$2^N$ binary digits can be placed in a circle so that all the $N$-digit clockwise subsequences are distinct.

For $N=3$, two such circular arrangements are possible, ignoring rotations:

For the first arrangement, the $3$-digit subsequences, in clockwise order, are:
$000$, $001$, $010$, $101$, $011$, $111$, $110$ and $100$.

Each circular arrangement can be encoded as a number by concatenating the binary digits starting with the subsequence of all zeros as the most significant bits and proceeding clockwise. The two arrangements for $N=3$ are thus represented as $23$ and $29$:

$$\begin{array}{rl}{00010111}_2& =23\\ {00011101}_2& =29\end{array}$$

Calling $S(N)$ the sum of the unique numeric representations, we can see that $S(3)=23+29=52$.

Find $S(5)$.