Approximated 2-Bit Adders for Parallel In-Memristor Computing With a Novel Sum-of-Product Architecture

Abstract

Conventional computing methods struggle with the exponentially increasing demand for computational power, caused by applications including image processing and machine learning (ML). Novel computing paradigms such as in-memory computing (IMC) and approximate computing (AxC) provide promising solutions to this problem. Due to their low energy consumption and inherent ability to store data in a nonvolatile fashion, memristors are an increasingly popular choice in these fields. There is a wide range of logic forms compatible with memristive IMC, each offering different advantages. We present a novel mixed-logic solution that utilizes properties of the sum-of-product (SOP) representation and propose a full-adder circuit that works efficiently in 2-bit units. To further improve the speed, area usage, and energy consumption, we propose two additional approximate (Ax) 2-bit adders that exhibit inherent parallelization capabilities. We apply the proposed adders in selected image processing applications, where our Ax approach reduces the energy consumption by $\mathrm {31~\!\%}$ – $\mathrm {40~\!\%}$ and improves the speed by $\mathrm {50~\!\%}$ . To demonstrate the potential gains of our approximations in more complex applications, we applied them in ML. Our experiments indicate that with up to $6/16$ Ax adders, there is no accuracy degradation when applied in a convolutional neural network (CNN) that is evaluated on MNIST. Our approach can save up to 125.6 mJ of energy and 505 million steps compared to our exact approach.

Keywords

• Adder
• approximate computing (AxC)
• image processing
• in-memory computing (IMC)
• machine learning
• memristor