Boolean Equation simlification

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SUMMARY

The discussion focuses on simplifying the Boolean equation x = ab'c'd' + a'd + a'c + a'b using only XOR and OR gates. The initial attempt at simplification combines terms to x = ab'c'd' + a'(d + c + b). Participants suggest applying DeMorgan's Laws to further simplify the expression, particularly on the term (b + c + d). The goal is to achieve a more efficient representation of the equation suitable for digital logic design.

PREREQUISITES
  • Understanding of Boolean algebra and simplification techniques
  • Familiarity with XOR and OR gate functionalities
  • Knowledge of DeMorgan's Laws in Boolean expressions
  • Experience with digital logic design principles
NEXT STEPS
  • Study Boolean algebra simplification techniques
  • Learn about the implementation of XOR and OR gates in digital circuits
  • Explore DeMorgan's Laws and their applications in circuit design
  • Research methods for optimizing Boolean expressions for logic minimization
USEFUL FOR

Students in electrical engineering, digital circuit designers, and anyone interested in optimizing Boolean expressions for logic circuits.

stosw
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Homework Statement



I'm trying to simplify the following to only use XOR and OR gates.

[EQ]x = ab'c'd' + a'd + a'c + a'b[/EQ]

The Attempt at a Solution



My only thought would be to

[EQ]x = ab'c'd' + a'd + a'c + a'b[/EQ]
[EQ]x = ab'c'd' + a'(d + c + b)[/EQ]

But I have no idea what else to do. Can anyone suggest something for me to check into or any tips/hints?
 
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Use DeMorgan's Laws on (b+c+d).
 

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