Simplifying output for a XOR gate using Boolean Algebra

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Homework Help Overview

The discussion revolves around simplifying the output of an XOR gate using Boolean algebra, specifically aiming to demonstrate that the output can be expressed as ##F=A'B+AB'##.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of De Morgan's laws and the distributive law in simplifying the expression derived from the circuit output. There is an attempt to identify where the original poster may have gone wrong in their reasoning.

Discussion Status

Some participants have provided guidance on simplifying the expression further, suggesting the use of the distributive law. There is recognition of a mistake in the original attempt, but no explicit consensus on the final outcome has been reached.

Contextual Notes

Participants are working within the constraints of Boolean algebra rules and are focused on the logical structure of the XOR gate output. The original poster expresses uncertainty about their approach, indicating a need for clarification on the simplification process.

Potatochip911
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Homework Statement


I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##,
480px-XOR_from_NOR.svg.png


Homework Equations


##(A+B)'=A'\cdot B'##
##(A\cdot B)'=A'+B'##

The Attempt at a Solution



From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot B)+(A+B)']'=(A\cdot B)'\cdot (A+B)=(A\cdot B)'\cdot (A+B)=(A'+B')\cdot (A+B)=0##? I can't seem to figure out what I'm doing wrong.
 
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Potatochip911 said:

Homework Statement


I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##,
480px-XOR_from_NOR.svg.png


Homework Equations


##(A+B)'=A'\cdot B'##
##(A\cdot B)'=A'+B'##

The Attempt at a Solution



From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot B)+(A+B)']'=(A\cdot B)'\cdot (A+B)=(A\cdot B)'\cdot (A+B)=(A'+B')\cdot (A+B)=0##? I can't seem to figure out what I'm doing wrong.
You did it right, but simplify the last expression applying the distributive law.
 
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ehild said:
You did it right, but simplify the last expression applying the distributive law.
yikes, can't believe I missed that one!
 
Potatochip911 said:
yikes, can't believe I missed that one!
Never give up hope :)
 
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