O.
Semenova, A. Semenov, O. Wojciechowska
Vinnytsya
National Technical University
The quaternary
logic elements synthesis
using the fuzzy
approach
Nowadays the systems of automatics and computing are
being developed using logic algebra, not only binary one, but also multi-valued
and fuzzy those. It is necessary to define the most convenient type of logic
for a system. Fuzzy logic is much more alike human mind and works in uncertain
cases providing very accurate results. 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 quaternary logic [1].
The quaternary logic devices, presented in literature
[2, 3], have either low quick-action because of a great amount of blocks or low
noise-stability because of pulse-amplitude signals. In order to provide high
noise-stability we propose to use not pulse-amplitude signals but
pulse-duration ones. In order to provide high quick-action we propose to use
the fuzzy-logic approach. The fuzzy-logic elements performing logical
operations have fewer blocks than the well-known logic elements [2].
The point is that quaternary logic operation of
inversion, conjunction and disjunction are alike the fuzzy-logic operation of
complement, minimum and maximum accordingly:
The quaternary logic operation of inversion is
performed so
.
The fuzzy logic operation of complement is performed
so
.
The quaternary logic operation of conjunction is
performed so
.
The fuzzy logic operation of minimum is performed so
.
The quaternary logic operation of disjunction is
performed so
.
The fuzzy logic operation of maximum is performed so
.
The work [2] is dedicated to designing logic
pulse-duration elements. According to it, every logic pulse-duration element
can be regarded as consisting of several basic blocks; they are: addition
block, subtraction block, and selection block. We propose to use such block as:
addition, subtraction and division [4]. The
operation of 
is performed by the
addition block, named A-block. The operation of 
is performed by the
subtraction block, named S-block. The operation of 
is performed by the
division block, named D-block.
In the proposed elements the pulse-duration coding of
logical values is used. According to it, every duration is defined so 
. Let the 0-level responds to duration of 
; the 1-level
responds to duration of 
; the 2-level
responds to duration of 
; the 3-level
responds to duration of 
; the auxiliary
duration equals 
.
The inversion element is a subtraction block (fig. 1).
The input pulse-duration signal comes at its first input terminal. The
auxiliary signal comes at its second input terminal. The output pulse-duration
signal comes from the output terminal.
Thus, we get:
if
, then
;
if
, then
;
if
, then 
;
if
, then 
.
So, the operation of quaternary
inversion is
performed.
The conjunction element consists of one addition
block, two subtraction blocks, and one division block (fig. 2).
The input pulse-duration signal 
comes at the first
input terminal of the addition block and at the first input terminal of the
first subtraction block. The input pulse-duration signal 
comes at the second
input terminal of the addition block and at the second input terminal of the
first subtraction block.
At the output terminal of the addition block one gets
the 
signal, it comes at
the first input terminal of the second subtraction block. At the output
terminal of the first subtraction block one gets the 
signal, it comes at
the second input terminal of the second subtraction block. At the output
terminal of the second subtraction block one gets either the 
signal if 
or the 
signal if 
.
The signal goes from the output terminal of the second
subtraction block to the input terminal of the division block; at its output
terminal one gets the 
signal.
So, the operation of quaternary conjunction is performed.
The disjunction element consists of two addition
blocks, one subtraction block, and one division block (fig. 3).
The input pulse-duration signal comes at the first
input terminal of the first addition block
and at the first input terminal of the subtraction block. The
input pulse-duration signal comes at the second
input terminal of the first addition block
and at the second input terminal of the subtraction block.
At the output terminal of the first addition block
one gets the signal, it comes at
the first input terminal of the second addition block.
At the output terminal of the subtraction block one gets the signal, it comes at
the second input terminal of the second addition block.
At the output terminal of the second addition block
one gets either the 
signal if or the 
signal if .
The signal goes from the output terminal of the second
addition block to the input terminal of the division block; at
its output terminal one gets the 
signal.
So, the operation of quaternary disjunction is performed.
Thus, it is easy to develop the quaternary logic
elements with high quick-action and noise stability using the fuzzy-logic
approach.
References
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