Solution

The correct answer is Option 2.

Key Points

• The Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
• To calculate the Hamming distance between the binary strings 10101 and 11110, compare each corresponding position:

• Position 1: 1 vs 1 (no difference)
• Position 2: 0 vs 1 (difference)
• Position 3: 1 vs 1 (no difference)
• Position 4: 0 vs 1 (difference)
• Position 5: 1 vs 0 (difference)

• There are 3 positions where the corresponding bits differ.

Hence, the Hamming distance between 10101 and 11110 is 3.

Additional Information

• The Hamming distance is used in error detection and correction in data transmission.
• It is named after Richard Hamming, an American mathematician and computer scientist.
• It is particularly useful in coding theory for designing error-correcting codes.
• The concept can be extended to other types of data, such as text strings and DNA sequences.