How the Binary Parity Calculator Works
1. Read the Binary String
The calculator validates that the input contains only 0 and 1.
2. Count Set Bits
Every occurrence of 1 is counted.
3. Check the Count
An even number of 1s means even parity; an odd number means odd parity.
4. Calculate Parity Bits
The calculator also determines the bit required for even and odd parity schemes.
Even Parity vs Odd Parity
| Parity Type | Rule |
|---|---|
| Even Parity | Total number of 1 bits must be even. |
| Odd Parity | Total number of 1 bits must be odd. |
Example: Parity of 1010
Example: Parity of 11001
Binary Parity Examples
| Binary | Number of 1s | Current Parity | Even Parity Bit | Odd Parity Bit |
|---|---|---|---|---|
0 |
0 | Even | 0 | 1 |
1 |
1 | Odd | 1 | 0 |
10 |
1 | Odd | 1 | 0 |
11 |
2 | Even | 0 | 1 |
1010 |
2 | Even | 0 | 1 |
1110 |
3 | Odd | 1 | 0 |
1111 |
4 | Even | 0 | 1 |
11001 |
3 | Odd | 1 | 0 |
How Is an Even Parity Bit Calculated?
An even parity bit is chosen so that the total number of 1 bits, including the parity bit, becomes even.
How Is an Odd Parity Bit Calculated?
An odd parity bit is chosen so that the total number of 1 bits becomes odd.
Parity and Hamming Weight
Binary parity is directly determined from Hamming weight, which is the number of set bits in a binary string.
Why Is Parity Used?
Error Detection
Parity can detect certain bit changes during data transmission or storage.
Digital Communication
Parity bits have historically been used in serial communication protocols.
Memory Systems
Basic parity can be used to identify some memory data errors.
Teaching Binary Logic
Parity is useful for understanding XOR, bit counting, and error-detection concepts.
Can Parity Detect Every Error?
No. A single parity bit can detect any error that changes an odd number of bits, including a single-bit error.
However, if an even number of bits change, the parity may remain unchanged. Therefore parity is a simple error-detection method, not a complete error-correction system.
Related BinaryCon Tools
Binary Parity Calculator FAQs
What is parity in binary?
What is the parity of binary 1010?
1010 contains two 1 bits, so it has even parity.
What is the parity of binary 11001?
11001 contains three 1 bits, so it has odd parity.
What is the even parity bit for 11001?
11001 already contains three 1s, an additional
1 makes the total four. Therefore the even parity bit is 1.