  To simulate the quantum systems at classical or quantum computers, it is
necessary to reduce continuous observables (e.g. coordinate and momentum or
energy and time) to discrete ones. In this work we consider the continuous
observables represented in the positional systems as a series of powers of the
radix mulitplied over the summands (``digits``), which turn out to be Hermitean
operators with discrete spectrum. We investigate the obtained quantum
mechanical operators of digits, the commutation relations between them and the
effects of choice of numeral system on the lattices and representations.
Furthermore, during the construction of the digital representation
renormalizations of diverging sums naturally occur.
