Redundant Binary (RBR) number representations have been extensively used in the past for high-throughput Digital Signal Processing (DSP) systems. Data-path components based on this number system have smaller critical path delay but larger area compared to conventional two's complement systems. This work explores the use of RBR number representation for implementing high-throughput DSP systems that are also energy-efficient. Data-path components such as adders and multipliers are evaluated with respect to critical path delay, energy and Energy-Delay Product (EDP). A new design for a RBR adder with very good EDP performance has been proposed. The corresponding RBR parallel adder has a much lower critical path delay and EDP compared to two's complement carry select and carry look-ahead adder implementations. Next, several RBR multiplier architectures are investigated and their performance compared to two's complement systems. These include two new multiplier architectures: a purely RBR multiplier where both the operands are in RBR form, and a hybrid multiplier where the multiplicand is in RBR form and the other operand is represented in conventional two's complement form. Both the RBR and hybrid designs are demonstrated to have better EDP performance compared to conventional two's complement multipliers. The hybrid multiplier is also shown to have a superior EDP performance compared to the RBR multiplier, with much lower implementation area. Analysis on the effect of bit-precision is also performed, and it is shown that the performance gain of RBR systems improves for higher bit precision. Next, in order to demonstrate the efficacy of the RBR representation at the system-level, the performance of RBR and hybrid implementations of some common DSP kernels such as Discrete Cosine Transform, edge detection using Sobel operator, complex multiplication, Lifting-based Discrete Wavelet Transform (9, 7) filter, and FIR filter, is compared with two's complement systems. It is shown that for relatively large computation modules, the RBR to two's complement conversion overhead gets amortized. In case of systems with high complexity, for iso-throughput, both the hybrid and RBR implementations are demonstrated to be superior with lower average energy consumption. For low complexity systems, the conversion overhead is significant, and overpowers the EDP performance gain obtained from the RBR computation operation.
- Energy-efficient DSP system design based on the Redundant Binary number system
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by Rupa Mahadevan