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In this brief, we propose a new design: a Boolean Neural Network (BNN) for the 0-1 linear programming problem under inequalities constraints by using the connection between concave programming and integer programming problems. This connection is based on the concavity and penalty function methods. The general objective function obtained, which combines the objective function and constraints is fixed as the energy of the system. The simulation results for the new BNN show that the system converge rapidly within a few neural time constant.