Reduce the boolean expression as much as possible

  • Thread starter dba
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In summary, the given expression can be simplified using the rules of Boolean algebra, specifically the relation a+a'b = a+b. After applying this rule, the expression can be reduced to xw + wy'z + xy'z + wxy, with some terms being eliminated.
  • #1
dba
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Homework Statement


Reduce,
x(w+y'+z') + (w+x)y'z + wx'yz + wxy


Homework Equations



+ stands for OR
* (multiplication) stands for AND
' NOT

The Attempt at a Solution


I tried to combine some terms but I cannot find a good start...
x(w+y'+z') + (w+x)y'z + wx'yz + wxy
= xw + xy'+ xz' + wy'z + xy'z + wx'yz + wxy

I do not see what I can do. Any hint would be great. I thought maybe multiplication with one or addition of zero would help but nothing seems to work.
Some rules are x+x=1 x+1=1 x+x'=1 x*x'=0

Thanks for any help.
 
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  • #2
Show us what you have so far. I can see a couple of terms you can get rid of using the rules you've already listed.

You may find the relation a+a'b = a+b useful.
 

1. What is a boolean expression?

A boolean expression is an algebraic expression that evaluates to either true or false. It is typically made up of variables, logical operators (such as AND, OR, and NOT), and parentheses.

2. Why is it important to reduce a boolean expression?

Reducing a boolean expression means simplifying it to its most basic form. This can make the expression easier to understand and work with, as well as potentially reducing the number of operations needed to evaluate it.

3. How do you reduce a boolean expression?

To reduce a boolean expression, you can use boolean algebra rules and laws to simplify the expression. This involves combining like terms, using distributive and associative properties, and applying De Morgan's laws.

4. Can reducing a boolean expression change its truth value?

No, reducing a boolean expression will not change its truth value. The simplified expression will have the same truth value as the original expression for any given set of variable values.

5. When should I reduce a boolean expression?

It is a good idea to reduce a boolean expression whenever it is possible and makes the expression easier to understand or evaluate. This is especially important when working with complex expressions or when trying to optimize a logical system.

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