Introduction:
In coding theory, error correcting codes are used to detect and correct errors that occur during data transmission. These codes are designed to introduce redundancy into the transmitted data, allowing the receiver to identify and correct errors.

Explanation:
To determine the maximum number of bit errors that can be corrected by a given error correcting code, we need to analyze the code words provided.

Code words:
The given code words are:
1. 00000000
2. 00001111
3. 01010101
4. 10101010
5. 11110000

Hamming distance:
The Hamming distance between two code words is defined as the number of bit positions in which the two code words differ. It represents the minimum number of bit errors required to transform one code word into another.

Identifying the minimum Hamming distance:
To determine the maximum number of bit errors that can be corrected, we need to find the minimum Hamming distance among all pairs of code words.

Comparing the given code words, we can observe the following:
- The Hamming distance between code words 1 and 2 is 4.
- The Hamming distance between code words 1 and 3 is 4.
- The Hamming distance between code words 1 and 4 is 4.
- The Hamming distance between code words 1 and 5 is 4.
- The Hamming distance between code words 2 and 3 is 4.
- The Hamming distance between code words 2 and 4 is 4.
- The Hamming distance between code words 2 and 5 is 4.
- The Hamming distance between code words 3 and 4 is 8.
- The Hamming distance between code words 3 and 5 is 4.
- The Hamming distance between code words 4 and 5 is 4.

Minimum Hamming distance:
The minimum Hamming distance among all pairs of code words is 4.

Maximum number of bit errors that can be corrected:
The maximum number of bit errors that can be corrected by the given error correcting code is equal to (minimum Hamming distance - 1).

In this case, the minimum Hamming distance is 4, so the maximum number of bit errors that can be corrected is (4 - 1) = 3.

Therefore, the correct answer is option 'd) 3'.