Analogue & Digital Electronics on Comparators

38 views 47 slides Oct 21, 2024
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About This Presentation

Comparator circuits for different conversions


Slide Content

Department of ECE
INTRODUCTION OF COMBINATIONAL CIRCUITS
A combinational circuit consists of input variables, logic gates, and
output variables. The output of combinational circuit at any instant,
depends only on the levels present at input terminals.
-It does not use any memory
-it can have number inputs and outputs.
Example:
1.Adder, Substractor
2.Comparator
3.Code Converters
4.Encoders, Decoders
5.Multiplexers and Demutiplexers

Department of ECE
Digital Comparator
▪A magnitude digital Comparator is a combinational circuit that
compares two digital or binary numbers in order to find out
whether one binary number is equal, less than or greater than the
other binary number.
▪We logically design a circuit for two inputs one for A and other for B
and have three output terminals, one for A > B condition, one for A = B
condition and one for A < B condition.
Module 2

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Digital Comparator
1-Bit Magnitude Comparator
▪A comparator used to compare two bits is called a single bit comparator.
▪It consists of two inputs each for two single bit numbers and three output.
▪The truth table for a 1-bit comparator is given below:
▪From the above truth table logical expressions for each output can be
expressed as follows:
A>B:AB'
A<B:A'B
A=B:A'B'+AB
3
Module 2

Department of ECE
Digital Comparator
▪A comparator used to compare
two binary numbers each of two
bits is called a 2-bit Magnitude
comparator. It consists of four
inputs and three outputs to
generate less than, equal to and
greater than between two binary
numbers.
▪The truth table for a 2-bit
comparator is given below:
4
Module 2
2-Bit Magnitude Comparator

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2-Bit Magnitude Comparator
From the above truth table K-map for each output can be drawn as follows:
5
Module 2

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2.2 Magnitude Comparator (K-map simplification)
2-Bit Magnitude Comparator
A>B:A
1B
1’+A
0B
1’B
0’+A
1A
0B
0’
A=B:A
1’A
0’B
1’B
0’+A
1’A
0B
1’B
0+A
1A
0B
1B
0+A
1A
0’B
1B
0’
=A
1’B
1’(A
0’B
0’+A
0B
0)+A
1B
1(A
0B
0+A
0’B
0’)
=(A
0B
0+A
0’B
0’)(A
1B
1+A
1’B
1’)
=(A
0Ex-NorB
0)(A
1Ex-NorB
1)
A<B:A
1’B
1+A
0’B
1B
0+A
1’A
0’B
0
6
Module 2
22EC401 DIGITAL SYSTEM DESIGN

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Logic Diagram
2-Bit Magnitude Comparator
7
Module 2

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IC-7485 (4-bit Comparator)
8
Pin diagram and logic diagram of IC-7485
IC 7485 is a four-bit comparator IC. It can be used to compare two 4-bit binary data
and output can be received from the output pins in the form of HIGH and LOW state.
It can be used for comparison of straight binary numbers and BCD coded number
It includes cascading inputs to allow for comparison of larger bit numbers by
connecting multiple 7485 ICs. It indicates if the higher bits are greater, smaller and
equal.

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IC-7485 (4-bit Comparator)
9
Functional table for IC-7485
Comparing 8 bit number by cascading two 7485 IC’s-

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Digital Comparator
Applications
1.Comparators are used in central processing units (CPUs) and
microcontrollers (MCUs).
2.These are used in control applications in which the binary numbers
representing physical variables such as temperature, position, etc.
are compared with a reference value.
3.Comparators are also used as process controllers and for Servo
motor control.
4.Used in password verification and biometric applications.
10

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Binary to BCD converter (Truth table)
11
•In BCD code, 0 to 9 numbers represent the equivalent binary numbers. For the
numbers above 10, LSB of a decimal number is represented by its equivalent binary
number and MSB of a decimal number is also represented by their equivalentbinary
number.
•The converter has 5 outputs D
0, D
1, D
2, D
3and D
4. From the truth table,
themintermscan be obtained for each output.
•D
4= ∑m(10, 11, 12, 13, 14, 15),
• D
3= ∑m(8, 9), D
2= ∑m(4, 5, 6, 7, 14, 15),
•D
1= ∑m(2, 3, 6, 7, 12, 13),
•D
0= ∑m(1, 3, 5, 7, 9, 11, 13, 15)

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Binary to BCD converter (Truth table)
12

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Binary to BCD converter (K-map)
13

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Binary to BCD converter (Logical diagram)
14

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BCD to Excess -3 code converter (Truth table)
15
•For this conversion process, 4-bit BCD code is considered
as input, which is converted into 4-bit Excess-3 code.
Since 4-bit is considered for BCD code, the output is
produced only for the inputs from 0 to 9.
•For the remaining input combinations, the output cannot
be predicted. So they are don’t care outputs.
•Output minterms are:
•E
3= ∑m(5, 6, 7, 8, 9),
•E
2= ∑m(1, 2, 3, 4, 9),
•E
1= ∑m(0, 3, 4, 7, 8),
•E
0= ∑m(0, 2, 4, 6, 8,)

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BCD to Excess -3 code converter (Truth table)
16

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BCD to Excess -3 code converter
(K-map)
17

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BCD to Excess -3 code converter
(Logical diagram)
18

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BCD to Gray code converter
(Truth table)
19
•The truth table having the conversion from BCD code to
gray code is shown below. Since the BCD code has only
4 bits, a total of 9 BCD digits have been considered. The
output is unpredictable for other input combinations.

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BCD to Gray code converter
(Truth table)
20

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BCD to Gray code converter
(K-map)
21

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BCD to Gray code converter
(Logical diagram)
22

Department of ECE
WhatisParityGenerator?
•AParityGeneratoris aCombinationalLogicCircuitthat
GeneratestheParitybitintheTransmitter.
•AParitybitisusedforthepurposeofdetectingerrorsduring
transmissionsofbinary information.
•Itis anextrabitincludedwiththe binarymessageto make
the numberof1’seitherOddorEven.

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TwoTypesofParity
•InEvenParity,theaddedParitybitwillMaketheTotal
Numberof 1’sanEvenAmount.
•InOddParity,the addedParitybitwillMaketheTotal
Numberof 1’sanOddAmount.

Department of ECE
Parity GeneratorTruthTableandLogic Diagram
3-bitMessage Odd
Parity
Bit
Even
Parity
Bit
X Y Z
0 0 0 1 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 0 1

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EvenPair
P=&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;
+&#3627408459;&#3627408460;&#3627408461;+&#3627408460;&#3627408461;=&#3627408459;&#3627408460;&#3627408461;+&#3627408460;&#3627408461;
=&#3627408459;&#3627408460;⨁&#3627408461;+&#3627408459;&#3627408460;⨁&#3627408461;
0101
1010
YZ
X 00011110
0
1
BooleanExpression
K-MapSimplification
=X⨁(&#3627408460;⨁&#3627408461;)
OddPair
P=&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;
=&#3627408459;&#3627408460;&#3627408461;+&#3627408460;&#3627408461;+&#3627408459;&#3627408460;&#3627408461;+&#3627408460;&#3627408461;
=&#3627408459;&#3627408460;⨁&#3627408461;+&#3627408459;&#3627408460;⨁&#3627408461;
=&#3627408459;⨁(&#3627408460;⨁&#3627408461;)
1010
0101
X
YZ
00011110

Department of ECE
ParityChecker
•ACircuitthatCheckstheParityin theReceiver is called
ParityChecker.
•TheParityChecker circuitchecksforpossibleerrorsinthe
Transmission.
•SincetheInformationTransmittedwithEvenParity,the
Receivermusthavean evennumberof1’s.Ifithasodd
numberof1’s,itindicatesthatthereisan erroroccurred
during Transmission.
•TheOutputof theParityCheckerisdenotedbyPEC(Parity
ErrorChecker).Ifthereiserror,thatis,ifithasoddnumberof
1’s,itwillindicate1.IfnothenPEC willindicate0.

Department of ECE
Decimal
Equivalent
FourBitsReceived ParityError
P A B C PEC
0 0 0 0 0 0
1 0 0 0 1 1
2 0 0 1 0 1
3 0 0 1 1 0
4 0 1 0 0 1
5 0 1 0 1 0
6 0 1 1 0 0
7 0 1 1 1 1
8 1 0 0 0 1
9 1 0 0 1 0
10 1 0 1 0 0
11 1 0 1 1 1
12 1 1 0 0 0
13 1 1 0 1 1
14 1 1 1 0 1
15 1 1 1 1 0
EvenParityCheckerTruthTable

Department of ECE
LogicDiagram BooleanExpression
+??????&#3627408436;&#3627408437;&#3627408438;+&#3627408437;&#3627408438;+PEC=??????&#3627408436;&#3627408437;&#3627408438;+&#3627408437;&#3627408438;
??????&#3627408436;&#3627408437;&#3627408438;+&#3627408437;&#3627408438;+??????&#3627408436;(&#3627408437;&#3627408438;+
&#3627408437;&#3627408438;)
=??????&#3627408436;&#3627408437;⨁&#3627408438;+??????&#3627408436;&#3627408437;⨁&#3627408438;+??????&#3627408436;&#3627408437;⨁&#3627408438;+
??????&#3627408436;&#3627408437;⨁&#3627408438;
=(??????&#3627408436;+??????&#3627408436;)B⨁&#3627408438;
=(??????⨁&#3627408436;)&#3627408437;⨁&#3627408438;
+??????&#3627408436;+??????&#3627408436;&#3627408437;⨁&#3627408438;
+??????⨁&#3627408436;&#3627408437;⨁&#3627408438;
=(P⨁&#3627408436;)⨁(&#3627408437;⨁ C)
0101
1010
0101
1010
00011110
00
01
11
10
PA
K-Map
Simplification
BC

Department of ECE
IC74181–Arithmetic LogicUnit
➢Averypopular&widelyusedcombinational
circuitisALUwhichiscapableofperforming
arithmeticaswellaslogicaloperation.
➢ArithmeticOperatingModes:
✓Addition
✓Subtraction
✓ShiftOperation
✓MagnitudeComparison
✓12otherarithmeticoperations
8/29/20
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Department of ECE
IC 74381–4BitArithmeticLogicUnit
➢Features:
✓Low inputloadingminimizesdriverequirements
✓Performs sixteenarithmeticand16 logical
functions
✓Carrygenerateandpropagateoutputsforuse
withcarrylookaheadgenerator
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IC74181–BlockDiagram & Pin description
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M=0 (Arithmetic operation)
M=1 (Logical operation)
G & P is for cascading to make
operation faster.

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IC74181–PinDiagram
33

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IC74181–FunctionTable
34

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SevenSegmentDisplay
a
b
c
d
e
f
g
dp
8/29/20
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3
5
✓IC 7447 as BCD to 7- Segment
decoder driver

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SevenSegmentDisplay
9
9
Segments Display
Numbe
r
a b c d e f g
ON ON ON ON ON ONOFF 0
OFF ON ON OFFOFF OFFOFF 1
ON ON OFF ON ON OFFON 2
ON ON ON ONOFF OFFON 3
OFF ON ON OFFOFF ONON 4
ON OFFON ONOFF ONON 5
ON OFFON ON ON ONON 6
ON ON ON OFFOFF OFFOFF 7
ON ON ON ON ON ONON 8
ON ON ON ONOFF ONON 9

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TypesofSevenSegmentDisplay
➢CommonCathodeDisplay
➢CommonAnodeDisplay
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CommonCathodeDisplay
BCD
Input
R
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38
R
R
R
R
R
R
R
a
BCDto
7
Seg
ment
Deco
der
b
c
d
e
f
g
dp

Department of ECE
BCD to7SegmentDecoder Driver ICs
Sr.No. ICNumber Specifications
1 IC7446,
IC74246
ActiveLow open
collectoroutputs,
maximumvoltage30V,
maximumcurrentsinkingcapability40mA
2 IC7447,
IC74247
ActiveLow open
collectoroutputs,
maximumvoltage15V,
maximumcurrentsinkingcapability40mA
3 IC7448,
IC74248
ActiveHighopen
collectoroutputs, Pullup
resistor2kohm,
maximumvoltage5.5V,
maximumcurrentsinkingcapability6.4mA
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Department of ECE
IC7447
Pins Description
A,B,C,D BCDInputs
atog
ActiveLow Outputs
LT
LampTest
RBI
RippleBlankingInput
BI
BlankingInput
RBO
RippleBlankingoutput
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Department of ECE
–BlankingInput
✓IfBIisconnectedto0,thenthedisplaywillbe
switched offirrespectiveoftheBCDinput.
✓Thisfeatureisusedinthemultiplexeddisplay
inordertosave power.
✓Inthenon-multiplexeddisplaysthisinputis
permanentlyconnected to Vcc(1)
BI/RBO
41

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✓Thispincanbeusedtocheckwhetherallthe
segmentsofthedisplayareworkingproperly
ornot.
✓IfLTisforcedlowwithRBOatlogic1oropen,
thenalltheoutputterminalswillbeforcedto
theiractivestate.
LT-LampTest
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Department of ECE
-RippleBlankingInput
✓Forthenormaldecodingoperation,thisinput
shouldbeconnectedtologic1.
✓IfRBIisconnectedtoground,thenitswitches
offthedisplaywhenBCDinputs
correspondingto0.(0 0 0 0)
✓Fornon-zeroBCDinputs,thedecoderoutput
willbenormalandtheBCDnumberwillbe
displayed.
✓RBI=0isconnectedforblankingoutthe
RBI
107
leadingzeros inmultidigitdisplays.

Department of ECE
a
b
c
d
e
g
dp
R
R
R
R
R
R
1
2
6
7
3
5
4
13
R
12
11
10
9
15
16
14
8
BCD
Inputs
LSB
MSB
IC7447
a
b
c
d
e
f
g
dp
LT
RBI
BI/RBO
Vcc
Gnd
A0
A1
A2
A3
CircuitDiagram
+5V
a
b
c
f
d
e
f
g
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Common

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DisplayConfiguration–LTS542
11
2
a
b
c
d
e
f
g
dp
ab
ced
fg
dp
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Common
Common

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DisplayConfiguration
46

Department of ECE
References
✓DigitalPrinciplesby
MalvinoLeach
✓Modern Digital
ElectronicsbyR.P.Jain
✓Digital Electronics,
PrinciplesandIntegrated
CircuitsbyAnilK.Maini
✓DigitalTechniquesbyA.
AnandKumar
47
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