A boolean function $F=F(x_{1},x_{2},x_{3},x_{4})$ has the vector of its values $w(F)=1010101000111111$ (the leftmost $1$ is $F(0,0,0,0)$ and so on).
I need to find the vector of values for $F_1=F(x_{4},x_{3},x_{2},x_{1})$.
Problem: of course, I can do it manually. But is there a witty verbal explanation that can describe the transformation of $w(F)$ into $w(F_1)$? I tried to draw a truth table to see which 4-bit set becomes what, but, for example, $0000 -> 0000$, and $0001 -> 1000$ and $0010 -> 0100$ and I don't see how it could be useful.