Commutative Approximate Adders: Analysis and Evaluation

Abstract

Ripple Carry Adders (RCAs) made of approximate cells are used in many applications to reduce power dissipation and delay. Unlike its exact counterpart, an approximate RCA may have a non-commutative feature due to the characteristics of the approximate cells. This paper analyses the commutative property of approximate RCAs. Initially, the Boolean equations and state diagram of approximate cells in the design of RCA are presented and conditions for an approximate cell to compute a non-commutative addition (NCA) are provided. The analysis shows that only a few approximate adders do not affect the commutative property. Then, an extensive analysis using images from a public library is performed by considering two-image addition. As expected, the non-commutative operation causes variations in the quality of output images; performance metrics such as PSNR, MED (Mean Error Distance) and MaxED (Maximum Error Distance) vary as the inputs are reversed. The results show that the absolute difference of PSNR, MED and MaxED (DPSNR, DMED, DMaxED) by reversing the inputs for non-commutative adders increases when the number of applied approximate cells increases. Among the non-commutative approximate adders, AMA3 has the lowest average DPSNR and DMaxED, 54% and 43% (to the maximum) of the highest one (AMA4). The average DMED for AMA4 is also the highest, so 9.23 and 2 times higher than AMA1 and AMA3 respectively.