A system and a method of quantizing a pre-trained neural network, includes determining by a layer/channel bit-width determiner for each layer or channel of the pre-trained neural network a minimum quantization noise for the layer or the channel for each master bit-width value in a predetermined set of master bit-width values; and selecting by a bit-width selector for the layer or the channel the master bit-width value having the minimum quantization noise for the layer or the channel. In one embodiment, the minimum quantization noise for the layer or the channel is based on a square of a range of weights for the layer or the channel that is multiplied by a constant to a negative power of a current master bit-width value.