This paper proposes a binary adaptation of the recently proposed meta-heuristic, Equilibrium Optimizer (EO), called Discrete EO (DEO) to solve binary optimization problems. A U-shaped transfer function has been used to map the continuous values of EO into the binary domain. To further improve the exploitation capability of DEO, Simulated Annealing (SA) has been used as a local search procedure and the combination has been named as DEOSA. The proposed DEOSA algorithm has been applied over 18 well-known UCI datasets and compared with a wide range of algorithms. The results have been statistically validated using Wilcoxon rank-sum test. In order to test the scalability and robustness of DEOSA, it has been additionally tested over 7 high-dimensional Microarray datasets and 25 binary Knapsack problems. The results clearly demonstrate the superiority and merits of DEOSA when solving binary optimization problems.