The binary represectation of quantum observables

To model a quantum system on quantum computer one needs to represent continuous observables (coordinates, momenta, etc.) in terms of binary observables. The problem is considered in terms of representation of observables by series of powers of 2, similar to binary representation of real numbers. The coefficients of series ("digits") are orthogonal projector operators. The representations provides a natural method of renormalization of infinite series and integrals.