Development of Circuits for Antilogarithmic Converters with Efficient Error–Area–Delay Product Using the Fractional-Bit Compensation Scheme for Digital Signal Processing Applications

Abstract

Digital signal processing (DSP) has been widely adopted in sensor systems, communication systems, digital image processing, artificial intelligence, and Internet of Things applications. However, these applications require circuits for complex arithmetic computation. The logarithmic number system is a method to reduce the implementation area and transmission delay for arithmetic computation in DSP. In this study, we propose antilogarithmic converters with efficient error–area–delay products (eADPs) based on the fractional-bit compensation scheme. We propose three mathematical approximations—case 1, case 2, and case 3—to approximate the accurate antilogarithmic curve with different DSP requirements. The maximum percentage errors of conversion for case 1, case 2, and case 3 are 1.9089%, 1.7330%, and 1.2063%, respectively. Case 1, case 2, and case 3 can achieve eADP savings of 15.66%, 80.80%, and 84.61% compared with other methods reported in the literature. The proposed eADP-efficient antilogarithmic converters can achieve lower eADP and digitalized circuit implementation. The hardware implementation utilizes Verilog Hardware Description Language and the digital circuits are created via very-large-scale integration by the Taiwan Semiconductor Manufacturing Company with 0.18 µm CMOS technology. This proposed antilogarithmic converter can be efficiently applied in DSP.