# Discrete Structures: Bit Strings

So my professor gave us an HW assignment which includes this question:

"How many bit strings consist of 1 through 5 bits. (Note 10 and 00010 are considered distinct even though they are both representations for 2)"

My answer is 62. Is this correct? Thanks

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There are $2^1 = 2$ bit strings consisting of exactly $1$ bit.
There are $2^2 = 4$ bit strings consisting of exactly $2$ bits.
There are $2^3 = 8$ bit strings consisting of exactly $3$ bits.
So, following this pattern, you have $2+4+8+16+32 = 62$ bit strings.
Or you could just say it's 111110 in binary ($= 1\cdot2^5 + 1\cdot2^4 + 1\cdot2^3 + 1\cdot2^2 + 1\cdot2^1 + 0\cdot2^0$). ;)) –  r.e.s. Dec 8 '11 at 3:24