  Complementary idempotent paravectors and their ordered compositions, are used
to represent multivector basis elements of geometric Clifford algebra for 3D
Euclidean space as the states of a geometric byte in a given frame of
reference. Two layers of information, available in real numbers, are
distinguished. The first layer is a continuous one. It is used to identify
spatial orientations of similar geometric objects in the same computational
basis. The second layer is a binary one. It is used to manipulate with 8D
structure elements inside the computational basis itself. An oriented unit cube
representation, rather than a matrix one, is used to visualize an inner
structure of basis multivectors. Both layers of information are used to
describe unitary operations -- reflections and rotations -- in Euclidian and
Hilbert spaces. The results are compared with ones for quantum gates. Some
consequences for quantum and classical information technologies are discussed.
