Example: Binary Counter A[0,...,k-1]

A[0] is the low-order bit.

A[k-1] is the high-order bit.

   Increment(A)
      i = 0
      while i < length(A) and A[i] = 1
         A[i] = 0
         i = i+1
      if i < length(A)
      then A[i] = 1

• The worst case run time is $\Theta(k)$,
• Over n calls, worst case is O(nk),
• But actual worst-case run time for n calls is O(n).