Attenuation, when your regressor is measured with noise

The true model is $y = \beta x^* + \varepsilon$, but you cannot observe $x^*$ cleanly. You measure $x = x^* + u$, where $u$ is independent measurement noise (independent of $x^*$ and $\varepsilon$). You regress $y$ on the noisy $x$.

Derive what your estimated slope converges to, and describe the bias.