O. Semenova, A. Semenov, O. Wojciechovska
The fuzzy approach
to the ternary logic elements synthesis
The
ternary number system is the most effective, comparing to the binary and
non-binary number systems, especially in sequential and memory facilities. Also,
it has higher quick-action than the binary number system has [1].
The
ternary logic devices presented in literature [2] have either low quick-action
because of a great amount of blocks or low noise-stability because of pulse-amplitude
signals. So, there is a problem of developing the ternary logic elements of
high quick-action and noise-stability.
In
order to provide high noise-stability we propose to use not pulse-amplitude
signals but pulse-frequency ones.
In order
to provide high quick-action we propose to use the fuzzy-logic approach. The
point is, that ternary logic operations of inversion, conjunction and
disjunction are alike the fuzzy-logic operations of complement, minimum and
maximum accordingly; the fuzzy-logic elements performing these operations have
less blocks than the well-known ternary logic elements [3].
In the
proposed elements the pulse-frequency coding of logical values is used.
According to it, every frequency is defined so 
.
Let the
0-level respond to a frequency of 
.
Let the
1-level respond to a frequency of 
.
Let the
2-level respond to a frequency of 
.
The
auxiliary frequency equals 
.
The inversion element is a frequency mixer (fig. 1).
The input pulse-frequency signal comes on its first input terminal. The
auxiliary signal comes on its second input terminal. The output pulse-frequency
signal comes from the output terminal.
Thus,
we get:
if 
, then
;
if 
, then
;
if 
, then 
.
So, the operation of ternary inversion
is performed.
The conjunction
element consists of three frequency mixers and a frequency divider (fig. 2).
The input pulse-frequency signal 
comes on the first
input terminal of the first mixer and on the first input terminal of the
second mixer. The input pulse-frequency signal 
comes on the second
input terminal of the first mixer and on the second input terminal of the
second mixer. On the output terminal of the first mixer one gets the
signal, it comes on
the first input terminal of the third mixer. On the output terminal of the
second mixer one gets the 
signal, it comes on
the second input terminal of the third mixer. On the output terminal of the
third mixer one gets either the 
signal if 
or the 
signal if
. The
signal goes from the output terminal of the third mixer to the input terminal
of the frequency divider; on its output terminal one gets the 
signal.
So, the operation of ternary conjunction is performed.
The disjunction
element consists of three frequency mixers and a frequency divider (fig. 3).
The input pulse-frequency signal comes on the first
input terminal of the first mixer and on the first input terminal of the
second mixer. The input pulse-frequency signal comes on the second
input terminal of the first mixer and on the second input terminal of the
second mixer. On the output terminal of the first mixer one gets the
signal, it comes on
the first input terminal of the third mixer. On the output terminal of the
second mixer one gets the signal, it comes on
the second input terminal of the third mixer. On the output terminal of the
third mixer one gets either the 
signal if or the 
signal if. The
signal goes from the output terminal of the third mixer to the input terminal
of the frequency divider; on its output terminal one gets the 
signal.
So, the operation of ternary disjunction is performed.
Thus, using
the fuzzy-logic principles it is possible to develop the ternary logic elements
with high quick-action and noise stability.
References
1. Лысиков
Б.Г. Арифметические и логические основы ЭЦВМ.
– Минск: Вышэйшая школа, 1974. -264с.
2. Кичак
В.М. Синтез частотно-імпульсних елементів цифрової техніки. Монографія. – Вінниця:
УНІВЕРСУМ-Вінниця, 2005. – 266с.
3. Семенова О.О.,
Войцеховська О.О. Структурний синтез фазі-логічних елементів з
частотно-імпульсним представленням інформації // Матеріали ІІІ-ї міжнародної науково-технічної конференції “Сучасні
проблеми мікроелектроніки, радіоелектроніки, телекомунікацій та приладобудування”
СПРТП-2007. – Вінниця. – 2007. – с.185.