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This article is concerned with the H∞ state estimation problem for a class of bidirectional associative memory (BAM) neural networks with binary mode switching, where the distributed delays are included in the leakage terms. A couple of stochastic variables taking values of 1 or 0 are introduced to characterize the switching behavior between the redundant models of the BAM neural network, and a general type of neuron activation function (i.e., the sector-bounded nonlinearity) is considered. In order to prevent the data transmissions from collisions, a periodic scheduling protocol (i.e., round-robin protocol) is adopted to orchestrate the transmission order of sensors. The purpose of this work is to develop a full-order estimator such that the error dynamics of the state estimation is exponentially mean-square stable and the H∞ performance requirement of the output estimation error is also achieved. Sufficient conditions are established to ensure the existence of the required estimator by constructing a mode-dependent Lyapunov-Krasovskii functional. Then, the desired estimator parameters are obtained by solving a set of matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the proposed estimator design method.