4 Binary Counter Suppose that you are given a binary counter with an infinite number of digits of the set (0, 1) and the starting position of all digits being 0. Turning a number costs one unit of power. Show that in- crementing the counter only costs amortized constant units of power (i.e. it runs in amortized O(1)). Reminder: A binary counter's increment operations would look like this (for a binary counter with three digits): 1. Binary counter showing 0: 0 0 2. Binary counter showing 1: 0 0 1 3. Binary counter showing 2: 0 1 0 4. Binary Counter showing 3:0 1 5. Binary Counter showing 4: 1 0 0

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