In the present study, an approach based on binary Gibbs energy-composition (G-x) plots is used for understanding the phase constitution in high-entropy alloys (HEAs). Equimolar HEAs CoCrMnNi, CoCrCuMnNi and AlCoCrMnNi were made using vacuum arc melting and heat treated for 24 h at 1000 °C. XRD and SEM were used for the characterization of constituent phases. A method based on the G-x plots of binary sub-systems was devised for the interpretation of the constituent phases in these alloys and a few other HEAs reported in the literature, namely CoCrFeMnNi and CoCuFeMnNi. The competition between phases and demixing tendencies were correlated with the G-x plots. These plots revealed that in CoCrMnNi and CoCrFeMnNi, tendency for formation of intermetallic phases and demixing were absent. This correlated well with their single-phase disordered FCC (A1) microstructure. On the other hand, the CoCrCuMnNi alloy had a duplex microstructure consisting of two FCC phases that can be attributed to the strong demixing tendency for FCC phase in the Cr-Cu system. The microstructure of the CoCuFeMnNi consisted only single FCC phase. Though, two of the constituent binaries showed tendency for demixing of this FCC phase, it is not strong enough to cause immiscibility. The AlCoCrMnNi alloy gave a duplex microstructure of an ordered (B2) and a disordered (A2) BCC phase. G-x plots showed that the competition from B2 phase in binaries is so strong that its formation inevitably occurred in this HEA. Such crucial insights into how strongly the thermodynamics of the binary sub-systems control the phase constitution in HEAs are offered by the present approach. Although the results can in principle be interpreted using comprehensive Calphad calculations, one requires reliable multicomponent Gibbs energy databases to do so. The approach presented here is rather simple, as it requires only Gibbs energy functions of relevant phases of the constituent binary systems. © 2018 Elsevier B.V.