  In this paper we consider block languages, namely sets of words having the
same length, and we propose a new representation for these languages. In
particular, given an alphabet of size $k$ and a length $\ell$, these languages
can be represented by bitmaps of size $k^\ell$, in which each bit indicates
whether the correspondent word, according to the lexicographical order, belongs
to the language (bit equal to 1) or not (bit equal to 0). This representation
turns out to be a good tool for the investigation of several properties of
block languages, making proofs simpler and reasoning clearer. After showing how
to convert bitmaps into minimal deterministic and nondeterministic finite
automata, we use this representation as a tool to study the deterministic and
nondeterministic state complexity of block languages, as well as the costs of
basic operations on block languages, in terms of the sizes of the equivalent
finite automata.
