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Inspired by the bamboo growth process, Chu et al. proposed the Bamboo Forest Growth Optimization (BFGO) algorithm. It incorporates bamboo whip extension and bamboo shoot growth into the optimization process. It can be applied very well to classical engineering problems. However, binary values can only take 0 or 1, and for some binary optimization problems, the standard BFGO is not applicable. This paper firstly proposes a binary version of BFGO, called BBFGO. By analyzing the search space of BFGO under binary conditions, the new curve V-shaped and Taper-shaped transfer function for converting continuous values into binary BFGO is proposed for the first time. A long-mutation strategy with a new mutation approach is presented to solve the algorithmic stagnation problem. Binary BFGO and the long-mutation strategy with a new mutation are tested on 23 benchmark test functions. The experimental results show that binary BFGO achieves better results in solving the optimal values and convergence speed, and the variation strategy can significantly enhance the algorithm's performance. In terms of application, 12 data sets derived from the UCI machine learning repository are selected for feature-selection implementation and compared with the transfer functions used by BGWO-a, BPSO-TVMS and BQUATRE, which demonstrates binary BFGO algorithm's potential to explore the attribute space and choose the most significant features for classification issues.