L2_BooleanAlgebra

# L2_BooleanAlgebra - Boolean Algebra ECE 152A Fall 2006...

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1 Boolean Algebra ECE 152A – Fall 2006 October 3, 2006 ECE 152A - Digital Design Principles 2 Reading Assignment ± Brown and Vranesic ² 2 Introduction to Logic Circuits ± 2.5 Boolean Algebra ² 2.5.1 The Venn Diagram ² 2.5.2 Notation and Terminology ² 2.5.3 Precedence of Operations ± 2.6 Synthesis Using AND, OR and NOT Gates ² 2.6.1 Sum-of-Products and Product of Sums Forms

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2 October 3, 2006 ECE 152A - Digital Design Principles 3 Reading Assignment ± Brown and Vranesic (cont) ² 2 Introduction to Logic Circuits (cont) ± 2.7 NAND and NOR Logic Networks ± 2.8 Design Examples ² 2.8.1 Three-Way Light Control ² 2.8.2 Multiplexer Circuit October 3, 2006 ECE 152A - Digital Design Principles 4 Reading Assignment ± Roth ² 2 Boolean Algebra ± 2.3 Boolean Expressions and Truth Tables ± 2.4 Basic Theorems ± 2.5 Commutative, Associative, and Distributive Laws ± 2.6 Simplification Theorems ± 2.7 Multiplying Out and Factoring ± 2.8 DeMorgan’s Laws
3 October 3, 2006 ECE 152A - Digital Design Principles 5 Reading Assignment ± Roth (cont) ² 3 Boolean Algebra (Continued) ± 3.1Multiplying Out and Factoring Expressions ± 3.2 Exclusive-OR and Equivalence Operation ± 3.3 The Consensus Theorem ± 3.4 Algebraic Simplification of Switching Expressions October 3, 2006 ECE 152A - Digital Design Principles 6 Reading Assignment ± Roth (cont) ² 4 Applications of Boolean Algebra Minterm and Maxterm Expressions ± 4.3 Minterm and Maxterm Expansions ² 7 Multi-Level Gate Circuits NAND and NOR Gates ± 7.2 NAND and NOR Gates ± 7.3 Design of Two-Level Circuits Using NAND and NOR Gates ± 7.5 Circuit Conversion Using Alternative Gate Symbols

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4 October 3, 2006 ECE 152A - Digital Design Principles 7 Boolean Algebra ± Axioms of Boolean Algebra ² 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 October 3, 2006 ECE 152A - Digital Design Principles 8 Boolean Algebra ± 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 postulates and definitions of switching algebra with respect to the two operations and the two constants.
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L2_BooleanAlgebra - Boolean Algebra ECE 152A Fall 2006...

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