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Boolean AlgebraBoolean Algebra

Circuit analysis summary•After finding the circuit inputs and outputs, you can come up witheither 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 Functions summary•We can interpret high or low voltage as representing true orfalse.•A variable whose value can be either 1 or 0 is called a Booleanvariable.•AND, OR, and NOT are the basic Boolean operations.•We can express Boolean functions with either an expression or aCS231 Boolean Algebra3•truth table.•Every Boolean expression can be converted to a circuit.•Now, we’ll look at how Boolean algebra can help simplifyexpressions, which in turn will lead to simpler circuits.

Boolean Algebra•Last time we talked about Boolean functions, Boolean expressions, andtruth tables.•Today we’ll learn how to how use Boolean algebra to simplify Booleansexpressions.•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 tooutputs

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