Efficient scaling in the residue number system

A unified residue number system scaling technique that allows the designer a great deal of flexibility in choosing the scale factor is presented. The technique is based on the L(ε+δ)-CRT (Chinese remainder theorem). By embedding the scaling process in the CRT, the L(ε+δ)-CRT can also be used to simplify the residue-to-analog conversion problem. The flexibility in choosing the scale factor and a new reduced system modulus comes at the cost of potentially large errors, however. It is shown that the errors induced by the L(ε+δ)-CRT can be divided into two distinct bands: a band of small errors and a band of errors on the order of the reduced system modulus. For a given scale factor, the authors give inequalities that make it possible to choose a reduced system modulus so that the large error band is avoided