# Homework Help: Simplifying output for a XOR gate using Boolean Algebra

1. Apr 7, 2016

### Potatochip911

1. The problem statement, all variables and given/known data
I'm trying to show that the output of this XOR circuit is $F=A'B+AB'$,

2. Relevant equations
$(A+B)'=A'\cdot B'$
$(A\cdot B)'=A'+B'$
3. 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.

2. Apr 7, 2016

### ehild

You did it right, but simplify the last expression applying the distributive law.

3. Apr 7, 2016

### Potatochip911

yikes, can't believe I missed that one!

4. Apr 7, 2016

### ehild

Never give up hope :)