This document describes a project to design a 4-bit arithmetic circuit using multiplexers and full adders. It begins with an abstract stating that combinational logic circuits will be used to perform arithmetic operations on 4-bit binary numbers. It then provides descriptions of the key components used - multiplexers, full adders, and arithmetic logic units. The design section explains that the project will implement a 4-bit arithmetic circuit using multiplexers and full adders. Pin diagrams are also provided for the IC chips used in the multiplexers and full adders.

1. 1
PROJECT BASED LAB REPORT
On
Design a logic circuit for 4-bit arithmetic circuit using
Multiplexers, Full-Adders
Submitted in partial fulfilment of the
Requirements for the award of the Degree of
Bachelor of Technology
In
Electronics & Communication Engineering
By
K.BHANUSINDUSH-14004445
A.SARITHA-14004446
D.KRANTHIVEER-14004447
DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
(DST-FIST Sponsored Department)
K L University
Green Fields, Vaddeswaram, Guntur District-522 502
2015-16

2. 2
K L University
DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
(DST-FIST Sponsored Department)
This is to certify that this project based lab report entitled “Design a logic circuit for
4-bit arithmetic circuit using Multiplexers, Full-Adders” is a bonafide work done by
A.Saritha(14004446)in partial fulfilment of the requirement for the award of degree in
BACHELOR OF TECHNOLOGY in Electronics and Communication Engineering
during the academic year 2015-2016.
Faculty In Charge Head of the Department
CERTIFICATE

3. 3
K L University
DEPARTMENT OF ELECTRONICS AND COMMUNICATION
ENGINEERING
(DST-FIST Sponsored Department)
We hereby declare that this project based lab report entitled “Design a logic circuit for 4-
bit arithmetic circuit using Multiplexers, Full-Adders” has been prepared by us in partial
fulfilment of the requirement for the award of degree “BACHELOR OF TECHNOLOGY in
ELECTRONICS AND COMMUNICATION ENGINEERING” during the academic year
2015-2016. I also declare that this project based lab report is of our own effort and it has not been
submitted to any other university for the award of any degree.
Date: 21-4-2016 K.BHANUSINDUSH(14004445)
Place: KLUNIVERSITY A.SARITHA(14004446)
D.KRANTHIVEER(14004447)
DECLARATION

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ACKNOWLEDGEMENT
My sincere thanks to K.PHANISREENIVAS in the Lab for their outstanding support
throughout the project for the successful completion of the work
We express our gratitude to DR.A.S.C.S. SASTRY, Head of the Department for
Electronics and Communication Engineering for providing us with adequate facilities,
ways and means by which we are able to complete this term paper work.
We would like to place on record the deep sense of gratitude to the honourable Vice
Chancellor, K L University for providing the necessary facilities to carry the concluded
term paper work.
Last but not the least, we thank all Teaching and Non-Teaching Staff of our department
and especially my classmates and my friends for their support in the completion of our
term paper work.
K.Bhanusindush(14004445)
A.Saritha(14004446)
D.Kranthiveer(14004447)

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CONTENTS
Content PG.NO
1. ABSTRACT 6
2. DESCRIPTION 7-9
3. MODULES
3.1 Analyze the concepts ofMultiplexers and Full-adder 9-11
3.2 Understand the designof an arithmetic circuit 12
3.3 Designa 4-bit Arithmetic circuit using combinational
circuits
13
3. DESIGN 14
4. PROJECT DESCRIPTION 15
5. SNAPSHOTS OF OUTPUT 16
6. REFERENCES 17

6. 6
ABSTRACT
In digital circuit theory, combinational logic is a type of digital logic which is
implemented by Boolean circuits, where the output is a pure function of the present
input only. This is in contrast to sequential logic, in which the output depends not only
on the present input but also on the history of the input. In other words, sequential logic
has memory while combinational logic does not.
Combinational logic is used in computer circuits to perform Boolean algebra on input
signals and on stored data. Practical computer circuits normally contain a mixture of
combinational and sequential logic. For example, the part of an arithmetic logic unit, or
ALU, that does mathematical calculations is constructed using combinational logic.
Other circuits used in computers, such as half adders, full adders, halfsubtractor , full
subtractors, multiplexers, demultiplexers, encoders and decoders are also made by
using combinational logic.
Adders are essential building blocks for digital systems. There are many different adder
architectures that all compute the same result, but they get to the results in different
ways. Different adder architectures also differ in area, speed, and power, and there is no
architecture that dominates all other adders in all the areas .Therefore hardware
designers choose adders based on system area, speed, and power constraints.
In electronics, a multiplexer (or mux) is a device that selects one of several analog or
digital input signals and forwards the selected input into a single line. A multiplexer of 2n
inputs has n select lines, which are used to select which input line to send to the
output.[2] Multiplexers are mainly used to increase the amount of data that can be sent
over the network within a certain amount of time and bandwidth. A multiplexer is also
called a data selector.An electronic multiplexer makes it possible for several signals to
share one device or resource, for example one A/D converter or one communication
line, instead of having one device per input signal.
KEYWORDS:
ALU, Adder, Stores Information, Multiplexers, Combinational.

7. 7
DESCRIPTION
An arithmetic logic unit (ALU) is a digital circuit used to perform arithmetic and
logic operations. It represents the fundamental building block of the central processing
unit (CPU) of a computer. Modern CPUs contain very powerful and complex ALUs. In
addition to ALUs, modern CPUs contain a control unit (CU).
Most of the operations of a CPU are performed by one or more ALUs, which load data
from input registers. A register is a small amount of storage available as part of a CPU.
The control unit tells the ALU what operation to perform on that data and the ALU stores
the result in an output register. The control unit moves the data between these registers,
the ALU, and memory.
Arithmetic Logical Unit is the very important subsystem in the digital system design. An
Arithmetic logic Unit (ALU) is an integral part of a computer processor. It is a
combinational logic unit that performs its arithmetic and logic operations. ALUs of
various bit-widths are frequently required in very large-scale integrated circuits (VLSI)
from processors to application specific integrated circuits (ASICs). ALU is getting
smaller and more complex nowadays to enable the development of a more powerful but
smaller computer.
The demand for low power & high speed processing has been increasing as a result of
expanding computer and signal processing applications. Higher throughput arithmetic
operations are important to achieve the desired performance in many real-time signal and
image processing applications. The key arithmetic operations in such applications are
multiplication, addition, division and subtraction.
Fig 1.1: ARTHEMETIC LOGIC UNIT

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FEATURES OF ALU:
Low-power CMOS Process Technology
1. Total 16 arithmetic operations (add, subtract, plus, shift, plus 12 others)
2.Total 16 logic operations (XOR, AND, NAND, NOR, OR, plus 11 others)
3. Capable of active-high and active-low operation.
4. Full carry look-ahead for high-speed arithmetic operation.
5. Arithmetic operations expressed in 2s complement notation.
6. 4 selection lines are to perform the operations on two 4 bit inputs in both the units.
7. The 5th select line is used to select either one of the units.
A 4-bit high-speed parallel Arithmetic Logic Unit (ALU). Controlled by the four
Function Select inputs (S0–S3) and the Mode Control input (M), it can perform all the 16
possible logic operations or 16 different arithmetic operations on active-HIGH or active-
LOW operands. The Function Table lists these operations.
When the Mode Control input (M) is HIGH, all internal carries are inhibited and the
device performs logic operations on the individual bits as listed. When the Mode Control
input is LOW, the carries are enabled and the device performs arithmetic operations on
the two 4-bit words. The device incorporates full internal carry look ahead and provides
for either ripple carry between devices using the Cn+4 output, or for carry look-ahead
between packages using the signals P (Carry Propagate) and G (Carry Generate). In the
Add mode, P indicates that F is 15 or more, while G indicates that F is 16 or more. In the
Subtract mode, P indicates that F is zero or less, while G indicates that F is less than zero.
P and G are not affected by carry in. When speed requirements are not stringent, it can
be used in a simple Ripple Carry mode by connecting the Carry output (Cn+4) signal to
the Carry input (Cn) of the next unit. For high-speed operation the device is used in
conjunction with a carry look ahead circuit. One carry look ahead package is required for
each group of four F181 devices. Carry look ahead can be provided at various levels and
offers high-speed capability over extremely long word lengths.

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COMBINATIONAL CIRCUIT
In digital circuit theory, combinational logic (sometimes also referred to as time-
independent logic[1] ) is a type of digital logic which is implemented by Boolean circuits,
where the output is a pure function of the present input only. This is in contrast
to sequential logic, in which the output depends not only on the present input but also on
the history of the input. In other words, sequential logic has memory while combinational
logic does not.
Combinational logic is used in computer circuits to perform Boolean algebra on input
signals and on stored data. Practical computer circuits normally contain a mixture of
combinational and sequential logic. For example, the part of an arithmetic logic unit, or
ALU, that does mathematical calculations is constructed using combinational logic. Other
circuitsusedincomputers,suchas halfadders, fulladders, multiplexers, demultiplexers, enco
ders and decoders are also made by using combinational logic.
An alternate term is combinatorial logic,
Fig 1.2: COMBINATIONAL CIRCUIT
Design of a combinational circuit begins with a behavioral specification and selection of
the implementation technique. These are then followed by simplification, hardware
synthesis, and verification. Combinational circuits can be specified via Boolean logic
expressions, structural descriptions, or truth tables. Various implementation techniques,
using fixed and programmable components, are outlined in the rest of this article.
Combinational circuits implemented with fixed logic tend to be more expensive in terms
of design effort and hardware cost, but they are often both faster and denser and consume
less power. They are thus suitable for high-speed circuits and/or high-volume production.

10. 10
Analyze the concepts of Multiplexers and Full-adders
MULTIPLEXER
In electronics, a multiplexer (or mux) is a device that selects one of
several analog or digital input signals and forwards the selected input into a single
line.[1] A multiplexer of 2n inputs has n select lines, which are used to select which input
line to send to the output.[2] Multiplexers are mainly used to increase the amount of data
that can be sent over the network within a certain amount of time and bandwidth.[1] A
multiplexer is also called a data selector.
An electronic multiplexer makes it possible for several signals to share one device or
resource, for example one A/D converter or one communication line, instead of having
one device per input signal.
Conversely, a demultiplexer (or demux) is a device taking a single input signal and
selecting one of many data-output-lines, which is connected to the single input. A
multiplexer is often used with a complementary demultiplexer on the receiving end.
An electronic multiplexer can be considered as a multiple-input, single-output switch, and
a demultiplexer as a single-input, multiple-output switch. The schematic symbol for a
multiplexer is an isosceles trapezoid with the longer parallel side containing the input pins
and the short parallel side containing the output pin. The schematic on the right shows a
2-to-1 multiplexer on the left and an equivalent switch on the right. The wire
connects the desired input to the output
ADDER:
In electronics, an adder or summer is a digital logic circuit that
performs addition of numbers. In many computers and other kinds of processors, adders
are used not only in the arithmetic logic units, but also in other parts of the processor,
where they are used to calculate addresses, table indices, increment and decrement
operators, and similar operations.
Although adders can be constructed for many numerical representations, such as binary-
coded decimal or excess-3, the most common adders operate on binary numbers. In cases
where two's complement or ones' complement is being used to represent negative

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numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number
representations require a more complex adder
Fig1.4: 1 BIT ADDER
A adder adds binary numbers and accounts for values carried in as well as out. A
one-bit full adder adds three one-bit numbers, often written as A, B, and Cin; A and B are
the operands, and Cin is a bit carried in from the previous less significant stage.The full
adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit binary
numbers. The circuit produces a two-bit output, output carry and sum typically
represented by the signals Cout and S,
A full adder can be implemented in many different ways such as with a
custom transistor-level circuit or composed of other gates. One example implementation
with and .
In this implementation, the final OR gate before the carry-out output may be replaced by
an XOR gate without altering the resulting logic. Using only two types of gates is
convenient if the circuit is being implemented using simple IC chips which contain only
one gate type per chip.
A full adder can be constructed from two half adders by connecting A and B to the input
of one half adder, connecting the sum from that to an input to the second adder,
connecting Ci to the other input and OR the two carry outputs. The critical path of a full
adder runs through both XOR-gates and ends at the sum bit . Assumed that an XOR-
gate takes 3 delays to complete, the delay imposed by the critical path of a full adder is
equal to

12. 12
The carry-block subcomponent consists of 2 gates and therefore has a delay of
UNDERSTAND THE DESIGN OF ARTHEMETIC CIRCUIT
ARTHEMETIC CIRCUIT COMLEXITY:
In computational complexity theory, arithmetic circuits are the standard model
for computing polynomials. Informally, an arithmetic circuit takes as inputs either
variables or numbers, and is allowed to either add or multiply two expressions it already
computed. Arithmetic circuits give us a formal way for understanding the complexity of
computing polynomials. The basic type of question in this line of research is `what is the
most efficient way for computing a given polynomial f?
FigE1.5: ARTHEMETIC CIRCUIT COMPLEXITY
An arithmetic circuit C overthe fieldFand the setof variablesx1,...,xn isadirected
acyclicgraph as follows.Everynode init withindegree zeroiscalledan inputgateand islabeled
by eitheravariable xi or a fieldelementinF.Everyothergate islabeledbyeither+or ; inthe
firstcase itis a sumgate andin the seconda productgate.Anarithmetic formula isa circuitin
whicheverygate has outdegree one (andsothe underlyinggraphisa directedtree).
A circuit has two complexity measures associated with it: size and depth. The size of a
circuit is the number of gates in it, and thedepth of a circuit is the length of the longest
directed path in it. For example, the circuit in the figure has size six and depth two.
An arithmetic circuit computes a polynomial in the following natural way. An input gate
computes the polynomial it is labeled by. A sum gate v computes the sum of the
polynomials computed by its children (a gate u is a child of v if the directed edge (u,v) is
in the graph). A product gate computes the product of the polynomials computed by its

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children. Consider the circuit in the figure, for example: the input gates compute (from
left to right) x1,x2 and 1, the sum gates compute x1 + x2 and x2 + 1, and the product gate
computes (x1 + x2)x2(x2 + 1).
Designa 4-bit Arithmetic circuit using combinationalcircuits
The project is designed to implement 4-bit arthemetic circuit using multiplexers
and full adder.The project consists of following ic pin diagrams,the project consists of
two ic pins 74153,7483
Fig1.6: IC PIN DIAGRAM OF 74153
Fig 1.7:IC PIN DIAGRAM FOR 7483

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CIRCUIT DIAGRAM FOR 4-BIT ARTHEMETIC CIRCUIT
USING MULTIPLEXER’S AND FULL-ADDERS
`
Fig 1.8:CIRCUIT DIAGRAM OF ARTHEMETIC LOGIC CIRCUIT

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OUTPUT USING MULTISIM:
Fig 1.9:OUPUT USING MULTISIM
PROJECTDESCREPTION:
 If two selected lines are given at low level and also carry(input) also given at low
level then ADD operation is performed
 If two selected lines are given at low level and also carry(input) is given at high
level
Then the ADD WITH CARRY operation is performed
 if two selected lines one of the given is low level and another one is given as high
level and carry(input) is also given low level then SUBTRACT WITH
BORROW operation is performed
 if two selected lines one of the given is low level and another one is given as high
level and carry(input) is also given high level then SUBTRACT operation is
performed
 if two selected lines one of the given is low level and another one is given as high
level and carry(input) is also given low level then only A values are obtained

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 if two selected lines one of the given is low level and another one is given as high
level and carry(input) is also given high level then INCREMENT operation is
performed
 if two selected lines one of the given is high level and another one is given as
high level and carry(input) is also given low level then DECREMENT
operation is performed
 if two selected lines one of the given is high level and another one is given as
high level and carry(input) is also given high level then the A values are obtained
RESULTS:
Fig 1.11: FINAL OUTPUT
CONCLUSION:
To stay competitive in today’s market, engineers must take a design from
engineering through manufacturing with shorter design cycles and faster time to market.
To be successful, we need a set of powerful, intuitive, and integrated tools that work
seamlessly across the entire design flow.
We have studied well about arithmetic & logic unit. Here we have implemented 4-bit
arithmetic logic unit successfully. The full integrated circuit is designed and simulated in

17. 17
standard 350 nm CMOS technology. Here the RTL coding is done first using a Verilog
HDL and simulation is done by using MultiSim 6.2. The experimental waveforms, power
measurements have also been presented
REFERENCES:
1.Budd, T. (1997b), An Introduction to Object-Oriented Programming, 2nd edn,
Addison-Wesley.
2.Ghezzi, C., Jayazeri, M. & Mandrioli, D. (1998), Fundamentals of Software
Engineering, 2nd edn,Prentice-Hall.
3.K. Appel and W. Haken. (1976), Every Planar Map is 4-colorable, Bull. Amer. Math.
Soc., vol. 82, pp. 711-712
.