A simple pipelined logarithmic multiplier

Abstract

Digital signal processing algorithms often rely heavily on a large number of multiplications, which is both time and power consuming. However, there are many practical solutions to simplify multiplication, like truncated and logarithmic multipliers. These methods consume less time and power but introduce errors. Nevertheless, they can be used in situations where a shorter time delay is more important than accuracy. In digital signal processing, these conditions are often met, especially in video compression and tracking, where integer arithmetic gives satisfactory results. This paper presents and compare different multipliers in a logarithmic number system. For the hardware implementation assessment, the multipliers are implemented on the Spartan 3 FPGA chip and are compared against speed, resources required for implementation, power consumption and error rate. We also propose a simple and efficient logarithmic multiplier with the possibility to achieve an arbitrary accuracy through an iterative procedure. In such a way, the error correction can be done almost in parallel (actually this is achieved through pipelining) with the basic multiplication. The hardware solution involves adders and shifters, so it is not gate and power consuming. The error of proposed multiplier for operands ranging from 8 bits to 16 bits indicates a very low relative error percentage.