Real number computation through Gray code embedding

We propose an embedding G of the unit open interval to the set {0, 1}⊥,1ω of infinite sequences of {0, 1} with at most one undefined element. This embedding is based on Gray code and it is a topological embedding with a natural topology on {0, 1}⊥,1ω. We also define a machine called an indeterministic multihead Type 2 machine which input/output sequences in {0, 1}ω⊥,1, and show that the computability notion induced on real functions through the embedding G is equivalent to the one induced by the signed digit representation and Type 2 machines. We also show that basic algorithms can be expressed naturally with respect to this embedding.