We propose an embedding G of the unit open interval to the set {0, 1}(perpendicular to)(omega),(1) of infinite sequences of 10, 11 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}(perpendicular to)(omega),(1). We also define a machine called an indeterministic multihead Type 2 machine which input/output sequences in {0,1}(perpendicular toomega),(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. (C) 2002 Elsevier Science B.V. All rights reserved.