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03-BooleanAlgebra - Circuit analysis summary After finding...

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CS231 Boolean Algebra 1 Circuit analysis summary After finding thecircuit inputs and outputs, you can comeup with either an expression or a truth tableto describewhat thecircuit does. You can easily convert between expressions and truth tables. Find thecircuit’s inputs and outputs Find a Boolean expression for thecircuit Find a truth table for thecircuit
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CS231 Boolean Algebra 2 Boolean operations summary Wecan interpret high or low voltageas representing trueor false. A variablewhosevaluecan beeither 1 or 0 is called a Boolean variable. AND, OR, and NOT arethebasic Boolean operations. Wecan express Boolean functions with either an expression or a truth table. Every Boolean expression can beconverted to a circuit. Nex, we’ll look at how Boolean algebra can help simplify expressions, which in turn will lead to simpler circuits.
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June 11, 2002 ©2000-2002 Howard Huang 3 Boolean algebra Last timewetalked about Boolean functions, Boolean expressions, and truth tables. Today we’ll learn how to how useBoolean algebra to simplify Booleans expressions. Last time, wesaw this expression and converted it to a circuit: (x + y’)z + x’ Can wemakethis circuit “better”? Cheaper: fewer gates Faster: fewer delays frominputs to outputs
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CS231 Boolean Algebra 4 Expression simplification Normal mathematical expressions can besimplified using thelaws of algebra For binary systems, wecan use Boolean algebra , which is superficially similar to regular algebra Therearemany differences, dueto having only two values (0 and 1) to work with having a complement operation theOR operation is not thesameas addition
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CS231 Boolean Algebra 5 Formal definition of Boolean algebra A Boolean algebra requires
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