Data Conversion in Residue Number System

This thesis tackles the problem of data conversion in the Residue Number System (RNS). The RNS has been considered as an interesting theoretical topic for researchers in recent years. Its importance stems from the absence of carry propagation between its arithmetic units. This facilitates the realization of high-speed, low-power arithmetic. This advantage is of paramount importance in embedded processors, especially those found in portable devices, for which power consumption is the most critical aspect of the design. However, the overhead introduced by the data conversion circuits discourages the use of RNS at the applications. In this thesis, we aim at developing efficient schemes for the conversion from the conventional representation to the RNS representation and vice versa. The conventional representation can be in the form of an analog continuous-time signal or a digital signal represented in binary format. We present some of the currently available algorithms and schemes of conversion when the signal is in binary representation. As a contribution to this field of research, we propose three different schemes for direct conversion when interaction with the real analog world is required. We first develop two efficient schemes for direct analog-to-residue conversion. Another efficient scheme for direct residue-to-analog conversion is also proposed. The performance and the efficiency of theses converters are demonstrated and analyzed. The proposed schemes are aimed to encourage the utilization of RNS in various real-time and practical applications in the future.