An artificial neural network device that utilizes one or more non-volatile memory arrays as the synapses. The synapses are configured to receive inputs and to generate therefrom outputs. Neurons are configured to receive the outputs. The synapses include a plurality of memory cells, wherein each of the memory cells includes spaced apart source and drain regions formed in a semiconductor substrate with a channel region extending there between, a floating gate disposed over and insulated from a first portion of the channel region and a non-floating gate disposed over and insulated from a second portion of the channel region. Each of the plurality of memory cells is configured to store a weight value corresponding to a number of electrons on the floating gate. The plurality of memory cells are configured to multiply the inputs by the stored weight values to generate the outputs. Various algorithms for tuning the memory cells to contain the correct weight values are disclosed.