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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.
Good Question. It looks like some kind of ripple counter. It repeats after 15 steps. Values (consider the outputs to be 8,4,2,1) as 8,4,2,9,12,6,11,5,10,13,14,15,7,3,1.
Zero only for one step after reset, not repeated.
