  We develop the theory of frames and Parseval frames for finite-dimensional
vector spaces over the binary numbers. This includes characterizations which
are similar to frames and Parseval frames for real or complex Hilbert spaces,
and the discussion of conceptual differences caused by the lack of a proper
inner product on binary vector spaces. We also define switching equivalence for
binary frames, and list all equivalence classes of binary Parseval frames in
lowest dimensions, excluding cases of trivial redundancy.
