Quantitative Transformation for Implementation of Adder Circuits in Physical Systems

TL;DR

This paper introduces a quantitative input transformation that simplifies the implementation of adder circuits in unconventional physical systems, avoiding complex wiring issues and enabling potential use in living substrates like slime mould.

Contribution

It proposes a novel input transformation method that reduces circuit complexity and demonstrates its feasibility in simulation and slime mould systems.

Findings

The transformation maps input combinations to correct outputs linearly.

Simulation shows the transformation's effectiveness in circuit implementation.

Potential for physical realization in slime mould systems is assessed.

Abstract

Computing devices are composed of spatial arrangements of simple funda- mental 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 impracti- cal 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 Physarum 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.