We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base β in C and a finite digit set A of contiguous integers containing 0. For a fixed base β, we focus on the question of the size of the alphabet that permits addition in constant time, independently of the length of representation of the summands. We produce lower bounds on the size of such alphabet A. For several types of well-studied bas es (negative integer, complex numbers -1 + i, 2i , and i√2, quadratic Pisot units, and non-integer rational bases), we give explicit parallel algorithms performing addition in constant time. Moreover we show that digit sets used by these algorithms are the smallest possible.