Hamming Distance Calculator
Calculate the Hamming distance between two strings of equal length
Calculate Hamming Distance
Choose the number system for your messages
Length: 0 characters (spaces ignored)
Length: 0 characters (spaces ignored)
Hamming Distance Results
Formula: Count the number of positions where corresponding characters differ
Requirement: Both messages must have the same length
Range: 0 to message length (0 = identical, max = completely different)
Distance Analysis
Example Calculations
Binary Example
Message 1: 10101
Message 2: 01100
Differences: Positions 1, 2, 5
Distance: 3
Decimal Example
Message 1: 12271995
Message 2: 02071895
Differences: Positions 1, 3, 5
Distance: 3
Text Example
Word 1: HAMMING
Word 2: HUMMING
Differences: Position 2
Distance: 1
Applications
Error Detection
Measure data corruption in transmission
Bioinformatics
Compare DNA/RNA sequences
Machine Learning
Feature comparison and classification
Data Storage
Error correction codes in memory
Distance Tips
Both messages must have equal length
Distance 0 means identical messages
Maximum distance equals message length
Higher distance means more differences
Hamming distance is symmetric
Understanding Hamming Distance
What is Hamming Distance?
The Hamming distance is a metric used in information theory to measure the difference between two strings of equal length. It counts the number of positions where the corresponding symbols are different.
Why is it Important?
- •Essential for error detection and correction
- •Used in coding theory and telecommunications
- •Applied in bioinformatics for sequence comparison
- •Fundamental in machine learning algorithms
How to Calculate
d(x,y) = Σ(xi ≠yi) for i = 1 to n
Key Property: The Hamming distance satisfies the mathematical definition of a metric: it's non-negative, symmetric, and satisfies the triangle inequality.
Distance Interpretation Guide
| Distance | Percentage | Interpretation | Example Use Case |
|---|---|---|---|
| 0 | 0% | Identical strings | Perfect data transmission |
| 1-25% | 1-25% | Very similar | Minor transmission errors |
| 26-50% | 26-50% | Moderate differences | Related sequences |
| 51-100% | 51-100% | Very different | Unrelated or heavily corrupted |