Conditions of A-completeness for linear automata over dyadic rationals

We consider the problem of $A$-completeness in the class of linear automata such that the sets of inputs, outputs and states are Cartesian products of dyadic rationals; systems checked for completeness are comprised of a variable finite set and a fixed additional set. We obtain conditions of $A$-completeness in terms of maximal subclasses in the cases when the additional set is the set of all unary automata and when the additional set consists of the adder.