Section \[experiments\], comparison experiments of BDNN and conventional DNN are analyzed. The last section is the conclusion part.

The binarized deep neural network {#BDNN}
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In this section, the recognition process (forward propagation) of BDNN is introduced. As mentioned above, only binary variables and Boolean operations are used in this process. Moreover, in order to use BDNN on non-binary input data, we also introduced the hybrid-BDNN, which contained both conventional neural network part and BDNN part.

The basic function for BDNN
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As shown in Fig. \[ANNbasic\], with this basic function, we can build network of any complicated structure. Therefore, the BDNN is actually a new definition of the basic function. Just like the conventional DNN, with the basic function of BDNN, any neural network structure can be built.

Usually, a basic function of neural network should contain two different types of calculation: the linear and nonlinear calculations. For example, as shown in Fig. \[ANNbasic\], in conventional neural network, the linear calculation is an inner product of the input neurons $\bm{\vec x}$ and the corresponding weights $\bm{\vec w}$, that is, the $\bm{\vec x} \cdot \bm{\vec w}$; the nonlinear calculation of conventional neural network is activation function (sigmoid, hyperbolic tangent, etc.) 