EE 202 : DIGITAL ELECTRONICSEE 202 : DIGITAL ELECTRONICSEE 202 : DIGITAL ELECTRONICSEE 202 : DIGITAL ELECTRONICS
CHAPTER 2 : BOOLEAN BOOLEAN BOOLEAN BOOLEAN OPERATIONSOPERATIONSOPERATIONSOPERATIONS by : Siti Sabariah Salihin
Electrical Engineering [email protected]
Programme Learning Outcomes, PLOProgramme Learning Outcomes, PLOProgramme Learning Outcomes, PLOProgramme Learning Outcomes, PLOUpon completion of the programme, graduates should be able to:
PLO 1PLO 1PLO 1PLO 1 : Apply knowledge of mathematics, scince and engineering fundamentals to well defined electrical and electronic engineering procedures and practices
Course Learning Outcomes, CLOCourse Learning Outcomes, CLOCourse Learning Outcomes, CLOCourse Learning Outcomes, CLO CLO 1CLO 1CLO 1CLO 1 : Illustrate the knowledge of digital number systems,codes
and ligic operations correctly CLO 2 CLO 2 CLO 2 CLO 2 : Simplify and design combinational and sequential logic
circuits by using the Boolean Algebra and the Karnaugh Maps.
CHAPTER 2 : BOOLEAN OPERATIONSBOOLEAN OPERATIONSBOOLEAN OPERATIONSBOOLEAN OPERATIONS
EE 202 : DIGITAL ELECTRONICS
EE 202 : DIGITAL ELECTRONICS
Upon completion of this Topic 2student 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 POS2.2.4 Simplify combinatinal Logic circuits using Boolean Laws and Karnaugh Map
EE 202 : DIGITAL ELECTRONICS
TRUTH TABLESTRUTH TABLESTRUTH TABLESTRUTH TABLESA truth table is a table that describes
the behavior of a logic gateThe number of input combinations will
equal 2N for an N-input truth table
4444EE 202 : DIGITAL ELECTRONICS
Circuits which perform logic functions are called gates
The basic gates are:I. NOT/INVERTER gateII. AND gateIII. OR gateIV. NAND gateV. NOR gateVI. XOR gateVII.XNOR gate
EE 202 : DIGITAL ELECTRONICS
LOGIC GATESLOGIC GATESLOGIC GATESLOGIC GATES
I.I.I.I. NOTNOTNOTNOT //// INVERTER INVERTER INVERTER INVERTER GateGateGateGate
SymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
II.II.II.II. AND AND AND AND GGGGateateateateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
III.III.III.III. OR gateOR gateOR gateOR gateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
IV. NAND IV. NAND IV. NAND IV. NAND GGGGateateateateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
V. V. V. V. NOR NOR NOR NOR GGGGateateateateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
VI.VI.VI.VI. XOR XOR XOR XOR GGGGateateateateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
VII.VII.VII.VII. XNOR XNOR XNOR XNOR GGGGateateateateSymbolSymbolSymbolSymbol
Truth TableTruth TableTruth TableTruth Table
Timing DiagramTiming DiagramTiming DiagramTiming Diagram
BOOLEAN ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRA
The Boolean algebra is an algebra dealing with binary variables and logic operation
The variables are designated by:
I. Letters of the alphabetII. Three basic logic operations AND,
OR and NOT
A Boolean function can be represented by using truth table. A truth table for a function is a list of all combinations of 1s and 0s 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 ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRA
ExamplesExamplesExamplesExamples F = A + BC
Truth TableTruth TableTruth TableTruth Table
Logic circuitLogic circuitLogic circuitLogic circuit
Boolean Algebra Exercise
Exercise:Exercise: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.
Solution
INPUTSINPUTSINPUTSINPUTS OUTPUT ATOUTPUT ATOUTPUT ATOUTPUT AT
AAAA BBBB CCCC DDDD QQQQ
Answer:
INPUTSINPUTSINPUTSINPUTS OUTPUT ATOUTPUT ATOUTPUT ATOUTPUT AT
AAAA BBBB CCCC DDDD QQQQ
0000 0000 1111 0000 0000
0000 1111 1111 1111 1111
1111 0000 1111 1111 1111
1111 1111 0000 0000 1111
Exercise
Find the Boolean algebra expression for the following system.
Solution:
BASIC IDENTITIES AND BOOLEAN BASIC IDENTITIES AND BOOLEAN BASIC IDENTITIES AND BOOLEAN BASIC IDENTITIES AND BOOLEAN LAWSLAWSLAWSLAWS
COMMUTATIVE LAWS
ASSOCIATIVE LAWS
BOOLEAN LAWSBOOLEAN LAWSBOOLEAN LAWSBOOLEAN LAWS
DISTRIBUTIVE LAWS
DEMORGANS THEOREMS
BOOLEAN LAWSBOOLEAN LAWSBOOLEAN LAWSBOOLEAN LAWS
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
Solution
CHAPTER 2 : EE202 DIGITAL ELECTRONICS
Exercise:Exercise:Exercise:Exercise:Using the Boolean laws, simplify the following expression: Q=Q=Q=Q= (A + B)(A + C) (A + B)(A + C) (A + B)(A + C) (A + B)(A + C)Solution: Solution: Solution: 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 Q Q Q = A + BC= A + BC= A + BC= A + BC ( Identity AND law (A.1 = A) )
Then the expression: Then the expression: Then the expression: Then the expression: Q= Q= Q= Q= (A + B)(A + C) (A + B)(A + C) (A + B)(A + C) (A + B)(A + C) can be simplified to can be simplified to can be simplified to can be simplified to Q= Q= Q= Q= A + BCA + BCA + BCA + BC
CHAPTER 2 : EE202 DIGITAL ELECTRONICS
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: REFERENCES: REFERENCES: REFERENCES:
Download Tutorials Chapter 2: Boolean Operations Download Tutorials Chapter 2: Boolean Operations Download Tutorials Chapter 2: Boolean Operations Download Tutorials Chapter 2: Boolean Operations @ CIDOS@ CIDOS@ CIDOS@ CIDOS
http://www.cidos.edu.myhttp://www.cidos.edu.myhttp://www.cidos.edu.myhttp://www.cidos.edu.my
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