I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if

$$L'_m$$ and $$L_n$$ are languages restricted to be over the same alphabet, with m and n quotients, respectively, the state complexity of any binary boolean operation on $$L'_m$$ and $$L_n$$ is mn, and that of the product (concatenation) is $$(m-1)2^n +2^{n-1}$$ . In contrast to this, I show that if $$L'_m$$ and $$L_n$$ are over their own different alphabets, the state complexity of union and symmetric difference is $$mn+m+n+1$$ , that of intersection is $$mn+1$$ , that of difference is $$mn+m+1$$ , and that of the product is $$m2^n+2^{n-1}$$ .