Figure 15. Translating between intermediate
encoded gates and hysteresis gates.
As can be seen Intermediate encoding is very expensive
in terms of resources. The wires are all doubled
and each encoded gate is several simple threshold
gates. The feedback solution is more practical
and economical.
Now that both forms of NULL Convention threshold
gates enforce the completeness of input criteria
for both DATA in relation to NULL and for NULL
in relation to DATA, their behavior again scales
up for circuits as a whole. Figure 16 shows the
data-NULL cycle for a single data value NULL Convention
Logic circuit.
Figure 16. NULL-DATA cycle for hysteresis gate
circuit.
Beginning with the circuit in an all NULL state
one DATA value is applied in one of the groups.
The result values remain all NULL since no threshold
is met. When a DATA value is applied in the second
group, a complete input data set is present, the
threshold of a gate is met which asserts a DATA
value which propagates to the result values. One
result value in each output group asserts a DATA
value which constitutes a complete result data
set and expresses the correct resolution of a
complete input data set. The circuit as a whole
enforces the completeness of input criteria for
DATA in relation to NULL and only asserts a complete
result data set when a complete input data set
is presented to the circuit.
One of the input DATA values becomes NULL, but
the threshold 2 gate and the circuit continue
asserting DATA result values. Only when all inputs
to the circuit are NULL does the threshold 2 gate
and hence the circuit transition their result
values to NULL. The circuit as a whole enforces
the completeness of input criteria for NULL in
relation to DATA and only asserts all NULL result
values when the input to the circuit is all NULL
and the NULL values have propagated through the
circuit.
As with the Boolean logic examples with three
and four value logic, the completion of resolution
of a complete input data set and the readiness
of the circuit to receive a new input data set
to resolve can be determined by simply monitoring
the result values. The circuit is symbolically
complete and manages quite on its own its interactions
with the rest of the world. |