Can XOR Gates Substitute OR Gates in Boolean Expressions?

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SUMMARY

The discussion centers on the question of whether XOR gates can substitute OR gates in Boolean expressions, specifically examining the equation x(y+z)=f and its transformation into x(z XOR y XOR zy). Participants suggest using a truth table to validate the equivalence of y+z and z ⨂ y ⨂ zy before attempting an algebraic proof. The conversation emphasizes the importance of visualizing Boolean operations to confirm logical relationships.

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  • Understanding of Boolean algebra and expressions
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  • Ability to construct and interpret truth tables
  • Basic knowledge of algebraic manipulation in Boolean logic
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jeffy
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Homework Statement



i have the equation x(y+z)=f some how it becomes x(z xor y xor zy)

Homework Equations





The Attempt at a Solution


xy+xz
xy(z+NOTz)+x(y+NOTy)z
x(yz+(y XOR z))


Thanks
 
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jeffy said:

Homework Statement



i have the equation x(y+z)=f some how it becomes x(z xor y xor zy)
You are wanting to show that y+z = z ⨂ y ⨂ zy ?

I suggest that you first draw up a truth table to demonstrate that it holds true, before trying to prove it algebraically.
 

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