Binary search is the ultimate divide-and-conquer algorithm. To find a key $k$ in a
large file containing keys $A[1..n]$ in sorted order, we first compare $k$ with $A[n/2]$, and
depending on the result we recurse either on the first half of the file, $A[1..n/2]$, or on
the second half, $A[n/2+1..n]$. The recurrence now is $T(n)=T(n/2)+O(1)$.
Plugging into the master theorem (with $a=1,b=2,d=0$) we get the familiar solution: a
running time of just $O(\log n)$.