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Binary Convolutional Neural Networks (CNNs) have significantly reduced the number of arithmetic operations and the size of memory storage needed for CNNs, which makes their deployment on mobile and embedded systems more feasible. However, the CNN architecture after binarizing requires to be redesigned and refined significantly due to two reasons: 1. the large accumulation error of binarization in the forward propagation, and 2. the severe gradient mismatch problem of binarization in the backward propagation. Even though the substantial effort has been invested in designing architectures for single and multiple binary CNNs, it is still difficult to find an optimal architecture for binary CNNs. In this paper, we propose a strategy, named NASB, which adopts Neural Architecture Search (NAS) to find an optimal architecture for the binarization of CNNs. Due to the flexibility of this automated strategy, the obtained architecture is not only suitable for binarization but also has low overhead, achieving a better trade-off between the accuracy and computational complexity of hand-optimized binary CNNs. The implementation of NASB strategy is evaluated on the ImageNet dataset and demonstrated as a better solution compared to existing quantized CNNs. With the insignificant overhead increase, NASB outperforms existing single and multiple binary CNNs by up to 4.0% and 1.0% Top-1 accuracy respectively, bringing them closer to the precision of their full precision counterpart. The code and pretrained models will be publicly available.