# Clever Math for Better Battery Life

The internet of things (IoT) spans several vertical markets, including smart cities, smart agriculture, smart buildings, smart environment, and the healthcare IoT. Despite the variety of applications, engineers invariably face five challenges known as the 5 C’s of IoT: connectivity, continuity, compliance, coexistence, and cybersecurity.

Providing continuity of operation via long battery life is usually perceived as a hardware challenge that requires cutting-edge circuit design expertise, but in some cases, a simple mathematical insight can significantly extend battery life. This principle was recently demonstrated by Md Kamruzzaman Shuvo, David E Thompson, and Haibo Wang of Southern Illinois University (SIU) in Carbondale, Illinois.

The SIU team recently published a paper entitled, “MSB-First Distributed Arithmetic Circuit for Convolution Neural Network Computation” that proves how a relatively simple mathematical insight can extend battery life.

A convolution neural network (CNN) is a powerful machine learning tool for image classification, object detection, and speech recognition. A typical CNN performs many billions of calculations, and then the results are often sent to a rectified linear activation layer called a ReLU. The ReLU's job is to pass along positive numbers and turn negative numbers to 0.

Depending on the nature of the application, roughly half of the values sent to the ReLU are negative, so the energy consumed in determining the exact value of these negative numbers, which are turned to 0 anyhow, largely has been wasted.

As an analogy, consider subtracting 8,106,039,992 from 7,892,445,108. You could go through the trouble of finding the exact answer to the problem, but if you're going to treat negative numbers as 0 anyhow, it is sufficient to say that 7 billion and whatever minus 8 billion and whatever is always negative and simply write 0 as the result.

By re-architecting the circuitry to perform subtraction from left to right and returning 0 as soon as it is clear that the answer is negative, the SIU team reduced the energy consumed by all of this logic circuitry by 1/3 and increased throughput by 38%.

Of course, clever mathematics is not the only way to improve continuity of operation for battery-powered devices. Depending on the device being tested, engineers also must make measurements with digital multimeters (DMMs), DC power analyzers, device current waveform analyzers, oscilloscopes, and other tools as appropriate. In addition, software tools capable of event-based power analysis and advanced waveform analytics can provide valuable insights that enable further breakthroughs in battery-powered devices.