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3. You will probably want to wait until after lecture on January 23 before attempting this problem. Suppose we have a counter that stores an arbitrary number of bits and counts in binary. It always begin at 0 . The only mutator operation it can perform is to increment, adding one to the current count. This changes one or more bits. Show that if we start at 0 and perform k increment operations, a total of O(k) bits will change. Correct answers will reason about the asymptotic behavior of the total number of bit changes. Hint: There are multiple ways to approach this problem. One approach could use a credit argument, and you should refer to the array expansion of array-based Stacks and Queues for inspiration here. Another approach is numerical analysis. Try to find patterns in the total number of bit changes as k increases and inductively reason about the overall asymptotic behavior