The International Conference on Application-specific Systems, Architectures and Processors (ASAP) has a long tradition in various hardware-related research topics, including computer arithmetic, application-specific instruction-set processors and accelerators, heterogeneous computing ranging from embedded systems to computing infrastructures, and reconfigurable computing. The 2020 edition of ASAP [1] was hosted by the Department of Computer Science at The University of Manchester, UK and took place as a virtual conference during July 6-7, 2020.This special issue of Springer's Journal of Signal Processing Systems covers various facets of the topics mentioned afore. The special issue is based on extended contributions of selected top-level papers presented at ASAP 2020 [2]. From 118 submitted papers, 21 long papers had been presented at ASAP 2020, and after a careful peer-review process, four extended manuscripts were accepted for inclusion in this special issue. It is our pleasure to introduce these articles in the following briefly.The initial two articles of this special issue deal with computer arithmetic.The first article, "A Reconfigurable Posit Tensor Unit with Variable-Precision Arithmetic and Automatic Data Streaming" by Neves, Tomás, and Roma [3], deals with the acceleration of deep neural networks (DNNs). The authors propose a reconfigurable tensor unit that deploys an array of variable-precision vector multiply-accumulate units. The new vector unit is compared against existing SIMD units * Frank Hannig