The present work deals with the study of palladium-silver (PdAg) and palladium-gold (PdAu) binary alloys over a broad range of temperatures and alloy compositions using density functional theory (DFT) to find possible conditions where the solubility of hydrogen (H) is significantly higher than that of pure palladium (Pd). Several alloy structures, such as Pd(100-x)Ag(x) with x = 14.81, 25.93, 37.04, and 48.51, Pd(100-x)Aux with x = 14.81, 25.93, and 37.04, and Pd(100-x)Cu(x) with x = 25.93 and 48.51 were considered. The lattice constants of these structures were optimized using DFT, and relaxed structures were used for the estimation of binding energy. It was found that the solubility of H in PdAg is higher than pure Pd with a maximum at approximately 30% Ag at 456 K. Also, the solubility of PdAu alloys was higher than pure Pd with a maximum at about 20% Au with a solubility 12 times higher than that of pure Pd. It was found that for a 3.7% H concentration in a PdAg alloy, a cell expansion of 0.15-0.2% occurs, which if ignored may affect the individual binding energy of the O-site by approximately 3.56% and may affect the predicted solubility by approximately 11.8%.