Abstract
By their very nature Spin Waves (SWs) enable the realization of energy
efficient circuits as they propagate and interfere within waveguides
without consuming noticeable energy. However, SW computing can be even
more energy efficient by taking advantage of the approximate computing
paradigm as many applications are error-tolerant like multimedia and
social media. In this paper we propose an ultra-low energy novel
Approximate Full Adder (AFA) and a 2-bit inputs Multiplier (AMUL). The
approximate FA consists of one Majority gate while the approximate MUL
is built by means of 3 AND gates. We validate the correct functionality
of our proposal by means of micromagnetic simulations and evaluate the
approximate FA figure of merit against state-of-the-art accurate SW, 7nm
CMOS, Spin Hall Effect (SHE), Domain Wall Motion (DWM), accurate and
approximate 45nm CMOS, Magnetic Tunnel Junction (MTJ), and Spin-CMOS FA
implementations. Our results indicate that AFA consumes 43% and 33%
less energy than state-of-the-art accurate SW and 7nm CMOS FA,
respectively, and saves 69% and 44% when compared with accurate and
approximate 45nm CMOS, respectively, and provides a 2 orders of
magnitude energy reduction when compared with accurate SHE, accurate and
approximate DWM, MTJ, and Spin-CMOS, counterparts. In addition, it
achieves the same error rate as approximate 45nm CMOS and Spin-CMOS FA
whereas it exhibits 50% less error rate than the approximate DWM FA.
Furthermore, it outperforms its contenders in terms of area by saving at
least 29% chip real-estate. AMUL is evaluated and compared with
state-of-the-art accurate SW and 16nm CMOS accurate and approximate
state-of-the-art designs. The evaluation results indicate that it saves
at least 2x and 5x energy in comparison with the state-of-the-art SW
designs and 16nm CMOS accurate and approximate designs, respectively,
and has an average error rate of 10%, while the approximate CMOS MUL
has an average error rate of 12.5%, and requires at least 64% less
chip real-estate.