Data conversion circuits with optimized common hardware convert numbers expressed in a first radix C to other radices m1, m2, etc., with the mode of operation being controlled to establish a radix C to radix m1 conversion in one mode, a radix C to radix m2 conversion in another mode, etc., on a selective basis, as desired. In a first embodiment, numbers represented in a binary (base 2) radix C are converted to a base 10 (m1) or base 12(m2) representation. In a second embodiment, numbers stored in a ternary (base 3) radix C representation are converted to a base 12 (m1) or base 10 (m2) representation. The circuits are predicated upon recognition of the fact that a number represented in a first radix can be converted readily to a second radix using shared hardware if the following equation is satisfied: