This research paper defines the digital electronics and its one type combinational circuits. Combinational circuits is based on the Boolean expression so also gives the brief introduction about Boolean algebra and also describes the different forms of circuits and also describes the minimization techniques of combinational logic circuits and some general application of combinational circuit Follow me on twitter @Tahiryasin971 Email: tahiryasin758@gmail.com

1. COMBINATIONAL LOGIC
CIRCUITS
TAHIR YASIN (18476)

2. ABSTRACT
This research paper is basically the overview on
the combination of circuits in the logical manner.
A combinational logic circuit is one in which the
present state of the combination of
the logic inputs decides the output. Combination
logic means combining of two or more logic gates
to form a required function where the output at a
given time depends only on the input. This paper
briefly discussed on the basic needs of logic
synthesis and also discusses few interesting facts
and consideration logic synthesis. This research
paper will be efficient to clear some basic concept

3. INTRODUCTIO
N
Digital signals are processed by the digital system which can be
built with various logic gates. These logic circuits are made of
various logic gates by connecting them in certain combinations.
In order to produce the required output, Digital logic circuits are
mainly classified into two types , sequential logic circuits and
combinational logic circuits. The difference between sequential
logic circuits and combinational logic circuits is the
combinational circuit is the independent circuit it doesn’t depend
on the previous input to generate any output. But sequential
logic circuits are those which are dependent on the clock cycles
and depend on present as well as past inputs to generate any
output.
The logic gates are the fundamental building blocks of a
combinational circuit. By using the combination of logic gates

4. A combinational circuit comprises of input variables, logic gates and
output variables. The logic gate accepts the inputs and depending on
the type of functioning of the logic gate, output signals are generated
from them. The required output data is obtained from this process by
transforming the binary information given at the input. The figure
below shows the schematic representation of a generalized
combinational logic circuit consisting of n input variable and m output
variable.
In the above figure, there are n input variables and hence there will be
2nd possible combinations of bits at the input. By a Boolean expression
of input variables, each output is expressed. So the result of above
generalized combinational logic circuit can be expressed by m Boolean

5. KEYWORDS
• Combinational logic
• Boolean function
• Digital electronics
• Multiple inputs.

6. DIGITAL SYSTEM:
The heart of digital system is binary number and many people has
shown their interest towards binary number but the major
contribution is done by these people first person is Gottfried Wilhelm
Leibniz. The modern binary number system was fully documented by
Gottfried Leibniz in the 17th century. He also invented the binary
system, foundation of virtually all modern computer architectures.
After Leibniz Efforts is done by many people in the progress of digital
electronics but huge contribution was done in nineteen century by.
George Boole he was from England he was one of the greatest
Mathematician of all time he combined arithmetic and logic
operations which has only two values either true or false who helped
establish modern symbolic logic and whose algebra of logic, now
called Boolean algebra, is basic to the design of digital
computer circuits. The main operations of Boolean algebra are the
conjunction (AND), the disjunction (OR) and the negation (NOT) are
his inventions. Augustus De Morgan also Provided his efforts towards
Digital Electronic best thing which was provided by him to digital

7. Theorem 1
• The left hand side
(LHS) of this theorem
represents a NAND
gate with inputs A and
B, whereas the right
hand side (RHS) of the
theorem represents an
OR gate with inverted
inputs.
• This OR gate is called
Table showing verification of the De
Morgan's first theorem –

8. •Theorem 2:
• The LHS of this theorem
represents a NOR gate with inputs
A and B, whereas the RHS
represents an AND gate with
inverted inputs.
• This AND gate is called
as Bubbled AND.
Table showing verification of the
De Morgan's second theorem −

9. But the Boolean algebra of George Boole was complex
which is simplified by Charles Sanders Peirce. A basic
difference between ordinary algebra and algebra of
logic is clearly mentioned by Price. Price explain symbol
which are used in ordinary algebra they denote things
without describing them i.e. in ordinary algebra indices
are blank and may be assigned any numerical value to
get some result. Peirce expresses de-Morgan’s low
symbolically as and. which was reported in 1885. This
representation are very useful to represent any logic by
a single operation, letter describe NOR and NAND. The
first axiom system based on NAND was given by Henry
Sheffer in 1913 After Price Allan Marquand student of

10. LOGIC EXECUTION
• Many logic are implemented by people during 19 century but some
Implementations are historical many people had implemented there
logics on the logic machine (The Logic Machine is the 1st full
functional mechanical device design for a general purpose truth
functional logic processor in which all the valid implications of a logical
proposition displayed in a systematic way) In 1890 Price and Marquand
made some improvement in the logic machine with the help
electromagnetic switching devices. After one year the company of Mr.
Almon Brown Strowger developed the first commercially successful
electromechanical stepping switch telephone exchange system is
known as Strowger switch or step-by-step switch. In 1907 Lee De
Forest's proposed that modified Fleming valve can be used for
implementation of AND logic. Walther Bothe, inventor of the
coincidence circuit, the first modern electronic AND gate in 1924, got

11. VERSION TECHNIQUE
Every logical expression can be executed by using logic gates
input variables, generally indicated by English letters value of
input either be (1) or (0), A Combinational circuit can be
represented in five different forms and descriptions are as under:
• Algebraic forms
• Tabulated forms
• Graphics forms
• Statement forms
• Code forms
ALGEBRAIC FORM
Y=A’B’C’+AB’C’+ABC’+ABC
Y=B’C’+AB
Y’=B+C.A’+C (A’+B’)

12. TABULATED FORM
GRAPHICS FORM

13. STATEMENT FORM
• module exp_y(Y, A, B, C) // Define
variable for input and output.
• input A, B, C; // Input variable
output Y;
• → Component 3 to 5 and 4 to 5
• not (b,B); // wire b logic value
complement of B not (c,C); // wire
c logic value complement of C and
(a0,b,c); // output a0 is b AND c
• and (a1,A,B); // output a1 is A
AND B or (Y,a0,a1); //

14. CODE FORM

15. MINIMIZATION OF BOOLEAN EXPRESSION
The process of simplifying the algebraic
expression of a Boolean function is
called minimization. ... It is clear from the
above image that the minimized version of
the expression takes a less number of logic
gates & also reduces the complexity of
the circuit substantially.
the diagram a defines the complex level of
combination In these circuit there is multiple
gates are used and also required much time
to run these this circuit But you noticed the
image (b) it is also performing same function
either the number of inputs are also same

16. APPLICATION OF COMBINATIONAL LOGICAL
CIRCUIT
Combinational logic is the hardware
implementation of Boolean logic functions.
That’s all there is to it. All the material you
need to learn about this is either how to
engineer arbitrary Boolean circuits with various
kinds of materials and components, or how to
construct Boolean logic functions to solve
various problems.
common combinational logic circuits include:

17. CONCLUSION
This research paper defines the digital electronics
and its one type combinational circuits.
Combinational circuits is based on the Boolean
expression so also gives the brief introduction
about Boolean algebra and also describes the
different forms of circuits and also describes the
minimization techniques of combinational logic
circuits and some general application of
combinational circuit.

18. REFERENCES
• Computinghistory.org.uk
• Britannica.com
• Tutorialspoint.com
• International Journal of Computer Applications (0975 – 8887)
Volume 127 – No.1, October 2015, on synthesis of
combinational Logic Circuits
• Aschoff, V., "The early history of the binary code," in IEEE
Communications Magazine, vol.21, no.1, (Jan. 1983), 4-10.
• Boole, George, "The mathematical analysis of logic," in
Philosophical Library, (1847).
• www.quora.com

19. “ THANKYOU ”