Hello, please provide solution and explanation(much appreciated), thank you. This is a C++ Data Structures course. The preferred format is on paper.

2. 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