Circle circle everywhere

Here's a question where you need to analyze the pattern and then answer the question.

A kindergarten kid may solve it in a couple of minutes. You need to think like a child:

$f(1265) = 1 \\ f(1678) = 3 \\ f(1111)=0 \\ f(8089) = 6 \\ f(0000)=4 \\ f(6238)= ?$