E-LESSON-5-6

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B.C.A 2 All right are reserved with CU-IDOL Digital Circuits and Logic Designs Course Code: BCA111 Semester: First SLM Units: e-Lesson No: 5-6 3 www.cuidol.in Unit-5, 6 (BCA111)

Boolean Algebra OBJECTIVES INTRODUCTION 33 Student will be able to Explain various Boolean INTRODUCTION operations In this session we are going to learn about Student will be able to Explain laws of Boolean •Various Boolean operations operations •Laws of Boolean operations •Simplification concepts of Boolean Student will be able to Explain simplification expression concepts of Boolean expression •Various Boolean techniques Student will be able to Describe various Boolean techniques www.cuidol.in Unit-5, 6 (BCA111) INASllTIrTigUhTtEaOreF DreISsTeArvNeCdE wAiNthDCOUN-LIDINOELLEARNING

TOPICS TO BE COVERED 4 1. Boolean operations, 2. logic expressions, 3. rules and laws of Boolean algebra 4. De Morgan’s theorems, 5. simplification of Boolean expressions using Boolean algebra techniques www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean laws 5 www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean Algebra 6 AND Function OR Function NOT function 00=0 0+0=0 0’=1 01=0 0+1=1 1’=0 10=0 1+0=1 A’’=A 11=1 1+1=1 A0=0 A+0=A 0A=0 0+A=A A1=A A+1=1 1A=A 1+A=1 AA=A A+A=A www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean Algebra 7 • Sometimes it is more easy to built a circuit using the complement of a function (and complementing its result) than it is to implement the function directly. • De Morgan’s law provides an simple way of finding the complement of a Boolean function. • Recall De Morgan’s law states: • www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean Algebra 8 • De Morgan’s law can be comprehensive to any number of variables. • Replace every variable by its complement and change all ANDs to ORs and all ORs to ANDs. • Thus, we find the complement of www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean Algebra 9  There are two canonical forms of Boolean expressions: sum-of-products (SOP) and product-of-sums (POS). Recall the Boolean product is AND operation and the Boolean sum is OR operation.  In the sum-of-products form, ANDed variables are ORed together. • For example: www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Boolean Algebra 10 • In the product-of-sums form, ORed variables are ANDed together: • For example www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

De Morgan’s law 11 www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

Multiple Choice Questions 12 1. The expression for Absorption law is given by _________ . (a) A + AB = A (b) A + AB = B (c) AB + AA’ = A (d) A + B = B + A 2. (A + B)(A’ * B’) = (a) 1 (b) 0 (c) AB (d) AB’ 3. The Boolean function A + BC is a reduced form of ____________ . (a) AB + BC (b) A’B + AB’C (c) (A + B)(A + C) (d) (A + C)B Answers: 1.(a) 2.(b) 3.(c) Unit-5, 6 (BCA111) All right are reserved with CU-IDOL www.cuidol.in

Multiple Choice Questions 13 4. In Boolean algebra, the OR operation is performed by which properties? (a) Associative properties (b) Commutative properties (c) Distributive properties (d) All of the mentioned 5. Simplify Y = AB’ + (A’ + B)C. (a) AB’ + C (b) AB + AC (c) A’B + AC’ (d) AB Answers: 4.(d) 5.(a) Unit-5, 6 (BCA111) All right are reserved with CU-IDOL www.cuidol.in

SUMMARY 14 Let us recapitulate the important concepts discussed in this session: •In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. •It is thus a formalism for describing logical operations in the same way that elementary algebra describes numerical operations. •The table used to represent the Boolean expression of a logic gate function called a truth table. •A logic gate is an electronic circuit that operates on one or more input signals to produce an output signal. •The switch contains two states which are ON or OFF. •The ON means the logic 1 and the OFF means the logic 0. www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTION Q1. Explain various Boolean operations. 15 Ans: (a) AND Laws , (b) OR Laws , (c) Commutative Laws , (d) Associative Laws , (e) Extra Laws For further details refer SLM unit 5. Q2. Explain laws of OR Gate. Ans: It is also known as “Inclusive - OR” gate. Consider A and B are inputs and Y is output. This gate is called any or all gate. Logic - If A is true or B is true then Y is true. It means that either A should be high or B should be high or the output is high. Boolean Equation Y = A + B. For further details refer SLM unit 5. Q3. what is Distributive law? Ans: The distributive laws states that factoring or multiplication of different term in an expression is allowed. They are expressed as follows: (a) A.(B+C) = AB + AC (b) A+(B.C) = (A+B)(A+C) For further details refer SLM unit 6. www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

REFERENCES 16 1. www.tutorialspoint.com 2. Self Learning Material, Institute of Distance and Online Learning, Chandigarh University 3. docplayer.net 4. www.csie.nuk.edu.tw 5. www.thevbprogrammer.com 6. probabilitylectures.narod.ru 7. ergopalkrishnawithc.blogspot.in 8. www.ensolt.com 9. www.encoder.com 10. Lala. \"Number Systems and Binary Codes\", Principles of Modern Digital Design, 11. www.slideshare.net 12. www.freepatentsonline.com www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL

17 THANK YOU www.cuidol.in Unit-5, 6 (BCA111) All right are reserved with CU-IDOL