This document discusses Chapter 2 of a Digital Electronics course, which covers Boolean operations. It begins by listing the programme and course learning outcomes. The chapter objectives are then stated, which are to understand logic gate symbols, operations, functions and truth tables, and apply Boolean algebra concepts to logic circuit analysis and design. The document proceeds to define logic gates such as AND, OR, NAND and NOR gates using symbols, truth tables and timing diagrams. It introduces Boolean algebra and shows an example of a Boolean expression and corresponding truth table and circuit. Exercises on constructing truth tables and simplifying Boolean expressions using identities and laws are also presented.

1. DEE2034 : DIGITAL ELECTRONICS
CHAPTER 2 : BOOLEAN
OPERATIONS by : Siti Sabariah Salihin
Electrical Engineering Department
sabariah@psa.edu.my

2. Programme Learning Outcomes, PLO
Upon completion of the programme, graduates should be able to:
• PLO 1 : Apply knowledge of mathematics, scince and engineering
fundamentals to well defined electrical and electronic engineering
procedures and practices
Course Learning Outcomes, CLO
• CLO 1 : Illustrate the knowledge of digital number systems,codes
and ligic operations correctly
• CLO 2 : Simplify and design combinational and sequential logic
circuits by using the Boolean Algebra and the Karnaugh Maps.
CHAPTER 2 : BOOLEAN OPERATIONS
EE 202 : DIGITAL ELECTRONICS
DEE2034 : DIGITAL ELECTRONICS

3. Upon completion of this Topic 2
student should be able to:
2.1 Know the symbols,operations and functions of logic gates.
2.1.1 Draw the symbols, operations and
functions of logic gates.
2.1.2 Explain the Function of Logic gates using Truth
Table.
2.1.3 Construct AND, OR and NOT gates using only
NAND gates.
2.2 Know the basic concepts of Boolean Algebra and use them in
Logic circuits analysis and design.
2.2.1 Construct the basic concepts of Boolean Algebra
and use them in logic circuits analysis and design.
2.2.2 State the Boolean Laws.
2.2.3 Develop logic expressions from the truth table from
the form of SOP and POS
2.2.4 Simplify combinatinal Logic circuits using Boolean
Laws and Karnaugh Map
DEE2034 : DIGITAL ELECTRONICS

4. TRUTH TABLES
A truth table is a table that describes
the behavior of a logic gate
The number of input combinations will
equal 2N for an N-input truth table
4DEE2034 : DIGITAL ELECTRONICS

5. • Circuits which perform logic
functions are called gates
• The basic gates are:
I. NOT/INVERTER gate
II. AND gate
III. OR gate
IV. NAND gate
V. NOR gate
VI. XOR gate
VII.XNOR gate
LOGIC GATES
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6. I. NOT / INVERTER
Gate
Symbol
Truth Table
Timing Diagram
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7. II. AND Gate
Symbol
Truth Table
Timing Diagram
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8. III. OR gateSymbol
Truth Table
Timing Diagram
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9. IV. NAND GateSymbol
Truth Table
Timing Diagram
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10. V. NOR GateSymbol
Truth Table
Timing Diagram
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11. VI. XOR GateSymbol
Truth Table
Timing Diagram

12. VII. XNOR GateSymbol
Truth Table
Timing Diagram
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13. DEA 2033 : DIGITAL PRINCIPLESDEE2034 : DIGITAL ELECTRONICS

14. BOOLEAN ALGEBRA
• The Boolean algebra is an algebra dealing
with binary variables and logic operation
• The variables are designated by:
I. Letters of the alphabet
II. Three basic logic operations AND,
OR and NOT
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15. • A Boolean function can be represented by using
truth table. A truth table for a function is a list of
all combinations of 1’s and 0’s that can be
assigned to the binary variable and a list that
shows the value of the function for each binary
combination
• A Boolean expression also can be transformed
into a circuit diagram composed of logic gates
that implements the function
BOOLEAN ALGEBRA
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16. • Examples
F = A + BC
Truth Table
Logic circuit
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17. Boolean Algebra Exercise
Exercise:
• Construct a Truth Table
for the logical functions at
points C, D and Q in the
following circuit and
identify a single logic gate
that can be used to
replace the whole circuit.
DEA 2033 : DIGITAL PRINCIPLESDEE2034 : DIGITAL ELECTRONICS

18. Solution
INPUTS OUTPUT AT
A B C D Q
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19. Answer:
INPUTS OUTPUT AT
A B C D Q
0 0 1 0 0
0 1 1 1 1
1 0 1 1 1
1 1 0 0 1
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20. Exercise
• Find the Boolean
algebra expression
for the following
system.
Solution:
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21. BASIC IDENTITIES AND BOOLEAN
LAWS`
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22. COMMUTATIVE LAWS
ASSOCIATIVE LAWS
BOOLEAN LAWS
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23. DISTRIBUTIVE LAWS
DEMORGAN’S THEOREMS
BOOLEAN LAWS
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24. • All these Boolean basic identities and Boolean Laws
can be useful in simplifying a logic expression, in
reducing the number of terms in the expression
• The reduced expression will produce a circuit that is
less complex than the one that original expression
would have produced.
• Examples
Simplify this function
F = A B C + A B C + A C
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25. Solution
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26. Exercise:
Using the Boolean laws, simplify the following expression:
Q= (A + B)(A + C)
Solution:
Q = (A + B)(A + C)
Q = AA + AC + AB + BC ( Distributive law )
Q = A + AC + AB + BC ( Identity AND law (A.A = A) )
Q = A(1 + C) + AB + BC ( Distributive law
Q = A.1 + AB + BC ( Identity OR law (1 + C = 1)
Q = A(1 + B) + BC ( Distributive law )
Q = A.1 + BC ( Identity OR law (1 + B = 1) )
Q = A + BC ( Identity AND law (A.1 = A) )
Then the expression: Q= (A + B)(A + C)
can be simplified to Q= A + BC
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27. continue chapter 2 Part B
1. "Digital Systems Principles And Application"
Sixth Editon, Ronald J. Tocci.
2. "Digital Systems Fundamentals"
P.W Chandana Prasad, Lau Siong Hoe,
Dr. Ashutosh Kumar Singh, Muhammad Suryanata.
REFERENCES:
Download Tutorials Chapter 2: Boolean Operations
@ http://www.portal.cidos.edu.my
DEE2034 : DIGITAL ELECTRONICS