Digital Electronics and Circuits
(Subject Code: BEC-12)
B.Tech (ECE), III Sem. (2nd Year)
Credit-5 (L T P: 3, 1, 2)
Unit-I: Digital System and Binary Numbers
Dr. Satish Chandra
Assistant Professor, ECE Deptt.
Madan Mohan Malaviya University of Technology, Gorakhpur (UP)
Email:scece@mmmut.ac.in; Contact:+91-9532997798;+91-7992370637
2-Sep-20
Sept 01, 2020
DIGITAL ELECTRONICS & CIRCUITS (BEC-12) 5 Credits (L T P:3-1-2)
Year
Second
Year
Course Name
Digital
Electronics and
Circuits
(BEC-12)
Course Objectives
❖ The course covers Number Systems, Boolean algebra, Error
Detection and Correcting Codes, Reduction techniques and
designing of logic circuits and end of unit logic families are
introduced and discussed.
❖ Discussion and realization of digital system designs based on
combinational and sequential circuits.
❖ In-depth understanding and realization of synchronous and
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asynchronous circuits is carried out.
2
DIGITAL ELECTRONICS & CIRCUITS (BEC-12)
5 Credits (L T P:3-1-2)
Year
Course
Name
2nd Digital
Year Electronics
and
Circuits
(BEC-12)
Course Outcome
Students are expected to be able to demonstrate the following knowledge, skills
and attitudes after completing this course (DEC, BEC-12):
1. Acquired knowledge about basics of digital electronics.
2. Acquired knowledge about solving problems related to number
systems and Boolean algebra.
3. Ability to identify, analyze and design combinational and sequential circuits.
4. Ability to design various synchronous and asynchronous sequential
circuits.
5. Acquired knowledge about internal circuitry and logic behind any
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digital system.
3
Unit-I
Digital System and Binary Numbers, Signed binary numbers, Floating
point number, Binary Codes, Cyclic codes, Error detecting and correcting
codes, Hamming codes. NAND and NOR implementation, Minimization
of circuit using K-map and Tabular method up to five variables, POS and
SOP simplification, Logic family- TTL, DTL, ECL, CMOS, HMOS.
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Unit-I
❖ Digital System [Q/Subpart of Q.]
❖ Binary Numbers, Signed Binary Numbers [Q]
❖ Floating Point Number [Q/Subpart of Q.]
❖ Binary Codes, Cyclic Codes [Q/Subpart of Q.]
❖ Error Detecting and Correcting Codes, Hamming Codes [Q]
❖ NAND and NOR Implementation [Q]
❖ Minimization of Circuit using K-map and Tabular Method up to Five
Variables [Q]
❖ POS and SOP Simplification [Q/Subpart of Q.]
❖ Logic Family: TTL, DTL, ECL, CMOS, HMOS [Q]
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Unit-II
Combinational Logic: Analysis and Design procedure for
Combinational circuits, Binary adder/subtractor, Binary multiplier,
Booth Algorithm, Magnitude comparator, Encoder/ Multiplexer,
Decoder/ Demultiplexer.
Unit-III
Sequential Logic: Sequential circuits, Latches, Flip-flops, Conversion
of flip-flops, Analysis of clocked sequential circuits, State reduction and
assignments.
Registers and Counters: Shift registers, Asynchronous counter,
Synchronous counter, Sequential circuit analysis and design
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procedure, Circuit with latches, Hazards.
Unit-IV
Memory and Programmable Logic: Introduction, Memory organization,
Classification and characteristics of memories, RAM, ROM, PLA, PAL.
Books & Reference:
1. Hill & Peterson, “Switching Circuit & Logic Design”, Wiley.
2. Malvino and Leach, Digital Principle and Applications, (TMH)
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Other Source of Materials for Digital Electronics and Circuits:
1. Ronald J. Tocci, Neal S. Widmer and Gregory L. Moss, “Digital Systems:
Principles and Applications”, 10th Edition, Pearson education, 2009.
2. R. P. Jain, Modern Digital Electronics, 4th Edition, Tata McGraw Hill
Education Pvt. Ltd., 2009.
3. M. Morris Mano and Michael D. Ciletti, Digital Design, 4th Edition, Pearson
Education (Prentice Hall).
4.Charles H. Roth, Jr., Fundamentals of Logic Design, 4th Ed.,Jaico Pub. 2010.
5. PPTs and Video Lecture (NPTEL and many more).
6. Digital Electronics and Circuits based various Recent Animation working
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circuits.
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Experiments: Digital Electronics and Circuits
1. Introduction to digital electronics lab- Nomenclature of digital ICs, specifications.
2. Verification of the truth tables of logic gates using TTL ICs.
3. Implementation of the given Boolean function using logic gates in both SOP and POS forms.
4. Verification of state tables of RS, JK, T and D flip-flops using NAND & NOR gates.
5. Implementation and verification of Decoder/De-multiplexer and Encoder using logic gates.
6. Implementation of 4x1 multiplexer using gates.
7. Implementation of 4-bit parallel adder using 7483 IC.
8. Design, and verify the 4-bit synchronous counter and asynchronous counter.
10. Implementation of a 3-bit SIPO and SISO shift registers using flip-flops.
11. Design of Seven segment display driver for BCD codes.
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12. BCD
Adders & Subtractors
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Digital Domain
Digital Signal
Electronic System
Digital System
Analog Domain
Analog Signal
Analog System
Analog Signal:
A continuous value is used to denote the information. Analog Signal Defined as any
physical quantity which varies continuously with respect to time.
Digital Signal:
The information is denoted by a finite sequence of discrete value or digits. A digital signal is
defined as any physical quantity having discrete values.
System:
A system
is a combination of devices designed to perform a specific function.
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Analog System:
A analog system is a system that process continuous or analog signals to perform specific
task. In Analog System the quantities can very over a continuous range of values.
Ex.: Amplifier can amplify the value from 0 to Max. limit.
Digital System:
D. S. which process digital signal. It is a combination of devices designed to perform
specific logical information or logical operations or physical quantity that are represented
in digital form.
Ex. Digital Displays, Digital Watch, Smart Mobile Phones.
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Other Definition of Analog and Digital Signal
• Analog system
X(t)
• The physical quantities or signals may
vary continuously over a specified range.
• Digital system
• The physical quantities or signals can
assume only discrete values.
• Greater accuracy
t
X(t)
Analog signal
t
Binary Digital Signal
• An information variable represented by physical quantity.
• For digital systems, the variable takes on discrete values.
• Two level, or binary values are the most prevalent values.
• Binary values are represented abstractly by:
• Digits 0 and 1
• Words (symbols) False (F) and True (T)
• Words (symbols) Low (L) and High (H)
• And words On and Off
• Binary values are represented by values or ranges of
values of physical quantities.
V(t)
Logic 1
undefine
Logic 0
t
Binary digital signal
Merits/Advantages of Digital Systems
1.Digital Systems are generally easier to Design.
2. Digital Information storage is easy.
3. Accuracy and Precision are higher as compared to the analog system.
4. Digital circuits are less affected by the noise.
5. More Circuitry can be fabricated on integrated Circuits (ICs) chips.
6. Display of data and other information is very convenient, accurate
and elegant using digital techniques.
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Limitation of Digital Systems
1. Only Analog Signal is available in the real world..
2. An extra hardware is required to convert analog signal to digital signal.
By Using
❖ Digital to Analog converter (DAC)
❖ Analog to digital converter (ADC)
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Number Systems
Number system is the language of digital system consisting a
set of symbols called digits with rules defined for mathematical
operations
❖ Positional Number System
❖ Non Positional Number System
▪ A number is formed by collection of digits.
▪ It has two components Integer and Fraction
❖ Example:(467.34)10
▪ Both are separated by decimal point
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Classification of Numbers System
❖ Binary number system base 2 (0, 1)
Bit (1), Nibble (4), Byte (8), Word (16), Double Word (32)
❖ Ternary number system base 3 (0, 1, 2)
❖ Quaternary number system base 4 (0, 1, 2, 3)
❖ Quinary number system base 5 (0, 1, 2, 3, 4)
❖ Octal number system base 8 (0, 1, 2, 3, 4, 5, 6, 7)
❖ Decimal number system base 10 (0 to 9)
❖ Duo decimal number system base 12 (0 …9, A, B)
❖ Hexa-decimal number System base 16 (0…9, A, B, C, D, E, F)
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Conversion of Common Number Systems
❖ Binary to other Number Systems
❖ Decimal to other Number Systems
❖ Octal to other Number Systems
❖ Hexadecimal to other Number Systems
❖ Other Number Systems to Binary Number
❖ Other Number Systems to Decimal Number
❖ Other Number Systems to Octal Number
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❖ Other Number Systems to Hexadecimal Number
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Q :Perform the following operations (Binary to Other Number System)
(a) (1011111)= ( )10
(b) (1011111.1101)= ( )10 and (11010.011)= (26.375)2
(c) (101101110) 2 = ( )8
(d) (101101110.100111) 2 = ( )8
(e) (101101110) 2 = ( )16
(f) (111011011.10010111)2 = ( )16
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Q :Perform the following operations (Decimal to Other Number System)
Sum of Weights Method
(a) ( 30)10 = ( 32+16+8+4+2+1)10 =( 0+16+8+4+2+0)10 = (011110)2 =(011110)2
(b) ( 60)10 = ( )2
(c) ( 64)10 = ( )2
Successive Division Method (Integer)/ Successive Division Method (Fractional)
(d) (13)10 = ( 1101)2
(e) (25)10 = ( 11001)2
(f) (25.5)10= ( 11001.1 )2
(g) (10.625)10= ( 11001.1010 )2
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Q :Perform the following operations (Decimal to Other Number System)
Sum of Weights Method
(a) ( 172)10 = ( 254)8
(b) ( 172.878)10 = (254.7014 )8
(c) ( 786)10 = ( 312)16
(d) ( 786.983)10 = ( 312.FBA5)16
(e) ( 82.35)10 = ( 1102)4
(f) ( 82.35)10 = ( 1102.1121)4
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Practice Questions
Q1. Binary number (1011111)2, convert in
(a) Decimal number
(b) Octal number
(c) Hexa-decimal
Q2. Find the decimal, Octal and Hexadecimal of binary number
(I) (001000)2
(II) (1111)2 (III) (101100)2 (IV) (0111)2.
Q 3. Prove that a’b’c’ + a’b’c + a’bc’ + a’bc + ab’c’ = a’ + (b+c).
Q4. Simplify using K-map, F (A, B, C, D) = m (1, 4, 8, 9, 13, 14, 15) + d (2, 3, 11, 12). (a) Sum of
product (SOP), (b) Product of sum (POS).
Q5. Convert the decimal to binary
(I) 1231
(II) 673.23
(III) 104 (IV) 1998.
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Q6. Hexadecimal
Number F3A7C2 to binary, decimal and octal.
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Q :Perform following operations
(a) (36.4)8
=( )10
(b) (101101110) 2 =( )8
(c) (199.3) 10
=( )2
(d) (72.45) 10
=( ) 2
(e) (EEF2.F) 16
=()2
(f) (883.42) 9
= ( )8
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