Design and Evaluation of Approximate Logarithmic Multipliers for Low Power Error-Tolerant Applications

In this paper, the designs of both non-iterative and iterative approximate logarithmic multipliers (ALMs) are studied to further reduce power consumption and improve performance. Non-iterative ALMs, that use three inexact mantissa adders, are presented. The proposed iterative ALMs (IALMs) use a set-one adder in both mantissa adders during an iteration; they also use lower-part-or adders and approximate mirror adders for the final addition. Error analysis and simulation results are also provided; it is found that the proposed approximate LMs with an appropriate number of inexact bits achieve higher accuracy and lower power consumption than conventional LMs using exact units. Compared with conventional LMs with exact units, the normalized mean error distance of 16-bit approximate LMs is decreased by up to 18% and the power-delay product has a reduction of up to 37%. The proposed approximate LMs are also compared with previous approximate multipliers; it is found that the proposed approximate LMs are best suitable for applications allowing larger errors, but requiring lower energy consumption. Approximate Booth multipliers fit applications with less stringent power requirements, but also requiring smaller errors. Case studies for error-tolerant computing applications are provided.