The document provides an overview of digital logic circuits called adders, which are used for adding binary numbers in processors, classified into half adders and full adders. It further explains the roles and truth tables of both types of adders, as well as the concepts of multiplexers and demultiplexers, which handle multiple input/output signals in digital systems. Additionally, it briefly covers encoders and decoders, highlighting their functions in data conversion and processing.

1. INTRODUCTION
An adder is a digital logic circuit in electronics that is extensively used for the addition of
numbers. In many computers and other types of processors, adders are even used to
calculate addresses and related activities and calculate table indices in the ALU and even
utilized in other parts of the processors. These can be built for many numerical
representations like excess-3 or binary coded decimal.
Adders are basically classified into two types: Half Adder and Full Adder.

2. CLASSIFICATION OF ADDERS
Adders are broadly classified into two types. They are:
• Half Adder
• Full Adder
• Half Adder
Half Adder is a combinational arithmetic circuit that adds two binary numbers and produces sum bit
(S) and carry bit (C) as the output. It is used to add 2 single-bit binary numbers.
Full Adder
It is a combinational arithmetic circuit constructed by combining two Half Adder circuits. It is used
to add 3 one-bit binary numbers.

3. CLASSIFICATION (PICTORIAL FORM)
HALF ADDER FULL ADDER

4. HALF ADDER
• Half adder adds two binary digits where the input
bits are termed as augend and addend.
• It produces two outputs one is the sum and the
other is carry.
• XOR is applied to both the inputs.
• AND gate is applied to both inputs to produce
carry.

5. TRUTH TABLE FOR HALF ADDER
• The 2-bit half adder truth table :
0+0 = 1
0+1 = 1
1+0 = 1
1+1 = 10
INPUTS OUTPUTS
A B SUM CARRY
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1

6. HALF ADDER TRUTH TABLE
• The simplest expression uses the exclusive OR
function:
Sum = AÅB
• An equivalent expression in terms of the basic AND,
OR and NOT is:
Sum = SUM=A|.B+A.B'

7. FULL ADDER
• Full adder adds 3 one-bit numbers.
• One of the three bits can be referred to as
operands.
• The other is termed as bit carried in.
• The produced output is 2-bit output and these can
be referred to as output carry and sum.

8. TRUTH TABLE FOR FULL ADDER
INPUTS OUTPUTS
A B C-IN
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
C-OUT S
0 0
0 1
0 1
1 0
0 1
1 0
1 0
1 1

9. FULL ADDER TRUTH TABLE
• The output carry is designated as C-OUT and the
normal output is represented as S which is ‘SUM’.
• With the above full adder truth-table, the
implementation of a full adder circuit can be
understood easily. The SUM ‘S’ is produced in two
steps:
1. By XORing the provided inputs ‘A’ and ‘B’
2. The result of A XOR B is then XORed with the C-IN

10. THE RELATION BETWEEN
HALF ADDER AND FULL ADDER
• Half adder produces results and full adder uses half adder to produce some other
results.
• Similarly, the full adder is of two half adders.
• The Full-Adder is the actual block that we use to create the arithmetic circuits.

11. WHAT IS
MULTIPLEXER???
 Multiplexer is a device that has multiple inputs
and a single line output.
 The select lines determine which input is
connected to output and also to increase the
amount of data that can be sent over a network
with certain time.
 It is called as data selector.

12. MULTIPLEXER
TYPES
1. 2-1 Multiplexer(1 select line)
2. 4-1 Multiplexer(2 select line)
3. 8-1 Multiplexer(3 select line)
4. 16-1 Multiplexer(4 select line)

13. 4 TO 1 MULTIPLEXER

14. APPLICATIONS OF MULTIPLEXER
 Communication System:
 Acommunication system has a great impact by
multiplexer.
 By using a multiplexer, the efficiency can be
increased.
 Computer Memory:
 Multiplexers are used in computer memory.
 Reduces copper lines to connect the memory
to other parts of the computer.

15. Telephone Network:
 In telephone networks, multiple audio signals are
integrated.
Transmission from the Computer of a
Satellite:
 Multiplexer is used to transmit the data signals.
 From satellite to ground
 By using GSM satellite.
APPLICATIONS OF MULTIPLEXER

16. WHAT IS
DEMULTIPLEXER???
 De-multiplexer is also a device with one
input and multiple output lines. It is used
to send a signal to one of the many devices.
 The main difference between a multiplexer
and a de-multiplexer is that a multiplexer
takes two or more signals and encodes
them on a wire, whereas a de-multiplexer
does reverse to what the multiplexer does.

17. TYPES OF
DEMULTIPLEXER
De-multiplexers are classified into
four types :
 1-2 demultiplexer (1 select line)
 1-4 demultiplexer (2 select lines)
 1-8 demultiplexer (3 select lines)
 1-16 demultiplexer (4 select lines)

18. 1-4
DEMULTIPLEXER
TR Truth Table

19. APPLICATIONS OF DEMULTIPLEXER
Communication System :
 DE multiplexer receives signal outputs from the
multiplexer.
 At the receiver end it converts them back to the original
form.
 Arithmetic Logic Unit (ALU) :
 The output of the ALU is fed as an input to the DE
multiplexer.
 And the output of the DE multiplexer is connected to a
multiple register.

20. Seriestoparallel
converter :
 This converter is used to
reconstruct parallel data.
 Serial data is given as an
input to the DE
multiplexer at a regular
interval.
 Acounter is attached to
detect the data signal.
APPLICATIONS OF DEMULTIPLEXER

21. Encoder and Decoder
Encoders and decoders are fundamental components in digital
electronics, primarily used for data conversion and signal
processing.
Both are combinational logic circuits, but they serve opposite
functions.

22. Feature Encoder Decoder
Input Lines 2n n
Output Lines n 2n
Function
Converts inputs to
binary code
Converts binary
code to outputs
Complexity Simpler operation
More complex
operation
Typical Use Transmitting data
Receiving and
processing data
Differences