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

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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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 0(1)).
Reminder: A binary counter's increment operations would look like this (for a binary counter with
three digits):
1. Binary counter showing 0:
2. Binary counter showing 1:
3. Binary counter showing 2:
4. Binary Counter showing 3:
5. Binary Counter showing 4:
0 0 0
0 0 1
0
0
1
1 0
1 1
0 0
2
Transcribed Image Text: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 0(1)). Reminder: A binary counter's increment operations would look like this (for a binary counter with three digits): 1. Binary counter showing 0: 2. Binary counter showing 1: 3. Binary counter showing 2: 4. Binary Counter showing 3: 5. Binary Counter showing 4: 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 2
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