Core-level binding energies of the component metals in bimetallic clusters of various compositions in the Ni-Cu, Au-Ag, Ni-Pd, and Cu-Pd systems have been measured as functions of coverage or cluster size, after having characterized the clusters with respect to sizes and compositions. The core-level binding energy shifts, relative to the bulk metals, at large coverages or cluster size, Delta E(a), are found to be identical to those of bulk alloys. By substracting the Delta E(a) values from the observed binding energy shifts, Delta E, we obtain the shifts, Delta E(c), due to cluster size. The Delta E(c) values in all the alloy systems increase with the decrease in cluster size. These results establish the additivity of the binding energy shifts due to alloying and cluster size effects in bimetallic clusters.