Commutative Approximate RCA.pdf (3.04 MB)
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On the Commutative Operation of Approximate CMOS Ripple Carry Adders (RCAs)

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posted on 2022-11-02, 04:04 authored by Junqi Huang, Nandha Kumar ThulasiramanNandha Kumar Thulasiraman, Haider AlmuribHaider Almurib, Fabrizio Lombardi

Approximate cells can be used to design Ripple Carry Adders (RCAs) for realizing approximate addition in energy-efficient CMOS digital circuits. As inputs of approximate cells could be non-commutative in nature, approximate adders may show different output values under a commutative operation, and this may have a significant effect on the generated sum. This paper presents a detailed analysis of the commutative addition in RCAs made of different approximate cells. Initially, the impact of a non-commutative addition (NCA) to RCAs by approximate cells is assessed by exhaustive simulation at adder level. The results show that at most 17% of additions executed using AFA3 suffer from the non-commutative property, while the values for other adder cells can reach 75%~99%. Then, an extensive analysis using images from a publicly available library is performed by comparing three-image additions with two-image additions. As a further evaluation, the adders are assessed in an image denoising application. As expected, the effect of NCA is especially pronounced for some non-commutative adders, such as AA2 and AMA4. NCA is also cumulative with the number of approximate additions, thereby causing a significant variation in the output image quality. In terms of metrics, the largest average difference in mean error distance (DMED) for three-image addition is 5.3 times higher than for two-image addition. Rankings of the non-commutative approximate adders show that AMA3 and AFA1 based adders are the best schemes with respect to commutative addition; they both also show good performance in image denoising.


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University of Nottingham in Malaysia

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  • Malaysia

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