# Simplifying output for a XOR gate using Boolean Algebra

• Potatochip911
In summary, the XOR circuit output can be simplified to F = A'B + AB' using De Morgan's laws and the distributive law.
Potatochip911

## 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 can't seem to figure out what I'm doing wrong.

Potatochip911 said:

## 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 can't seem to figure out what I'm doing wrong.
You did it right, but simplify the last expression applying the distributive law.

Potatochip911
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 :)

Potatochip911

## 1. What is a XOR gate?

A XOR gate, also known as an exclusive OR gate, is a digital logic gate that outputs a true value only when one of its inputs is true. It returns a false value if both inputs are either true or false.

## 2. How can Boolean Algebra be used to simplify the output of a XOR gate?

Boolean Algebra is a branch of mathematics that deals with logical operations and binary variables. It can be used to simplify the output of a XOR gate by reducing the number of terms and operations needed to represent the logic of the gate.

## 3. What are the basic laws of Boolean Algebra?

The basic laws of Boolean Algebra include the commutative law, associative law, distributive law, identity law, and complement law. These laws govern the manipulation of Boolean expressions and help simplify complex logic.

## 4. Can Boolean Algebra be used for other logic gates besides XOR gates?

Yes, Boolean Algebra can be used for all types of logic gates, including AND, OR, and NOT gates. It is a fundamental tool in digital logic design and can be applied to any logic circuit.

## 5. Are there any tools or software available to help simplify the output of a XOR gate using Boolean Algebra?

Yes, there are many tools and software programs available that can help with Boolean Algebra simplification, such as truth table generators and logic gate simulators. These tools can save time and effort in simplifying complex logic circuits.

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