Abstract: A conversion apparatus for quantizing an initial set of weights for a weighted sum signal processing system having one or more conversion arrays. Each conversion array stores a plurality of values to be converted, quantizes the values that are to be converted to produce a set of discrete values and a set of error values, and replaces the stored values with the set of discrete values. Each conversion array combines the set of error values with a set of transformation weights to form one or more transformed error sets. The conversion apparatus further includes a transfer device for successively combining the one or more transformed error sets most recently formed with the contents of a successive conversion array. The transfer device monitors the successively produced sets of error values and halts the successive conversions and combinations when a predetermined condition is satisifed. The invention also features methods of quantizing initial sets of weight.