How many values can be represented with n bits?

2⁹ = 512 values, because that’s how many combinations of zeroes and ones you can have.

What those values represent however will depend on the system you are using. If it’s an unsigned integer, you will have:

000000000 = 0 (min)
000000001 = 1
...
111111110 = 510
111111111 = 511 (max)

In two’s complement, which is commonly used to represent integers in binary, you’ll have:

000000000 = 0
000000001 = 1
...
011111110 = 254
011111111 = 255 (max)
100000000 = -256 (min) <- yay integer overflow
100000001 = -255
...
111111110 = -2
111111111 = -1

In general, with k bits you can represent 2^k values. Their range will depend on the system you are using:

Unsigned: 0 to 2^k-1
Signed: -2^k-1 to 2^k-1-1