If a function processes a two-digit decimal input by repeatedly dividing by 2 in a while loop, how many iterations will occur at minimum?

• A. 2
• B. 3
• C. 4
• D. at least 4

Answer: (D)

Halving a positive integer each time reduces the value, and with a loop that stops when the value reaches zero, the number of iterations corresponds to how many halvings are needed to go from the starting number to 0 using integer division.

For the smallest two-digit input, 10, the sequence under integer division by 2 is 10 -> 5 -> 2 -> 1 -> 0. That takes four iterations. Larger two-digit numbers will require the same or more halvings, so the loop will run at least four times. Hence the minimum number of iterations is four, i.e., at least 4.