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.