O. Semenova, A. Semenov, O.
Wojciechowska
Vinnytsya National
Technical University
Realization of ternary minimum and
maximum logic operations using parametrons
Modern
systems of automatics and computing are being developed using logic algebra,
not only binary one, but also multi-valued those. So, it is very important to
define the most convenient type of logic for a system.
The
multi-valued logic has some advantages then using in complex systems. The more
logic values a system has, the higher quick-action it has. But the less logic
values a system has the higher noise stability it has. So, the compromise
between quick-action and noise stability can be achieved by using ternary logic
[1].
In
order to decrease a number of interconnections we propose to use the
pulse-phase information coding method [2].
A
pulse-phase element is the parametron. It works acocording to majority logic
[3]. But the parametron has a disadvantage: its complexity increases as
increases a number of logic levels. That is why in order to simplify
implementation of ternary logic operations using the parametron we will use so
called double wire logic.
Thus,
an every logical value is presented as two phase shifts: one on the first wire
and other on the second wire.
According
to it, we propose the next coding.
A logical “0”
corresponds to “0” and “0” phases.
A logical “1”
corresponds to “0” and “π” phases.
A logical “2”
corresponds to “π” and “π” phases.
So, one pulse-phase
element consists of two three-input parametrons. A block diagram of the
proposed phase ternary logic element is presented at fig.1.
This element operates
according to table 1.
The first inputs give.
The
second inputs give .
The outputs gives .
The auxiliary inputs give .
Table 1. Operation of
the phase ternary logic element
First inputs |
Second inputs |
Auxiliary inputs |
Outputs |
|
||||
x11 |
x21 |
x12 |
x22 |
y1 |
y2 |
z1 |
z2 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
π |
0 |
0 |
0 |
0 |
|
0 |
0 |
π |
π |
0 |
0 |
0 |
0 |
|
0 |
π |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
π |
0 |
π |
0 |
0 |
0 |
π |
|
0 |
π |
π |
π |
0 |
0 |
0 |
π |
|
π |
π |
0 |
0 |
0 |
0 |
0 |
0 |
|
π |
π |
0 |
π |
0 |
0 |
0 |
π |
|
π |
π |
π |
π |
0 |
0 |
π |
π |
|
0 |
0 |
0 |
0 |
π |
π |
0 |
0 |
|
0 |
0 |
0 |
π |
π |
π |
0 |
π |
|
0 |
0 |
π |
π |
π |
π |
π |
π |
|
0 |
π |
0 |
0 |
π |
π |
0 |
π |
|
0 |
π |
0 |
π |
π |
π |
0 |
π |
|
0 |
π |
π |
π |
π |
π |
π |
π |
|
π |
π |
0 |
0 |
π |
π |
π |
π |
|
π |
π |
0 |
π |
π |
π |
π |
π |
|
π |
π |
π |
π |
π |
π |
π |
π |
|
Let be some ternary
function of
, so that
,
where are variables,
is a constant.
For the ternary minimum
operation we have:
.
For the ternary maximum
operation we have:
.
In order to simplify the
description we propose to use a matrix.
For the ternary minimum
operation we have:
,
For the ternary maximum
operation we have:
,
.
So, we have proposed to
build up the ternary minimum and maximum elements on parametrons. These
elements work on double wire logic. Also we have proposed the pulse-phase
information coding method and the matrix description.
References
1. Ëûñèêîâ Á.Ã. Àðèôìåòè÷åñêèå
è ëîãè÷åñêèå îñíîâû ÝÖÂÌ. – Ìèíñê: Âûøýéøàÿ
øêîëà, 1974. -264ñ.
2. Ìîë÷àíîâ À.À., Âîëêîãîí Â.Ï., Ëîçà Þ.Õ., ßëîâåãà Ã.È.
Ïðîåêòèðîâàíèå ìíîãîôóíêöèîíàëüíûõ èíòåãðàëüíûõ ñõåì. –Ê.: “Òåõí³êà”, 1984. – 143ñ.
3. Êíîððå
Ã.Ê., Òóçîâ Â.Ì., Øóð Ã.È. Ôàçîâûå è ÷àñòîòíûå èíôîðìàöèîííûå ÑÂ× ýëåìåíòû.
–Ì.: Ñîâ. ðàäèî, 1975. –352ñ.