# How many binary bit strings of length 32 are there

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 $2^5$ ?

• It would be $2^{32}$, since there are two choices for every bit and there are $32$ bits. – user26486 Mar 31 '15 at 16:44
• so if it asked How many binary bit strings of length 1692 are there? it would just be $2^{1692}$ – Yusha Mar 31 '15 at 16:47
• yes. ${}{}{}{}$ – user26486 Mar 31 '15 at 16:47

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.

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