  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.
