  In the introductory paper, [Physics Letters A 373 (2009) 911-918],
arXiv:0808.3162, about noise-based logic, we showed how simple superpositions
of single logic basis vectors can be achieved in a single wire. The
superposition components were the N orthogonal logic basis vectors. Supposing
that the different logic values have "on/off" states only, the resultant
discrete superposition state represents a single number with N bit accuracy in
a single wire, where N is the number of orthogonal logic vectors in the base.
In the present paper, we show that the logic hyperspace (product) vectors
defined in the introductory paper can be generalized to provide the discrete
superposition of 2^N orthogonal system states. This is equivalent to a
multi-valued logic system with 2^(2^N) logic values per wire. This is a similar
situation to quantum informatics with N qubits, and hence we introduce the
notion of noise-bit. This system has major differences compared to quantum
informatics. The noise-based logic system is deterministic and each
superposition element is instantly accessible with the high digital accuracy,
via a real hardware parallelism, without decoherence and error correction, and
without the requirement of repeating the logic operation many times to extract
the probabilistic information. Moreover, the states in noise-based logic do not
have to be normalized, and non-unitary operations can also be used. As an
example, we introduce a string search algorithm which is O(M^0.5) times faster
than Grover's quantum algorithm (where M is the number of string entries),
while it has the same hardware complexity class as the quantum algorithm.
