Boolean Algebra Simplification Property Question

In summary, The conversation discusses simplifying a Boolean expression and determining which property is used to simplify it. It is determined that the distributive property of OR over AND, combined with the complementation principle, is used. The question is also asked if two equivalent Boolean expressions can always be reduced to being identical, to which the answer is yes.
  • #1
Bigworldjust
54
0
Hi I am not sure where to post this question but I am trying to simplify this expression:

r*c'w+c (As in R AND NOT C AND W OR C) to c+wr (As in C OR W AND R) and I know that it simplifies to this and they are both equivalent; however my question is which boolean simplification property is used here? Is it the Absorption principle? Thank you!
 
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  • #2
No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?
 
  • #3
MisterX said:
No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?

No it's a worked example left for us to solve if we wanted extra practice. And that's what I thought initially. So it is using the distributive property and then the complement theory. Thank you.
 
  • #4
Also one last question. When expressions are functionally equivalent like the two above, can they always be reduced to being identical? I am assuming yes, because they are equal to begin with, correct?
 
  • #5
Two Boolean expressions that have the same variables are equal if and only if they have identical truth tables.
 

1. What is the commutative property in Boolean algebra simplification?

The commutative property in Boolean algebra simplification states that the order of operations does not affect the final result. In other words, the order in which the variables are multiplied or added does not change the outcome as long as they are grouped together correctly.

2. What is the associative property in Boolean algebra simplification?

The associative property in Boolean algebra simplification states that the grouping of variables in an operation does not affect the final result. This means that parentheses can be moved as long as the variables remain grouped together in the same way.

3. What is the distributive property in Boolean algebra simplification?

The distributive property in Boolean algebra simplification states that a common variable in an operation can be factored out and distributed to the remaining variables. This can help simplify complex expressions by breaking them down into smaller, more manageable parts.

4. What is the identity property in Boolean algebra simplification?

The identity property in Boolean algebra simplification states that the presence of certain values or operations does not change the final outcome. For example, the identity value for addition is 0 and the identity value for multiplication is 1. Any expression multiplied by 1 or added to 0 will result in the same value.

5. How can Boolean algebra simplification be used in logic circuits?

Boolean algebra simplification is an essential tool in designing and analyzing logic circuits. By simplifying complex Boolean expressions, circuits can be made more efficient and easier to understand. It can also help identify potential errors or redundancies in the circuit design.

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