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Quantitative transformation for implementation of adder circuits in physical systems

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

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James Whiting
Occasional Associate Lecturer - CATE - ENG


© 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.


Jones, J., Whiting, J. G. H., & Adamatzky, A. (2015). Quantitative transformation for implementation of adder circuits in physical systems. BioSystems, 134, 16-23.

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
Electronic ISSN 1872-8324
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 134
Pages 16-23
Keywords full adder, logic gate, frequency, Physarum polycephalum, oscillatory dynamics
Public URL
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