Quantitative transformation for implementation of adder circuits in physical systems

Jones, Jeff; Whiting, James G. H.; Adamatzky, Andrew

Abstract

© 2015 Elsevier Ireland Ltd. Computing devices are composed of spatial arrangements of simple fundamental logic gates. These gates may be combined to form more complex adding circuits and, ultimately, complete computer systems. Implementing classical adding circuits using unconventional, or even living substrates such as slime mould Physarum polycephalum, is made difficult and often impractical by the challenges of branching fan-out of inputs and regions where circuit lines must cross without interference. In this report we explore whether it is possible to avoid spatial propagation, branching and crossing completely in the design of adding circuits. We analyse the input and output patterns of a single-bit full adder circuit. A simple quantitative transformation of the input patterns which considers the total number of bits in the input string allows us to map the respective input combinations to the correct outputs patterns of the full adder circuit, reducing the circuit combinations from a 2:1 mapping to a 1:1 mapping. The mapping of inputs to outputs also shows an incremental linear progression, suggesting its implementation in a range of physical systems. We demonstrate an example implementation, first in simulation, inspired by self-oscillatory dynamics of the acellular slime mould P. polycephalum. We then assess the potential implementation using plasmodium of slime mould itself. This simple transformation may enrich the potential for using unconventional computing substrates to implement digital circuits.

• Journal Article Type: Article
• Acceptance Date: May 20, 2015
• Online Publication Date: May 22, 2015
• Publication Date: Aug 1, 2015
• Deposit Date: Aug 25, 2015
• Publicly Available Date: Aug 1, 2016
• Journal: BioSystems
• Print ISSN: 0303-2647
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 134
• Pages: 16-23
• DOI: https://doi.org/10.1016/j.biosystems.2015.05.005
• Keywords: full adder, logic gate, frequency, Physarum polycephalum, oscillatory dynamics
• Public URL: https://uwe-repository.worktribe.com/output/830515
• Publisher URL: http://dx.doi.org/10.1016/j.biosystems.2015.05.005
• Contract Date: Aug 1, 2016