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Boolean Algebra: Simplification of Expressions and Circuits

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Added on  2021-07-13

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This article explains how to simplify Boolean algebra expressions and circuits using axioms and DeMorgan's law. It covers finding inputs and outputs, truth tables, and standard forms. The article is relevant to CS231 Boolean Algebra and is suitable for students in college or university. Get study material and solved assignments on Desklib.

Boolean Algebra: Simplification of Expressions and Circuits

   Added on 2021-07-13

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Boolean Algebra: Simplification of Expressions and Circuits_1
Circuit analysis summary•After finding the circuit inputs and outputs, you can come up with either an expression or a truth table to describe what the circuit does.•You can easily convert between expressions and truth tables.Find the circuit’sinputs and outputsCS231 Boolean Algebra2Find a Booleanexpressionfor the circuitFind a truth tablefor the circuit
Boolean Algebra: Simplification of Expressions and Circuits_2
Boolean Functions summary•We can interpret high or low voltage as representing true or false.•A variable whose value can be either 1 or 0 is called a Boolean variable.•AND, OR, and NOT are the basic Boolean operations.•We can express Boolean functions with either an expression or a CS231 Boolean Algebra3•truth table.•Every Boolean expression can be converted to a circuit.•Now, we’ll look at how Boolean algebra can help simplify expressions, which in turn will lead to simpler circuits.
Boolean Algebra: Simplification of Expressions and Circuits_3
Boolean Algebra•Last time we talked about Boolean functions, Boolean expressions, and truth tables.•Today we’ll learn how to how use Boolean algebra to simplify Booleans expressions.•Last time, we saw this expression and converted it to a circuit:(x + y’)z + x’Can we make this circuit “better”?Cheaper: fewer gatesJune 11, 2002©2000-2002 Howard Huang4Can we make this circuit “better”?•Cheaper: fewer gates•Faster: fewer delays from inputs to outputs
Boolean Algebra: Simplification of Expressions and Circuits_4

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