  Parallel addition, i.e., addition with limited carry propagation, has been so
far studied for complex bases and integer alphabets. We focus on alphabets
consisting of integer combinations of powers of the base. We give necessary
conditions on the alphabet allowing parallel addition. Under certain
assumptions, we prove the same lower bound on the size of the generalized
alphabet that is known for alphabets consisting of consecutive integers. We
also extend the characterization of bases allowing parallel addition to
numeration systems with non-integer alphabets.
