1. What is Hamming Distance?

The Hamming distance between two integers is the number of positions at which the corresponding bits are different. It's commonly used in computer science for error detection and correction.

2. How Does the Calculator Work?

The calculator uses the Python formula:

Where:

• \( a \) — First integer
• \( b \) — Second integer
• \( \oplus \) — Bitwise XOR operation
• \( \text{bin}() \) — Converts to binary string
• \( \text{count}('1') \) — Counts '1' bits in the result

Explanation: The XOR operation highlights differing bits, and counting the '1's gives the number of differing bit positions.

3. Importance of Hamming Distance

Details: Hamming distance is crucial in error detection/correction codes, cryptography, DNA sequence comparison, and network routing algorithms.

4. Using the Calculator

Tips: Enter two non-negative integers. The calculator will compute the number of bit positions that differ between them.

5. Frequently Asked Questions (FAQ)

Q1: What's the maximum Hamming distance between two n-bit numbers?
A: The maximum is n, when all bits are different between the two numbers.

Q2: What's the Hamming distance between 0 and any number?
A: It's equal to the number of '1' bits in the binary representation of the other number (its population count).

Q3: How is Hamming distance used in error correction?
A: Error-correcting codes use minimum Hamming distance between codewords to determine how many errors can be detected and corrected.

Q4: What's the difference between Hamming distance and Levenshtein distance?
A: Hamming distance compares equal-length sequences (bit strings), while Levenshtein distance measures edits needed to make strings equal (insertions, deletions, substitutions).

Q5: Can Hamming distance be used for non-binary data?
A: Yes, it can be extended to compare any equal-length sequences where position-wise comparison makes sense.