Binary star systems are assumed to be co-natal and coeval, and thus to have identical chemical composition. In this work, we aim to test the hypothesis that there is a connection between observed element abundance patterns and the formation of planets using binary stars. Moreover, we also want to test how atomic diffusion might influence the observed abundance patterns. We conduct a strictly line-by-line differential chemical abundance analysis of seven binary systems. Stellar atmospheric parameters and elemental abundances are obtained with extremely high precision (<3.5 per cent) using the high-quality spectra from Very Large Telescope/ultraviolet-visual Echelle spectrograph and Keck/high-resolution Echelle spectrometer. We find that four of seven binary systems show subtle abundance differences (0.01-0.03 dex) without clear correlations with the condensation temperature, including two planet-hosting pairs. The other three binary systems exhibit similar degree of abundance differences correlating with the condensation temperature. We do not find any clear relation between the abundance differences and the occurrence of known planets in our systems. Instead, the overall abundance offsets observed in the binary systems (four of seven) could be due to the effects of atomic diffusion. Although giant planet formation does not necessarily imprint chemical signatures on to the host star, the differences in the observed abundance trends with condensation temperature, on the other hand, are likely associated with diverse histories of planet formation (e.g. formation location). Furthermore, we find a weak correlation between abundance differences and binary separation, which may provide a new constraint on the formation of binary systems.