A method for implementing a neural network system in an integrated circuit includes presenting digital pulses to word line inputs of a matrix vector multiplier including a plurality of word lines, the word lines forming intersections with a plurality of summing bit lines, a programmable Vt transistor at each intersection having a gate connected to the intersecting word line, a source connected to a fixed potential and a drain connected to the intersecting summing bit line, each digital pulse having a pulse width proportional to an analog quantity. During a charge collection time frame charge collected on each of the summing bit lines from current flowing in the programmable Vt transistor is summed. During a pulse generating time frame digital pulses are generated having pulse widths proportional to the amount of charge that was collected on each summing bit line during the charge collection time frame.