Binary Error Detection Tool

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.

✓ Even / Odd Parity ✓ Count 1 Bits ✓ Even Parity Bit ✓ Odd Parity Bit ✓ Instant Result
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Binary Parity Check
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Enter a binary bit string using only digits 0 and 1. Leading zeros are preserved.
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✓ Parity Result
Even Parity
Current parity of the entered binary data
Number of 1 Bits 0
Even Parity Bit 0
Odd Parity Bit 1
Parity Breakdown

What Is Binary Parity?

Binary parity describes whether the number of 1 bits in a binary string is even or odd.

For example: 1010 contains two 1 bits. Because 2 is even: 1010 has even parity

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

Binary data: 1010 Count the set bits: 1 + 0 + 1 + 0 Number of 1s = 2 Since 2 is even: Current parity = Even For even-parity transmission: Parity bit = 0 For odd-parity transmission: Parity bit = 1

Example: Parity of 11001

Binary: 11001 Number of 1s: 3 Three is odd, therefore: Current parity = Odd To create even parity: Add parity bit 1 To retain odd parity: Add parity bit 0

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.

If the data contains an even number of 1s: Even parity bit = 0 If the data contains an odd number of 1s: Even parity bit = 1

How Is an Odd Parity Bit Calculated?

An odd parity bit is chosen so that the total number of 1 bits becomes odd.

If the data already contains an odd number of 1s: Odd parity bit = 0 If the data contains an even number of 1s: Odd parity bit = 1

Parity and Hamming Weight

Binary parity is directly determined from Hamming weight, which is the number of set bits in a binary string.

If: Hamming weight mod 2 = 0 then the parity is even. If: Hamming weight mod 2 = 1 then the parity is odd.

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.

Important: parity indicates whether the count of set bits is even or odd. It does not identify which bit is incorrect and cannot detect every possible multi-bit error.

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Binary Parity Calculator FAQs

What is parity in binary?
Parity indicates whether the number of 1 bits in a binary string is even or odd.
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?
Since 11001 already contains three 1s, an additional 1 makes the total four. Therefore the even parity bit is 1.
What is the odd parity bit for 11001?
The data already contains an odd number of 1s, so the odd parity bit is 0.
Does zero have even parity?
Yes. A binary string containing zero set bits has even parity because zero is an even number.
Is parity the same as Hamming weight?
No. Hamming weight is the exact number of 1 bits. Parity only tells whether that count is even or odd.
Can parity detect a single-bit error?
Yes. A single-bit change flips the parity, so a standard parity check can detect it.
Can parity detect two-bit errors?
Not reliably. Two changed bits can leave the overall parity unchanged.
Do leading zeros affect parity?
No. Leading zeros do not add any 1 bits, so they do not change parity.
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