Let Q be a quadratic polynomial. If the sum of the roots of Q^{100}(x) (where Q^2(x) is defined by Q^1(x)=Q(x), Q^i(x)=Q\left(Q^{i-1}(x)\right) for integers \left.i \geq 2\right) is 8 and the sum of the roots of Q is S, compute \left|\log _2(S)\right|.