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L2 - Boolean Algebra

L2 - Boolean Algebra - Boolean Algebra ECE 152A Summer 2009...

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1 Boolean Algebra ECE 152A – Summer 2009 June 24, 2009 ECE 152A - Digital Design Principles 2 Reading Assignment square6 Brown and Vranesic boxshadowdwn 2 Introduction to Logic Circuits square6 2.5 Boolean Algebra boxshadowdwn 2.5.1 The Venn Diagram boxshadowdwn 2.5.2 Notation and Terminology boxshadowdwn 2.5.3 Precedence of Operations square6 2.6 Synthesis Using AND, OR and NOT Gates boxshadowdwn 2.6.1 Sum-of-Products and Product of Sums Forms
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2 June 24, 2009 ECE 152A - Digital Design Principles 3 Reading Assignment square6 Brown and Vranesic (cont) boxshadowdwn 2 Introduction to Logic Circuits (cont) square6 2.7 NAND and NOR Logic Networks square6 2.8 Design Examples boxshadowdwn 2.8.1 Three-Way Light Control boxshadowdwn 2.8.2 Multiplexer Circuit June 24, 2009 ECE 152A - Digital Design Principles 4 Reading Assignment square6 Roth boxshadowdwn 2 Boolean Algebra square6 2.3 Boolean Expressions and Truth Tables square6 2.4 Basic Theorems square6 2.5 Commutative, Associative, and Distributive Laws square6 2.6 Simplification Theorems square6 2.7 Multiplying Out and Factoring square6 2.8 DeMorgan’s Laws
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3 June 24, 2009 ECE 152A - Digital Design Principles 5 Reading Assignment square6 Roth (cont) boxshadowdwn 3 Boolean Algebra (Continued) square6 3.1Multiplying Out and Factoring Expressions square6 3.2 Exclusive-OR and Equivalence Operation square6 3.3 The Consensus Theorem square6 3.4 Algebraic Simplification of Switching Expressions June 24, 2009 ECE 152A - Digital Design Principles 6 Reading Assignment square6 Roth (cont) boxshadowdwn 4 Applications of Boolean Algebra Minterm and Maxterm Expressions square6 4.3 Minterm and Maxterm Expansions boxshadowdwn 7 Multi-Level Gate Circuits NAND and NOR Gates square6 7.2 NAND and NOR Gates square6 7.3 Design of Two-Level Circuits Using NAND and NOR Gates square6 7.5 Circuit Conversion Using Alternative Gate Symbols
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4 June 24, 2009 ECE 152A - Digital Design Principles 7 Boolean Algebra square6 Axioms of Boolean Algebra boxshadowdwn Axioms generally presented without proof 0 · 0 = 0 1 + 1 = 1 1 · 1 = 1 0 + 0 = 0 0 · 1 = 1 · 0 = 0 1 + 0 = 0 + 1 = 1 if X = 0, then X’ = 1 if X = 1, then X’ = 0 June 24, 2009 ECE 152A - Digital Design Principles 8 Boolean Algebra square6 The Principle of Duality from Zvi Kohavi, Switching and Finite Automata Theory “We observe that all the preceding properties are grouped in pairs. Within each pair one statement can be obtained from the other by interchanging the OR and AND operations and replacing the constants 0 and 1 by 1 and 0 respectively. Any two statements or theorems which have this property are called dual , and this quality of duality which characterizes switching algebra is known as the principle of duality . It stems from the symmetry of the
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