chapter 2 ee202 boolean part a

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 Departmentsabariah@psa.edu.my

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 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

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 GateGateGateGateSymbolSymbolSymbolSymbol

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 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 ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRABOOLEAN ALGEBRA

• ExamplesExamplesExamplesExamples F = A + BC

Truth TableTruth TableTruth TableTruth Table

Logic circuitLogic circuitLogic circuitLogic circuit

Boolean Algebra ExerciseExercise: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

DEMORGAN’S 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

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