  It is well known that the Bernoulli convolution $\nu_{\beta}$ associated to
the golden mean has Hausdorff dimension less than 1, i.e. that there exists a
set $A$ with $\nu_{\beta}(A)=1$ and $dim_H(A)<1$. We construct such a set $A$
explicitly and discuss how our approach might be generalised to prove the
singularity of other Bernoulli convolutions
