Your recurrence is
T(n) = T(n / 2) + O(1)
Since the Master Theorem works with recurrences of the form
T(n) = aT(n / b) + nc
In this case you have
- a = 1
- b = 2
- c = 0
Since c = logba (since 0 = log2 1), you are in case two of the Master Theorem, which solves to Θ(nc log n) = Θ(n0 log n) = Θ(log n).
Hope this helps!