There is a step in the construction of this algorithm which I'm not understanding:
$\displaystyle \left[\sum_x \frac{| x \rangle}{\sqrt{2^n}}\right]\left[\frac{ | 0 \rangle -| 1 \rangle }{\sqrt{2}} \oplus | f(x) \rangle\right]=\sum_x \frac{(-1)^{f(x)} | x \rangle }{\sqrt{2^n}}\left(\frac{| 0 \rangle - |1 \rangle}{\sqrt{2}}\right)$
where $f:\{0,1\}^n \to \{0,1\}$.
I don't see how they are equal, and I believe part of my confusion is on how $\oplus$ work for $2$-qubits. $\oplus$ denotes addition $\!\!\!\!\mod 2$... so does it work in each element separately?