first layer if less than eight presentation are used.

The previous curves do not include the cost of random bit generation. If we use a simple eight-bit Linear Feedback Shift Register (LFSR) pseudo random number generator, the added energy is $0.52nJ/cycle$, and the added area is $48,000\ \mu m^2$. Both are therefore negligible. It has also been shown that Spin Torque MRAM technology can be adapted to provide very low energy true random numbers [@vodenicarevic2017low]. If such a technology was used, based on the numbers of [@vodenicarevic2017low], the energy cost of random bit generation would be $0.125nJ/cycle$, and the area much smaller than LFSR. The energy cost of random number generation is therefore negligible with regards to the consumption of the system seen in Fig. \[fig:energy\].

[These energy numbers are very attractive with regards to non binarized implementations at equivalent recognition rate. Non binarized neural networks require less neurons and synapses than BNNs to achieve equivalent recognition rate. For example, to match the performance obtained in Fig. \[fig:accuracy\] on Fashion-MNIST with three image presentations ($T=3$), one only needs a non-binarized neural network with eight-bit synapses with two layers of 500 neurons, while the BNN needs 1024 neurons per layer. However, 