This document provides information about a Digital Electronics course with the code ECT-155. It includes the course objectives, which are to understand the merits of digitization and number representation, and impart knowledge of digital circuits. The outcomes are listed as understanding digital systems and number representation, and designing combinational and sequential digital circuits. The syllabus covers topics like combinational circuits, sequential circuits, number systems, logic gates, and adders. Diagrams of half adders and full adders using logic gates are also presented.

1. www. cuchd.in Campus : Gharuan, Mohali
Digital Electronics
SUBJECT CODE : ECT-155
Embedded Systems and Robotics Research Group
Chandigarh University
#617, Block 6

2. Digital Electronics ECT-155
COURSE OBJECTIVES
To understand merits of digitization.
To enable students to understand common forms of number
representation in digital electronic circuits and to be able to convert
between different representation of number systems
To impart knowledge about various digital circuits and designing of
systems.
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3. Digital Electronics ECT-155
COURSE OUTCOMES
 Unit I
 Merits of digital systems, various number systems and their applications
 Unit II
 Combinational and Sequential Digital Designing and solution to basic digital
problems.
 Unit III
 Designing of sequential circuits and introduction to memory logic design
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4. Digital Electronics ECT-155
SYLLABUS
UNIT - II
 Combinational Circuits: Introduction to Combinational circuit design,
half adder, full adder, BCD Adder, Half Subtractor, Full Subtractor,
Multiplexer, Demultiplexer, encoder, decoder and magnitude comparator.
 Sequential Circuits : Introduction to sequential circuits, latch & flip flop
(SR, JK, D and T), race around condition, conversion of various flip flops.
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5. Digital Electronics ECT-155
DIGITAL
• Noise immune
• Flexibility
• No effect of aging on output
• Easy circuit design
• Expensive
• Deals with finite quantized levels of
signals
• Stores waveforms as bits
ANALOG
• Prone to noise
• Fixed task
• Output varies with aging and environment.
• Difficult to design
• Cheaper
• Continuous signals
• Stores signals as waveforms.
ANALOG VS DIGITAL ELECTRONICS
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6. Digital Electronics ECT-155
NUMBER SYSTEM
Decimal10 (0-9)
Binary2 (0,1)
Octal8 (0-7)
Hexadecimals16(??)
Binary coded Decimal
Gray
Excess -3
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Weighted Codes

7. Digital Electronics ECT-155
ALL CONVERSIONS
BINARY
{101101}
OCT
{55}
DEC
{45}
HEX
{2D}
DEC
{45}
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RDB . RMB 𝐝𝐢 𝐛𝐢
Groups of 3
Groups of 4

8. Digital Electronics ECT-155
SIGNED AND UNSIGNED NUMBERS
 SIGNED BINARY REPRESENTATION
{sign} {magnitude}
1’s complement
2’s complement
Signed number = sign bit | number
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9. Digital Electronics ECT-155
SUBTRACTION BY 1’s COMPLEMENT
• Add 1’s complement of Subtrahend
to Minuend
• If No carry produced
• Result is negative
• Result = 1’s complement of addition
• If carry is produced
• drop it
• add 1 to last bit
SUBTRACTION BY 2’s COMPLEMENT
• Add 2’s complement of Subtrahend
to Minuend
• If No carry produced
• Result is negative
• Result = 2’s complement of addition
• If carry is produced
• drop it
SIGNED BINARYARITHMETIC
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10. Digital Electronics ECT-155
BCD & GRAY CODES
DECIMAL BINARY BCD GRAY CODE
0 0000 0000 0000
1 0001 0001 0001
2 0010 0010 0011
3 0011 0011 0010
4 0100 0100 0110
5 0101 0101 0111
6 0110 0110 0101
7 0111 0111 0100
8 1000 1000 1100
9 1001 1001 1101
10 1010 0001 0000 1111
11 1011 0001 0001 1110
12 1100 0001 0010 1010
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11. Digital Electronics ECT-155
LOGIC GATES
A B NOT AND NAND OR NOR XOR XNOR
𝐴 𝐴. 𝐵 𝐴. 𝐵 𝐴 + 𝐵 𝐴 + 𝐵 𝐴 ⊕ 𝐵 𝐴 ⨁ 𝐵
0 0 1 0 1 0 1 0 1
0 1 1 0 1 1 0 1 0
1 0 0 0 1 1 0 1 0
1 1 0 1 0 1 0 0 1
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12. Digital Electronics ECT-155
LAWS OF BOOLEAN ALGEBRA
Commutative Laws
A+B = B+A
AB = BA
Associative Laws
A+(B+C) = (A+B)+C
A(BC) = (AB)C
Distributive Law
A(B+C) = AB + AC
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DeMorgan’s Theorems
 𝐗𝐘 = 𝑿 + 𝒀
 𝐗 + 𝒀 = 𝑿 𝒀
 A+0 = A
 A+1 = 1
 A . 0 = 0
 A . 1 = A
 A + A = A
 A + A = 1
 A . A = A
 A . A = 0
 A + AB = A
 A + AB = A + B
 (A+B)(A+C) = A + BC

13. Digital Electronics ECT-155
SUM OF PRODUCTS {SOP} FORM
 General Expression : A(B + CD)
 SOP Expression : AB + ACD
 Standard/Canonical SOP Expression :
𝑨𝑩𝑪𝑫 + 𝑨 𝑩𝑪𝑫 + 𝑨𝑩 𝑪𝑫
 A standard SOP expression is one in which all the variables in the domain
appear in each product term in the expression.
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14. Digital Electronics ECT-155
PRODUCTS OF SUM {POS} FORM
 General Expression : A(B + CD)
 POS Expression : (A + B)(A + 𝐵 + C)
 Standard POS Expression : ( 𝐴 + 𝐵 + 𝐶 + 𝐷)(𝐴 + 𝐵 + 𝐶 + 𝐷)
 A standard POS expression is one in which all the variables in the domain
appear in each sum term in the expression.
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15. Digital Electronics ECT-155
K-Map Simplification Process

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Logic that depends upon combination !
Combinational Logic

17. Digital Electronics ECT-155
Combinational Logic Circuits
Combinational Logic
 Logic level at the output depends upon the combination of logic levels
present at the inputs.
 No memory characteristic
 Output depends only on the current value of its inputs.
Combinational Logic Circuits
 Circuits that are made up of logic gates, that are connected together to
produce a specified output for certain specified combinations of input
variables.
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18. Digital Electronics ECT-155
Combinational Circuits - Uses
Analysis
 Given a circuit, find out its function
 Function may be expressed as
 Boolean Function
 Truth Table
Design
 Given a desired function, determine its circuit
 Function may be expressed as
 Boolean Function
 Truth Table
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19. Digital Electronics ECT-155
Analysis Procedure
 Boolean Expression Approach
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20. Digital Electronics ECT-155
Analysis Procedure
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21. Digital Electronics ECT-155
Design Procedure
Given a problem statement:
 Determine number of inputs and outputs
 Derive the truth table
 Simplify the Boolean expression for each output
 Produce the required output
Example
 Design a circuit to convert “BCD” code to “Excess-3” code.
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22. Digital Electronics ECT-155
ADDERS
Adders are important in computers and also in other types of
digital systems in which numerical data are processed.
An understanding of the basic adder operation is fundamental to
the study of digital systems.
Two types of adders:
 Half Adder
 Full Adder
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23. Digital Electronics ECT-155
HALF ADDER
 Rules for binary addition are:
 The half-adder accepts two binary digits on its inputs and produces
two binary digits on its outputs—a sum bit and a carry bit.
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24. Digital Electronics ECT-155
HALF ADDER LOGIC
Truth Table
Expressions can be derived from
truth table as
 𝑪 𝒐𝒖𝒕 = 𝑨. 𝑩
 𝚺 = 𝑨. 𝑩 + 𝑨. 𝑩 = 𝑨⨁𝑩
Circuit Diagram
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25. Digital Electronics ECT-15525

26. Digital Electronics ECT-155
 Using basic Gates
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27. Digital Electronics ECT-155
 Using AOI (AND, OR, INVERTER)
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28. Digital Electronics ECT-155
 Universal NAND Gate
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29. Digital Electronics ECT-15529
Universal NOR Gate

30. Digital Electronics ECT-155
 Using NAND Gates
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31. Digital Electronics ECT-15531

32. Digital Electronics ECT-155
 Using NOR Gates
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34. Digital Electronics ECT-155
FULLADDER
 The full-adder accepts two input bits and an input carry and
generates a sum output and an output carry.
 A full-adder has an input carry while the half-adder does not.
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35. Digital Electronics ECT-155
FULLADDER LOGIC
 Truth Table
 Expressions
 𝚺 = 𝑨⨁𝑩 ⨁𝑪𝒊𝒏
 𝑪 𝒐𝒖𝒕 = 𝑨. 𝑩 + 𝑨⨁𝑩 . 𝑪𝒊𝒏
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36. Digital Electronics ECT-155
FULLADDER FROM HALF ADDER
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37. 3737
Embedded Systems and Robotics Research Group,
Chandigarh University
THANK YOU!