What you can use is Polya's theory of counting, for alphabet size $k=2.$

An $(n, k)−$necklace is an equivalence class of words of length $n$
over an alphabet of size $k$ under rotation. The basic enumeration
problem is:

For a given $n$ and $k,$ how many $(n, k)-$necklaces are there?
Equivalently, we are asking how many orbits the cyclic group $C_n$
has on the set of all words of length $n$ over an alphabet of size $k.$
Denote this value by $a(n, k).$

**Theorem:**

$$a(n,k)=\frac{1}{n}\sum_{d|n} \phi(d) k^{n/d}.$$

Have fun!