Binary Parity

The *binary parity* of an integer $N$ is defined as follows: - First, write $N$ in binary. For example, $N = 13$ is written as $\texttt{1101}$ in binary, and $N = 5$ is written as $\texttt{101}$. - Compute $S_N$, the sum of the *binary digits* of $N$. For example, from the earlier examples, $S_{13} = 1+1+0+1 = 3$ and $S_{5} = 1+0+1 = 2$. - The binary parity of $N$ is then the parity$^\dagger$