RNS Digital Filtering Structures for Wafer-Scale Integration

Wafer-scale integration (WSI) compresses a large amount of microelectronics representing a complete digital system onto a single intact wafer. This approach is desirable for applications requiring extensive computational capabilities but only limited input and output connections. Its primary advantage is an improvement in total system density. However, such designs must have built-in fault tolerance. Parallel architectures are ideal for WSI. Thus, digital filtering implemented via the residue number system (RNS) is an application that naturally fits the requirements and advantages of WSI. A finite impulse response (FIR) filter readily lends itself to RNS implementation, and a system architecture employing both RNS and WSI is proposed. Means of introducing inherent fault tolerance using the RNS are briefly covered. After a tutorial introduction to the residue number system, methods of performing addition and multiplication operations in the RNS are explored on the basis of reducing area for a custom VLSI design. Modulo addition implemented with two conventional binary adders provides a compact design that may be externally programmed for the modulus that it operates in. Realization of mod multiplication via index addition is shown to be more effective than implementing the mod multiplication truth table directly. Conversions from binary to the RNS representation and vice versa are major bottlenecks in RNS design. Techniques for conversion into the RNS and out of the RNS based on a sequential division algorithm and the mixed-radix system expansion, respectively, are presented.