Unit 1

Combinational Circuit
Combinational Circuit
• A combinational circuit is a type of digital logic
circuit whose output depends on the combination
of input values.
• It can have n number of inputs and m number of
outputs.
• It does not depend on past input and output
values.
• It doesn’t have any memory element in its circuit.
• It does not have any feedback path between input
and output
• Ex: Binary Adders, Binary Subtractors, Decoders,
Encoders Multiplexers Demultiplxers
Block Diagram of Combinational Circuit

• Input Lines − The input lines are used to enter the input
values into the combinational circuit.
• Processing Unit − It is the main element that processes the
input values depending on the type of the circuit. For example,
a full adder adds three binary bits.
• Output Lines − The output lines are used to take results
generated by the circuit.
Half Adder
• The half adder is a combinational logic circuit with two
inputs and two outputs.
• It is designed to add two single-bit binary numbers A and B.
• It is the basic building block for the addition of two single-bit
numbers.
• This circuit has two outputs namely, sum and carry.
Half Adder
Full Adder
• The full adder is designed to overcome the drawback of a half
adder which is the ability to add only two bits.
• Therefore, the full adder is a three-input and two-output
combinational circuit.
• Where, the inputs are two one-bit numbers A and B, and a
carry C from the previous addition.
• The outputs are sum and carry output.
Full Adder
Cont..
Cont..
Cont..
• S=AꚚBꚚC
• Cout= AB+C(AꚚB)
Full Adder using Half Adder
Multiplexer
• A Multiplexer or Mux is a device that has many inputs and a
single output.
• It selects a single input to the output from several inputs.
• The particular input chosen for output is determined by the
value of the multiplexer’s control lines.
• To be able to select among n inputs, log2n control lines are
needed.
• A multiplexer is also called as a data selector.
• The main purpose of Mux is to perform high speed switching.
Block Diagram for Multiplexer

Output Data Lines

n Selection Lines
4x1 Multiplexer
Circuit Diagram for 4x1 multiplexer
8x1 Multiplexer
16X1 Multiplexer
Selection Inputs Output
S3 S2 S1 S0 Y
0 0 0 0 I0
0 0 0 1 I1
0 0 1 0 I2
0 0 1 1 I3
0 1 0 0 I4
0 1 0 1 I5
0 1 1 0 I6
0 1 1 1 I7
1 0 0 0 I8
1 0 0 1 I9
1 0 1 0 I10
1 0 1 1 I11
1 1 0 0 I12
1 1 0 1 I13
1 1 1 0 I14
1 1 1 1 I15
Cont..
 Advantages of Multiplexer
• Efficiency: The Mux has good efficiency in routing
multiple input signals to a single-out signal based on
control signals.
• Optimization: The Mux helps to conserve resources
such as wires, pins and integrated circuits (IC).
• Different Implementation: The Mux can be used to
implement different digital logic functions such
AND,OR etc.
• Flexibility: Mux can be easily configured according to
the requirements and accommodate different data
sources, enhancing system versatility.
Disadvantages
• Limited number of data sources: The number of input that
can be taken by a multiplexer is restricted by the number of
control lines, which can cause limitations in certain
applications.
• Delay: Multiplexers can have some delay in the signal path,
which can have an impact on the performance of the circuit.
• Complex control rationale: The control logic for
multiplexers can be complex, particularly for bigger
multiplexers with a large number of inputs.
• Power utilization: Multiplexers can consume more power
compared with another simple logic gate, particularly when
they have a large number of inputs.
Application of Multiplexer
• Data Routing: The Mux is used to select one of the several
data lines and re-route to the output.
• Data Selection: The Mux is used for data selection where
they select data sources according to the select lines.
• Analog-to-Digital Conversion(ADC): The Mux are used
in ADC to select different analog input channels.
• Address Decoding: The Mux are used
in Microprocessors or memory for address decoding.
• Logic Function Implementation: Muxes can be used to
implement various logic functions.
•
Decoder
• Decoder is a combinational logic circuit that
decodes the information.
• It comprises of n number of input lines and
maximum 2𝑛 number of output lines.
• In every probable input condition, only one output
signal will produce the logic one among the
various output signals.
• So, this is n-to-2𝑛 decoder, where n input lines
and 2𝑛 output lines.
• Generally, there are 3 types of line decoders (2-to-
4, 3-to-8 and 4-to-16).
Block Diagram of Decoder
2x4 Decoder

Inputs Outputs
E A B Y3 Y2 Y1 Y0
0 X X 0 0 0 0
1 0 0 0 0 0 1
1 0 1 0 0 1 0
1 1 0 0 1 0 0
1 1 1 1 0 0 0
Cont..
3x8 Decoder
Inputs Outputs
E A B C Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0
0 X X X 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 1
1 0 0 1 0 0 0 0 0 0 1 0
1 0 1 0 0 0 0 0 0 1 0 0
1 0 1 1 0 0 0 0 1 0 0 0
1 1 0 0 0 0 0 1 0 0 0 0
1 1 0 1 0 0 1 0 0 0 0 0
1 1 1 0 0 1 0 0 0 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0
Application of Decoders
• These are used for code conversions.
• Binary to Octal converter
• BCD to Decimal converter
• BCD to Seven Segment Display
• It is extensively used in the memory systems of computers.
• Boolean functions can be implemented using the decoder.
• It is used for de-multiplexing or data distribution.
• It is used in data routing applications where a very short
propagation delay is required.
• It is used to turn on and off digital devices at a specific time.
Encoder
• An Encoder is a combinational circuit that
performs the reverse operation of Decoder.
• It has a maximum of 2𝑛 input lines and ‘N’
output lines, hence it encodes the information
from 2 N inputs into an N-bit code.
• It will produce a binary code equivalent to the
input.
4x2 Encoder

Inputs Outputs
Y3 Y2 Y1 Y0 A1 A0

0 0 0 1 0 0

0 0 1 0 0 1

0 1 0 0 1 0

1 0 0 0 1 1
Cont..
• A1 = Y3+Y2
• A0 = Y3+Y1
Octal to Binary Encoder (8 to 3 Encoder)
Truth table for 8x3 Encoder
INPUTS OUTPUTS

Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0 A2 A1 A0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 1 0 0 0 1

0 0 0 0 0 1 0 0 0 1 0

0 0 0 0 1 0 0 0 0 1 1

0 0 0 1 0 0 0 0 1 0 0

0 0 1 0 0 0 0 0 1 0 1

0 1 0 0 0 0 0 0 1 1 0

1 0 0 0 0 0 0 0 1 1 1
Decimal to BCD Encoder
• A type of encoder that can convert a decimal number or
information represented using decimal number into its
equivalent binary-coded decimal (BCD) format is known as a
decimal to BCD encoder.
Truth table for Decimal to BCD Encoder
INPUTS OUTPUTS

Y9 Y8 Y7 Y6 Y5 Y4 Y3 Y2 Y1 Y0 A3 A2 A1 A0

0 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 0 1

0 0 0 0 0 0 0 1 0 0 0 0 1 0

0 0 0 0 0 0 1 0 0 0 0 0 1 1

0 0 0 0 0 1 0 0 0 0 0 1 0 0

0 0 0 0 1 0 0 0 0 0 0 1 0 1

0 0 0 1 0 0 0 0 0 0 0 1 1 0

0 0 1 0 0 0 0 0 0 0 0 1 1 1

0 1 0 0 0 0 0 0 0 0 1 0 0 0

1 0 0 0 0 0 0 0 0 0 1 0 0 1
BCD Equivalent of Decimal Numbers
Decimal
BCD Code
Digit
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
Logic Gate
Priority Encoder
• A 4 to 2 priority encoder has 4 inputs: Y3, Y2, Y1 & Y0, and 2
outputs: A1 & A0. Here, the input, Y3 has the highest priority,
whereas the input, Y0 has the lowest priority. In this case, even
if more than one input is ‘1’ simultaneously, the output will be
the (binary) code corresponding to the input, which is
having higher priority.
INPUTS OUTPUTS

Y3 Y2 Y1 Y0 A1 A0 V

0 0 0 0 X X 0

0 0 0 1 0 0 1

0 0 1 X 0 1 1

0 1 X X 1 0 1

1 X X X 1 1 1
Logical Expression

1 1 1 1
Logic Gates for Priority Encoder
Applications
• Encoders are very common electronic circuits
used in all digital systems.
• Encoders are used to translate the decimal
values to the binary in order to perform binary
functions such as addition, subtraction,
multiplication, etc.
• Other applications especially for Priority
Encoders may include detecting interrupts in
microprocessor applications.
Advantages
• Reduction in the number of lines: Encoders reduce
the number of lines required to transmit information
from multiple inputs to a single output, which can
simplify the design of the system and reduce the cost of
components.
• Improved reliability: By converting multiple inputs
into a single serial code, encoders can reduce the
possibility of errors in the transmission of information.
• Improved performance: Encoders can enhance the
performance of a digital system by reducing the amount
of time required to transmit information from multiple
inputs to a single output.
Disadvantages
• Increased complexity: Encoders are typically
more complex circuits than multiplexers,
requiring additional components to implement.
• Limited to specific applications: Encoders are
only suitable for applications where a parallel set
of inputs must be converted into a serial code.
• Limited flexibility: Encoders are limited in their
flexibility, as they can only encode a fixed
number of inputs into a fixed number of outputs.