Design and Implementation of Booth Multiplier using Approximate Adders

Abstract

Low power is an imperative requirement for portable multimedia devices employing various signal processing algorithms and architectures. In most multimedia applications, human beings can gather useful information from slightly erroneous outputs. Therefore, we do not need to produce exactly correct numerical outputs. Previous research in this context exploits error resiliency primarily through voltage overscaling, utilizing algorithmic and architectural techniques to mitigate the resulting errors. In this paper, we propose logic complexity reduction at the transistor level as an alternative approach to take advantage of the relaxation of numerical accuracy. We demonstrate this concept by proposing various imprecise or approximate full adder cells with reduced complexity at the transistor level, and utilize them to design approximate multi-bit adders. In addition to the inherent reduction in switched capacitance, our techniques result in significantly shorter critical paths, enabling voltage scaling. Keyword: Approximate computing, low power, mirror adder. Booths multiplier, Wallace tree multiplier I. INTRODUCTION Digital signal processing (DSP) blocks form the backbone of various multimedia applications used in portable devices. Most of these DSP blocks implement image and video processing algorithms, where the ultimate output is either an image or a video for human consumption. Human beings have limited perceptual abilities when interpreting an image or a video. This allows the outputs of these algorithms to be numerically approximate rather than accurate. This relaxation on numerical exactness provides some freedom to carry out imprecise or approximate computation. We can use this freedom to come up with low-power designs at different levels of design abstraction, namely, logic, architecture, and algorithm. The paradigm of approximate computing is specific to select hardware implementations of DSP blocks. It is shown in (1) that an embedded reduced instruction set computing processor consumes 70% of the energy in supplying data and instructions, and 6% of the energy while performing arithmetic only. Therefore, using approximate arithmetic in such a scenario will not provide much energy benefit when considering the complete processor. Programmable processors are designed for general-purpose applications with no application-specific specialization. Therefore, there may not be many applications that will be able to tolerate errors due to approximate computing. This also makes general-purpose processors not suited for using approximate building blocks. This issue has already been discussed in (13). Therefore, in this paper, we consider application-specific integrated circuit implementations of error-resilient applications like image and video compression.