  We give an expression for the Garsia entropy of Bernoulli convolutions in
terms of products of matrices. This gives an explicit rate of convergence of
the Garsia entropy and shows that one can calculate the Hausdorff dimension of
the Bernoulli convolution $\nu_\beta$ to arbitrary given accuracy whenever
$\beta$ is algebraic. In particular, if the Garsia entropy $H(\beta)$ is not
equal to $\log(\beta)$ then we have a finite time algorithm to determine
whether or not $\mathrm{dim}_\mathrm{H} (\nu_\beta)=1$.
