I have calculated the boolean functions for $ r$ and $ f$ :

$ f = \overline{s_1} \cdot s_0 + s_1 \cdot \overline{s_0}$ .

$ r = \overline{s_0 \cdot s_1 \cdot s_2 \cdot s_3}$ .

Do you have an idea what an application for this circuit can be? I don’t know where we would use it.