Suppose the 16 elements are sorted in the array 3, 22, 30, 33, 40, 44, 50, 60, 66, 78, 88, 99. Apply the binary search to search the value 50 from the sorted array.

Binary search is an efficient algorithm for finding an item from a sorted list of items. It works by repeatedly dividing in half the portion of the list that could contain the item, until you've narrowed down the possible locations to just one.

Here is how we can apply binary search to find the value 50 in the sorted array [3, 22, 30, 33, 40, 44, 50, 60, 66, 78, 88, 99].

1. Initialize: Start by initializing two pointers, low and high. low is initialized to the start of the array (index 0), and high is initialized to the end of the array (index 11 in this case).

   low = 0
   high = 11
   

2. Find the middle: Calculate the middle index of the array using the formula mid = low + (high - low) / 2. In our case, mid will be 5 (integer value of 5.5).

   mid = 0 + (11 - 0) / 2 = 5.5
   

   So, mid is 5. The element at index 5 is 44.

3. Compare: Compare the middle element with the target value (50).

- If the middle element is equal to the target, we have found the target in the array. Return the index. - If the middle element is greater than the target, the target can only lie in the first half of the array. So, we update high to mid - 1. - If the middle element is less than the target, the target can only lie in the second half of the array. So, we update low to mid + 1.

In our case, 44 is less than 50, so we update low to mid + 1, which is 6.

1. Repeat: Repeat steps 2 and 3 until low is not greater than high.

- Calculate mid again: mid = 6 + (11 - 6) / 2 = 8.5. So, mid is 8. The element at index 8 is 66. - 66 is greater than 50, so we update high to mid - 1, which is 7. - Calculate mid again: mid = 6 + (7 - 6) / 2 = 6.5. So, mid is 6. The element at index 6 is 50. - 50 is equal to 50. We have found the target at index 6.

So, the value 50 is found at index 6 in the array.

Here is a table summarizing each step:

Step	low	high	mid	Array[mid]	Action
1	0	11	5	44	low = mid + 1
2	6	11	8	66	high = mid - 1
3	6	7	6	50	Found at index 6

This is how binary search works. It is an efficient search algorithm as it has a time complexity of O(log n), where n is the number of elements in the array.