Final answer:
The maximum number of comparisons required when performing a binary search on a list of 500 entries is 10. This is calculated using the formula 'log2(n) + 1' and then rounding up the logarithm result to the next whole number.
Step-by-step explanation:
The maximum number of entries that must be interrogated when applying binary search to a list of 500 entries can be determined by using the concept of binary search which involves halving the list until the desired element is found or the list cannot be split further. The formula for finding the maximum number of comparisons in a binary search is ‘log2(n) + 1’, where ‘n’ is the number of entries in the list.
To find the maximum number of entries that must be interrogated:
- Take the logarithm to the base 2 of the number of entries (n = 500).
- Add 1 to the result of the logarithm.
By calculating, log2(500) is approximately 8.96578, which after rounding up, since you cannot have a fraction of a comparison, is 9. After adding 1, this yields a maximum of 10 comparisons that must be performed during the binary search.