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How many binary bit strings of length 32 are there?

I think I know the answer but I'm not sure...wouldn't it just be $2^5$ ?

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    $\begingroup$ It would be $2^{32}$, since there are two choices for every bit and there are $32$ bits. $\endgroup$ – user26486 Mar 31 '15 at 16:44
  • $\begingroup$ so if it asked How many binary bit strings of length 1692 are there? it would just be $2^{1692}$ $\endgroup$ – Yusha Mar 31 '15 at 16:47
  • $\begingroup$ yes. ${}{}{}{}$ $\endgroup$ – user26486 Mar 31 '15 at 16:47
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Each one of the $32$ bits can be either $0$ or $1$: So there are two options per bit.

That gives $$\underbrace {2\cdot 2\cdot 2\cdot \cdots \cdot 2}_{\large 32 \,\text{ factors of 2}} = 2^{32}$$ possible strings of length $32.$

Indeed, in creating a string of length $n$, there are $2^n$ possible such strings.

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  • $\begingroup$ so if it asked How many binary bit strings of length 1692 are there? it would just be $2^{1692}$ $\endgroup$ – Yusha Mar 31 '15 at 16:47
  • $\begingroup$ Yes, that's correct. $\endgroup$ – Jordan Glen Mar 31 '15 at 16:49

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