Among all the arithmetic operations, division operation takes most of the clock cycles resulting in more path delay and higher power consumption. Many algorithms, including logarithmic division (LD), have been implemented to reduce the critical path delay and power consumption of division operation. However, there is a high possibility to further reduce these vital issues by using the novel approximate LD (ALD) algorithm. In the proposed ALD, a truncation adder is used for mantissa addition. Using this adder, the power delay product (PDP) and normalized mean error distance (NMED) are minimized. From the error analysis and hardware evaluation, it is observed that the proposed ALD using truncation adder (ALD‐TA) with an appropriate number of inexact bits achieve lower power consumption and higher accuracy than existing LDs with exact units. The normalized mean error distance of 8‐, 16‐, and 32‐bit ALD‐TA is compared with LDs of same bits and observed a decrease of up to 21%, 20%, and 21%, and the PDP has a reduction of up to 33%, 51%, and 72%, respectively. Application of ALD‐TA to image processing shows that high performance can be achieved by using ALDs than exact LDs.

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SummaryThe ever‐increasing need for high‐performance signal processing blocks in avionics, machine learning (ML), IoT, neural networks, etc., has made the logarithmic arithmetic's as the front runner in advanced processors. The complex arithmetic operations such as multiplication and division can be easily performed in the logarithmic domain as they become addition and subtraction operations, respectively. However, the challenge is to perform the logarithmic and anti‐logarithmic conversions and to optimize the trade‐off between hardware complexity and accuracy. In this work, we propose a 32‐bit antilogarithmic converter, for/using Mitchell's algorithm. The obtained results are corrected using the weighted average method. The correction terms are stored and selected using 32 × 8 ROM to decreases the computational speed and hardware complexity of the antilogarithmic converter. The proposed antilogarithmic converter has a maximum error percentage of 1.199%, which is 6.147% for Mitchell's algorithm while maintaining the hardware metrics close to Mitchell's algorithm.

The need to implement high-speed Signal processing applications in which multiplication and division play a vital role made logarithmic arithmetic a prominent contender over the traditional arithmetic operations in recent years. But the logarithm and antilogarithm converters are the bottlenecks. In order to reduce the logarithmic conversion complexity, several works have been introduced from time to time for correcting the error in Mitchell’s algorithm but at the cost of hardware. In this work, we propose a 32-bit binary to the binary logarithmic converter with a simple correction circuit compared with existing techniques. Unlike the current methods that use the linear piece-wise approximation in the mantissa, we propose a weighted average method to correct the error in Mitchell’s approximation. The maximum error percentage from the proposed work is 0.91%, which is 16.9% of Mitchell’s error percentage.