# Simplifying output for a XOR gate using Boolean Algebra

## Homework Statement

I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, ## 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 cant seem to figure out what I'm doing wrong.

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ehild
Homework Helper

## Homework Statement

I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, ## 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 cant seem to figure out what I'm doing wrong.
You did it right, but simplify the last expression applying the distributive law.

• Potatochip911
You did it right, but simplify the last expression applying the distributive law.
yikes, can't believe I missed that one!

ehild
Homework Helper
yikes, can't believe I missed that one!
Never give up hope :)

• Potatochip911