This paper presents techniques for low-power addition/subtraction in the logarithmic number system (LNS) and quantifies their impact on digital filter VLSI implementation. The impact of partitioning the look-up tables required for LNS addition/subtraction on complexity, performance, and power dissipation of the corresponding circuits is quantified. Two design parameters are exploited to minimize complexity, namely the LNS base and the organization of the LNS word. A roundoff noise model is used to demonstrate the impact of base and word length on the signal-to-noise ratio of the output of finite impulse response (FIR) filters. In addition, techniques for the low-power implementation of an LNS multiply accumulate (MAC) units are investigated. Furthermore, it is shown that the proposed techniques can be extended to cotransformation-based circuits that employ interpolators. The results are demonstrated by evaluating the power dissipation, complexity and performance of several FIR filter configurations comprising one, two or four MAC units. Simulations of placed and routed VLSI LNS-based digital filters using a 90-nm 1.0 V CMOS standard-cell library reveal that significant power dissipation savings are possible by using optimized LNS circuits at no performance penalty, when compared to linear fixed-point two's-complement equivalents.

This paper discusses techniques for low-power addition/subtraction in the logarithmic number system (LNS) and evaluates their impact on digital filter implementation. Initially, the impact of partitioning the look-up tables (LUT) required for addition/subtraction on complexity, performance, and power dissipation is studied. Subsequently techniques for the low-power implementation of an LNS multiply- accumulate (MAC) unit are investigated. The obtained LNS MACs are used for the design of digital filters. Synthesis of LNS-based digital filters using a 0.18 mum 1.8 V CMOS standard-cell library, reveal that significant power dissipation savings are possible at no performance penalty, when compared to linear two's-complement equivalent.