Long-Term Memory, Simulated Qubits, Physical Qubits - Brain Theory from a Circuits and Systems Perspective - page 65

with n integer, the ratio becomes T o /T x ¼ n. A variable Γ is defined to be the

average time per T o that a waveform f x is high:

τ:

T o
T x

Γ ¼ (4.1)

The division T o /T x will be an integer only if f x and f 0 are related harmonically.
The fraction of time that a high occurs is

T o ¼ T x :

(4.2)

This is proportional to probability for a true. The probability of a true is defined
to be P which in percent may be written as

P ¼ τ f x 100 %: (4.3)

Using the above maximum duty cycle of 50 %, the ideal probability is 1/2 at f 1
and /T o at f 0 . The probability fraction of seeing a false is the complement of seeing

a true:

τ

P False ¼ ½ 1 τ f x 100 %: (4.4)

Under this system, 100 % chance of seeing a false occurs only for f x ¼ f 0 ! 0.

Harmonics Assumption

Beginning with f 0 , analysis of probabilities becomes easier if all frequencies are
assumed to be synchronized, and if all frequencies are assumed to be related by
integers, that is, harmonically related. This is a special case for the analysis,
since in practice frequencies are not generally restricted to be harmonics of a
fundamental.

Sampling Considerations

Multivibrator waveforms outputted at x are going to be sampled in order to capture
a logic value. The sampling circuitry must provide a rest voltage if a low level is
sampled, and a burst of pulses if a high level is sampled. Sampling should occur
within a time frame T o and sampling is usually just prior to when an output is