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The abstract mathematical rules of artificial neural network (ANN) are implemented through computation using electronic computers, photonics and in-vitro DNA computation. Here we demonstrate the physical realization of ANN in living bacterial cells. We created a single layer ANN using engineered bacteria, where a single bacterium works as an artificial neuron and demonstrated a 2-to-4 decoder and a 1-to-2 de-multiplexer for processing chemical signals. The inputs were extracellular chemical signals, which linearly combined and got processed through a non-linear log-sigmoid activation function to produce fluorescent protein outputs. The activation function was generated by synthetic genetic circuits, and for each artificial neuron, the weight and bias values were adjusted manually by engineering the molecular interactions within the bacterial neuron to represent a specific logical function. The artificial bacterial neurons were connected as ANN architectures to implement a 2-to-4 chemical decoder and a 1-to-2 chemical de-multiplexer. To our knowledge, this is the first ANN created by artificial bacterial neurons. Thus, it may open up a new direction in ANN research, where engineered biological cells can be used as ANN enabled hardware.