Reduction of Boolean Expression to its Lowest From

In summary, when reducing a Boolean Expression, it is helpful to look for similarities in terms and to use laws and rules to simplify the expression. It is important to stop at a point where no more laws or rules can be applied. Additionally, the use of XNOR gates can help simplify the expression further.
  • #1
George SA
3
0
Hey Guys

I am Currently doing my degree in information systems. At the moment the subject is PLC(Processing and Logic Concepts)

I understand all of it, I am not sertain on how to start reducing a boolean expression. Once the first step is done I normally get it and can complete the process of reduction using the Laws.

Does anyone know if i hint or a trick on where to start reducing a Boolean Expression

EX. F = AB'C + ABC + A'B'C' + A'BC'

I am not looking for the answer to the expression only a tip on how to start reducing these tipes of Expressions.

Thank You in Advance
 
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  • #2
I'm no expert on this but the first thing I would do is start looking for "similarities" in the terms. For example, I see both A and C in the first two, both A' and C' in the second two:

F= AB'C+ ABC+ A'B'C'+ A'BC'= A(B+ B')C+ A'(B+ B')C'
and, of course, those two now have the same "B+ B' " so is the same as
F= (B+ B')(AC+ A'C')_

You haven't said what you consider "reduced to its lowest form".
 
  • #3
HallsoIvy

Thank You for your reply. It helped me alot. What I mean by Reduced to its lowest form is - The Boolean Expression is reduced to a point where no more Laws or Rules can be applied to the remainder of the original expression.

Would I be correct if I reduced the expression from where you stopped to :

F = (B+B')(AC+A'C')
= (1)(AC+A'C')
= AC + A'C'
= AC

Thank You for your help
 
  • #4
George SA said:
HallsoIvy

Thank You for your reply. It helped me alot. What I mean by Reduced to its lowest form is - The Boolean Expression is reduced to a point where no more Laws or Rules can be applied to the remainder of the original expression.

Would I be correct if I reduced the expression from where you stopped to :

F = (B+B')(AC+A'C')
= (1)(AC+A'C')
= AC + A'C'
= AC

Thank You for your help

Stop at F = AC + A'C', you can't justify the last line.
 
  • #5
Thanks I see what you mean. I went to class last night and the same was said to me on how to start these expressions. Look for similarities, Thank You again for your assistance I am almost sure I got this now
 
  • #6
The last line can actually be done using an XNOR gate.

BiP
 

What is reduction of Boolean expression to its lowest form?

Reduction of Boolean expression to its lowest form is the process of simplifying a Boolean expression into its most basic and concise form. This is done by applying various logical laws and rules to the expression in order to reduce its complexity and make it easier to understand and work with.

Why is it important to reduce Boolean expressions to their lowest form?

Reducing Boolean expressions to their lowest form is important because it helps to eliminate unnecessary complexity and redundancy in a logical expression. This makes it easier to analyze and evaluate the expression, and can also help in optimizing the design of digital circuits and systems.

What are the steps involved in reducing a Boolean expression to its lowest form?

The steps involved in reducing a Boolean expression to its lowest form include identifying and eliminating redundant terms, applying logical simplification rules such as De Morgan's laws and distributive property, and combining like terms. The goal is to simplify the expression into its most basic form using the least number of terms and operations.

Can Boolean expressions be reduced to different forms?

Yes, Boolean expressions can be reduced to different forms depending on the specific rules and laws used in the reduction process. For example, a Boolean expression can be reduced to its sum-of-products (SOP) form or its product-of-sums (POS) form, both of which are considered to be in their lowest form.

Are there any tools or software available for reducing Boolean expressions?

Yes, there are various tools and software available for reducing Boolean expressions, such as logic simplification calculators and Boolean algebra software. These tools can help automate the reduction process and make it faster and more accurate. However, it is important to have a basic understanding of the reduction process in order to effectively use these tools.

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