In this study, the Binary Puma Optimizer (BPO) is introduced as a novel binary metaheuristic. The BPO employs eight Transfer Functions (TFs), consisting of four S-shaped and four V-shaped mappings, to convert the continuous search space of the original Puma Optimizer into binary form. To evaluate its effectiveness, BPO is applied to two well-known combinatorial optimization problems: the 0-1 Knapsack Problems (KPs) and the Uncapacitated Facility Location Problem (UFLP). The solver tailored for KPs is referred to as BPO1, while the solver for the UFLP is denoted as BPO2. In the UFLP experiments, only TFs are integrated into the solutions. Conversely, in the 0-1 KPs experiment, the additional mechanisms are (i) greedy-based population strategies; (ii) a crossover operator; (iii) a penalty algorithm; (iv) a repair algorithm; and (v) an improvement algorithm. Unlike KPs, the UFLP has no infeasible solutions, as facilities are assumed to be uncapacitated. Unlike KPs, the UFLP has no capacity constraints, as facilities are assumed to be uncapacitated. Thus, violations cannot occur, making improvement strategies unnecessary, and the BPO2 depends solely on TFs for binary adaptation. The proposed algorithms are compared with binary optimization algorithms from the literature. The experimental framework demonstrates the versatility and effectiveness of BPO1 and BPO2 in addressing different classes of binary optimization problems.