Answer
For $200$ entries: $8$ comparisons
For $100,000$ entries: $17$ comparisons
Work Step by Step
Binary search works by repeatedly dividing the search interval in half. The maximum number of entries that must be checked is equal to the ceiling of the base-2 logarithm of the number of entries:
Max comparisons $=⌈\log_2(n)⌉$
For $200$ entries we have:
$\log_2(200)\approx 7.64$
$⌈7.648⌉=8$
For $100,000$ entries we have:
$\log_2(100,000)\approx 16.61$
$⌈16.61⌉=17$
