# Algebra Definition

May 29th, 2015
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Part One: Core Knowledge -algebra noun 1. the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations

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LOGIC SIMPLIFICATION USING BOOLEAN ALGEBRAThe most obvious way to simplify Boolean expressions is to manipulate them in the same way as normal algebraic expressions are manipulated.With regards to logic relation in digital forms, a set of rules for symbolic manipulation is needed in order to solve for the unknowns.LAWS AND RULES OF BOOLEAN ALGEBRA1. Commutative LawsThe commutative law of addition for two variables is algebraically expressed asThe commutative law of multiplication for two variables is expressed as2. Associative LawsThe associative law of addition of addition of three variables is expressed asThe associative law of multiplication of three variables is expressed as3. Distributive LawsThe distribution law of three variables is expressed as follow:RULES OF BOOLEAN ALGEBRA:Rule NumberBoolean Expression123456 789101112DE MORGANS THEOREM:1. A2. EXAMPLE 1:Question:Simplify this circuit using Boolean Algebra to reduce the expression to its simplest form (Simplest defined as requiring the fewest gates to implement).Solution:EXAMPLE 2:Question:Simplify this circuit using Boolean Algebra to reduce

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