  Liouville numbers were the first class of real numbers which were proven to
be transcendental. It is easy to construct non-normal Liouville numbers. Kano
and Bugeaud have proved, using analytic techniques, that there are normal
Liouville numbers. Here, for a given base k >= 2, we give two simple
constructions of a Liouville number which is normal to the base k.
  The first construction is combinatorial, and is based on de Bruijn sequences.
A real number in the unit interval is normal if and only if its finite-state
dimension is 1. We generalize our construction to prove that for any rational r
in the closed unit interval, there is a Liouville number with finite state
dimension r. This refines Staiger's result that the set of Liouville numbers
has constructive Hausdorff dimension zero, showing a new quantitative
classification of Liouville numbers can be attained using finite-state
dimension.
  In the second number-theoretic construction, we use an arithmetic property of
numbers - the existence of primitive roots - to construct Liouville numbers
normal in finitely many bases, assuming a Generalized Artin's conjecture on
primitive roots.
