Parity Calculator
Calculate mathematical and computer science parity for decimal and binary numbers
Calculate Parity
Mathematical: Based on divisibility by 2. Computer Science: Based on count of 1s in binary representation.
Choose the base of your input number
Enter a positive integer in decimal format
Example Calculations
Decimal Even
Decimal Odd
Binary Message
Binary Even
Types of Parity
Mathematical Parity
Based on divisibility by 2. Even numbers are divisible by 2 with no remainder.
Computer Science Parity
Based on count of 1s in binary representation. Used in error detection.
Different Results
An odd number can have even parity in computer science and vice versa.
Quick Reference
Mathematical Even
Last digit: 0, 2, 4, 6, 8
Divisible by 2
Mathematical Odd
Last digit: 1, 3, 5, 7, 9
Not divisible by 2
Binary Parity
Count 1s in binary representation
Even count = even parity
Understanding Parity
Mathematical Parity
In mathematics, parity refers to whether a number is even or odd. This is determined by whether the number is divisible by 2. Even numbers leave no remainder when divided by 2, while odd numbers leave a remainder of 1.
Quick Methods:
- •Look at the last digit: 0,2,4,6,8 = even; 1,3,5,7,9 = odd
- •Use modulo operation: n mod 2 = 0 (even) or 1 (odd)
- •In binary: last bit is 0 (even) or 1 (odd)
Computer Science Parity
In computer science, parity refers to the count of 1s in the binary representation of a number or message. This concept is crucial for error detection in digital communications and data storage.
Applications:
- •Error detection in data transmission
- •Memory parity checking (RAM)
- •Checksum algorithms
- •Network protocol validation
Key Insight: An odd number (mathematically) can have even parity (in computer science) if its binary representation contains an even number of 1s.
Parity Comparison Examples
| Decimal | Binary | Math Parity | CS Parity | 1s Count |
|---|---|---|---|---|
| 6 | 110 | Even | Even | 2 |
| 9 | 1001 | Odd | Even | 2 |
| 11 | 1011 | Odd | Odd | 3 |
| 12 | 1100 | Even | Even | 2 |