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

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CS231 Boolean Algebra 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’s inputs and outputs Find a Boolean expression for the circuit Find a truth table for the circuit
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CS231 Boolean Algebra 2 Boolean operations 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 truth table. Every Boolean expression can be converted 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 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 gates Faster: fewer delays from inputs to outputs
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CS231 Boolean Algebra 4 Expression simplification Normal mathematical expressions can be simplified using the laws of algebra For binary systems, we can use Boolean algebra , which is superficially similar to regular algebra There are many differences, due to having only two values (0 and 1) to work with having a complement operation the OR operation is not the same as addition
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CS231 Boolean Algebra 5 Formal definition of Boolean algebra A Boolean algebra requires A set of elements B , which needs at least two elements (0 and 1)
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This note was uploaded on 04/15/2008 for the course CS 231 taught by Professor - during the Spring '08 term at University of Illinois at Urbana–Champaign.

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

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