8. Given the condition $p:|4 x-3|<1$;

condition $q: x^{2}-(2 a+1) x+a(a+1) \leqslant 0$.
If $p$ is a necessary but not sufficient condition for $q$, then the range of real number $a$ is $\qquad$.
8. $[0,0.5]$.

From $p$ being a necessary but not sufficient condition for $q$, we know that $q$ is a necessary but not sufficient condition for $p$.
Given $p: \frac{1}{2}<x<1, q: a \leqslant x \leqslant a+1$.
Therefore, $a+1 \geqslant 1$ and $a \leqslant \frac{1}{2}$.
Thus, $0 \leqslant a \leqslant \frac{1}{2}$.