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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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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.
June 11, 2002
©20002002 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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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
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.
 Spring '08
 

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