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IT2001PAEngineering Essentials (2/2)Chapter 7 - Boolean Algebra Lecturer Namelecturer_email@ite.edu.sg Nov 20, 2012Contact Number
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Chapter 7 - Boolean AlgebraLesson ObjectivesUpon completion of this topic, you should be able to: State the rules and functions of Boolean algebra. IT2001PA Engineering Essentials (2/2) 2
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Chapter 7 - Boolean AlgebraSpecific Objectives Students should be able to : State the function of Boolean algebra. State the 9 equalities of Boolean algebra. State the Commutative Law. State the Associative Law. State the Distributive Law. IT2001PA Engineering Essentials (2/2)
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Chapter 7 - Boolean AlgebraIntroduction Boolean Algebra is a set of algebraic rules, named after mathematician George Boole, in which TRUE and FALSE are equated to ‘0’ and ‘1’. Boolean algebra includes a series of operators (AND, OR, NOT, NAND (NOT AND), NOR, and XOR (exclusive OR)), which can be used to manipulate TRUE and FALSE values. It is the basis of computer logic because the truth values can be directly associated with bits. IT2001PA Engineering Essentials (2/2) 4
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Chapter 7 - Boolean AlgebraBoolean Algebra Laws Frequently, a Boolean expression is not in its simplest form. Boolean expressions can be simplified, but we need identities or laws that apply to Boolean algebra instead of regular algebra. These identities can be applied to single Boolean variables as well as Boolean expressions. IT2001PA Engineering Essentials (2/2) 5
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Chapter 7 - Boolean AlgebraCommutative Law The commutative law allows the change in position (reordering) of an ANDed or ORed variable. IT2001PA Engineering Essentials (2/2) 7
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Chapter 7 - Boolean AlgebraAssociative Law The Associative Law allows the regrouping of variables. IT2001PA Engineering Essentials (2/2) 8
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Chapter 7 - Boolean AlgebraDistributive Law The Distributive Law shows how OR distributes over AND and vice versa. IT2001PA Engineering Essentials (2/2) 9
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Chapter 7 - Boolean AlgebraBoolean Algebra Theorems Boolean theorems can help to simplify logic expression and logic circuits. IT2001PA Engineering Essentials (2/2) 10
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Chapter 7 - Boolean AlgebraBoolean Algebra Equalities or Identities (a) A . 0 =0 (j) A + AB = A + B (b) A . 1 =A A + AB = A + B (c) A . A =A (d) A . A =0 The variable A may represent (e) A + 0 = A an expression containing more (f) A + 1 = 1 than one variable. For instance, XY(XY) (g) A + A = A (h) A + A = 1 Let A = XY, (i) A =A then XY(XY) = A . A = 0 IT2001PA Engineering Essentials (2/2) 11
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Chapter 7 - Boolean AlgebraBoolean Algebra Equalities or Identities A*0 = 0 A*1 = A A A X = A*0 = 0 X = A*1 = A 0 1 Anything ANDed with a 0 is Anything ANDed with a 1 is • equal to 0. • equal to itself. A*A = A A*A = 0 A A A X = A*A = A 1 X = A*A = 0 Anything ANDed with itself is Anything ANDed with its own • equal to itself. • complement equals 0. IT2001PA Engineering Essentials (2/2) 12
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Chapter 7 - Boolean AlgebraBoolean Algebra Equalities or Identities A+0 = A A+1 = 1 A A X = A+0 = A X = A+1 = 1 0 1 Anything ORed with a 0 is Anything ORed with a 1 is • equal to itself. • equal to 1. A+A = A A+A = 0 A A A X = A+A = A 1 X = A+A = 1 Anything ORed with itself is Anything ORed with its own • equal to itself. • complement equals 1. IT2001PA Engineering Essentials (2/2) 13
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Chapter 7 - Boolean AlgebraBoolean Algebra Equalities or Identities A=A A A X=A=A A variable that is complemented twice will • return to its original IT2001PA Engineering Essentials (2/2) 14
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Chapter 7 - Boolean AlgebraElimination Law Equivalence is demonstrated by showing the truth table derived from the expression on the left side of the equation matches that on the right side. IT2001PA Engineering Essentials (2/2) 15
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