Q: When a binary number is incremented by 1, there may be a carry that may carry over several bit positions i.e. 1010111 is incremented and the carry distance is 3. Given a natural number n, find the average carry distance when incrementing a binary number b in the inverval 2(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}<=b <= 2^{n+1}, assuming all 2^{n}numbers in this interval occur equally often.

So far, I have gotten a pattern such that 2^{n}/ 2^{n}. However, this is just equal to 1. I am really stuck here. Any help, hints or clarification would be great, thanks.

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# Mathematical induction question?

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