Volume 03 Issue 12-2023
74
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
ISSUE
12
Pages:
74-78
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
This article presents several solutions for creating block diagrams from logic elements, including AND, NAND, OR, NOR
and other logic element block diagrams using the Sheffer element. Also, the article shows how to create logic element
block diagrams in the Multisim program.
KEYWORDS
Multisim software, logic element, Sheffer element, 2AND, NAND, 2OR, NOR logic elements.
INTRODUCTION
As we all know, when working with information,
working with it in digital form creates a number of
conveniences. Logical elements are devices designed
to process information in digital form. In other words,
a logical element (LE) is an electronic device that
performs a specific logical operation on input signals.
Physically logical elements are divided into mechanical,
electromechanical,
electronic
(by
diodes
and
transistors), pneumatic, hydraulic, optical and other
types. With the development of electrical engineering,
mechanical logic elements were transferred to
electromechanical logic elements (electromagnetic
relays), then electronic lamps, and then transistors. In
1946, after the confirmation of John von Neumann's
theory about the economics of positional number
systems, the advantages of binary and ternary systems
over the decimal number system became known.
Converts from decimal logical elements to binary
logical elements. Compared to binary and triple
fractions, this process significantly reduces the number
of operations and elements. It is possible to count
dozens of low-level integrated and high-level
integrated microcircuit components, independent
digital microcircuits, that is, logic elements.
Research Article
SHEFFER AND PEIRCE PERFORM ACTIONS ON OTHER LOGICAL
ELEMENTS BASED ON THE LOGICAL ELEMENT
Submission Date:
December 20, 2023,
Accepted Date:
December 25, 2023,
Published Date:
December 30, 2023
Crossref doi:
https://doi.org/10.37547/ajast/Volume03Issue12-13
S.K.Ramonova
Phd, Associate Professor Of The Department Of Natural And Scientific Sciences Of The Chirchik Higher Tank
Commanding Engineering Educational Institution, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 03 Issue 12-2023
75
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
ISSUE
12
Pages:
74-78
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
The basic operations in logical algebra (and the
corresponding digital electronic circuits) are AND, OR,
and NOT (or invert). In addition, there are five common
operations (or digital electronic functions) in logical
algebra that are produced by combining the functions
of these three basic operations.
Truth tables
The truth table is one of the most useful tools for
analyzing problems in logical algebra, and to show the
functions of the corresponding digital electronic
circuits.
As shown in Fig-1, the truth table consists of one
vertical column for each of the logic variables involved
in a given problem. The horizontal lines or rows of the
truth table are filled with all possible true-false
combinations the variables can assume with respect to
each other.
For example, two variables can assume four different
combinations at any of four different times: that is,
both true at the same time; both false at the same time;
and one true and one false. There are no other possible
combinations. The additional columns contain the
output or results produced by the combinations of
variables.
Two-variable truth table and a summary of truth tables
for logic gates
Table 1.
X
1
X
2
AND
NAND
OR
NOR
EXCLUSIVE
OR
EXCLUSIVE
NOR
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
The functional nodes and units are under design of the
digital electronic circuits fulfilling the elementary
(basic) logic operations. These circuits are called as
basic logical elements or gates. For implementation in
digital systems of various logic functions it is enough to
have the dial-up of logical elements named minimum
element base (or basis).
As minimum element basis can serve:
- A dial-up from two types of the logical elements one
of which fulfills operation AND, another - operation
NOT;
- A dial-up from two types of the logical elements one
of which fulfills operation OR, another - operation NOT;
- A dial-up of logical elements of Peirce, fulfilling
operation NOR (NOT-OR);
- A dial-up of logical elements Sheffer fulfilling
operation NAND.
Volume 03 Issue 12-2023
76
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
ISSUE
12
Pages:
74-78
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
In practice, for the purpose of abbreviation of the
nomenclature of elements and other reasons, use the
element basis, fulfilling operation NAND more often, or
NOR.
NAND and NOR gates are minimum element base.
The minimum element base is functionally full system
of logical elements. It means that set gates of minimum
base allows to implementing the logic operations of
the arbitrary complexity.
As an example, we consider performance of
operations AND, OR and NOT with usage of gates NOR
(fig.1) and with usage only gates NAND (fig.2).
1)AND
2)OR
3)NOT
Fig. 1. Implementation of the main logic operations 1)AND, OR, NOT on the basis of gates 2NOR.
1)AND
2)OR
3)NOT
Fig. 2. Implementation of the main logic operations AND, OR, NOT on the basis of gates 2NAND.
We will learn several solutions for creating 2AND, 2NAND, 2OR, 2NOR, and other logic block diagrams using Sheffer
logic. Buning uchun De Morgan’s theoremalarini bilish talab etiladi.
De Morgan’s theorems
x
х
=
2
1
__
__________
2
1
x
x
x
x
=
+
2
1
________
2
1
x
x
x
x
+
=
Issue 1.
Using gates 2NAND, design the circuit of the 4NAND operation, truth table.
Solution:
in this we use the basic axioms and laws of the algebra of logic - that is, from the law of transformation into
two,
Volume 03 Issue 12-2023
77
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
ISSUE
12
Pages:
74-78
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
х
1
·
х
2
·
х
3
·
х
4=
х
1
·
х
2
·
х
3
·
х
4
The block scheme is generated as follows:
х
1
х
2
х
3
х
4
Fig. 3. Implementation of the main logic operation 4NAND the basis of gates 2NAND.
Four-variable truth table and a summary of truth tables for logic gates
Table 2.
X
1
X
2
X
3
X
4
4NAND
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
&
&
&
&
&
Volume 03 Issue 12-2023
78
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
03
ISSUE
12
Pages:
74-78
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
(2023:
7.063
)
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
Base elements perform the necessary tasks for digital
integrated circuits. Therefore, it is not for nothing that
these base elements are also universal logical
elements. In conclusion, it can be said that we can
assemble an arbitrary logical element using the
elements of the base.
REFERENCES
1.
A.M.Abdullayev, S.K.Ramonova. Methodical
instructions on carrying out of practical works
on discipline “Digital logic design”. Tashkent:
TUIT. 2017.
2.
Ramonova S.K., Yusupova M.M., Foziljonov H.I.
Methodological instruction for practical work
on the su
bject” electronics and digital
technology". (Part 2).- Tashkent: TUIT. 2018.
3.
Prof. Aripov X.K., dos. Alimova N.B. Text of
lectures on electronics and circuit engineering.
TUIT, 2011.
4.
А.Г. Морозов. Электротехника, электроника
и импульсная техника. –
М.: Высшая школа,
1987.
