How Do I Simplify This Boolean Expression?

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SUMMARY

The discussion focuses on simplifying the Boolean expression !( (A*!B)*(A+C) ). The user, Lee, initially applied De Morgan's theorem to arrive at the expression (!A+B) + (!A*!C). However, the simplification process revealed that the first set of parentheses was unnecessary, and by applying the absorption rule, the expression can be further simplified to !A+B. This simplification is crucial for optimizing circuit design.

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  • Understanding of Boolean algebra
  • Familiarity with De Morgan's theorem
  • Knowledge of absorption rules in Boolean expressions
  • Basic concepts of circuit design
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This discussion is beneficial for electrical engineers, computer scientists, and students studying digital logic design who are looking to enhance their skills in simplifying Boolean expressions for circuit optimization.

LF07LAN
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Homework Statement



I have collected all the boolean terms on a circuit and I'm having trouble simplifying the following section of the circuit:

Key:
Not is !
OR is +
AND is *

I started with !( (A*!B)*(A+C) ) and used demorgans to get

(!A+B) + (!A*!C)


I cannot see beyond the parenthesis and do not know which rules to apply to maintain order

Please can someone help with a little workthrough

Thanks in advance,
Lee
 
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LF07LAN said:
(!A+B) + (!A*!C)

The first set of parenthesis is unnecessary.

Next, you can use one of the absorption rules.

!A!C is only true when !A is true. !A!C is false when !A is false.
 
So that was it. I just couldn't see past the parenthesis and didn't know where to apply the associative rule.

So the simple answer is !A+B

This is only part of the whole circuit so I should be able to go on and do the rest

Thanks
 

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