# Reduce the boolean expression to two literals

• annpaulveal
In summary, the given expression is simplified to BD, with the final steps being BD(A+A') and then BDA. This can also be reached by using the identity A+BC=(A+B)(A+C).
annpaulveal

## Homework Statement

ABC'D + A'BD + ABCD

## The Attempt at a Solution

Here is as far as I have gotten:

BD (AC' + A' + AC)
BD (AC' + A')

According to Wolfram Alpha, the answer should just be BD. Can someone help me get there?

Last edited:
Given the problem statement is correct you have two errors in the first line (a missing negation and a case of swapped symbol). I recommend you start from the beginning and take each step slowly, making sure all the symbols are transformed correctly along the way.

I fixed the errors, sorry. Can someone tell me where to go next?

Never mind, just solved it!

Last steps:

BD (A(C+C') + A')
BD (A+A')
BD

Are you familiar with A+BC=(A+B)(A+C)?

EDIT: Nvm, this isn't going to help.

## What does it mean to "reduce a boolean expression to two literals?"

Reducing a boolean expression to two literals means simplifying the expression to only include two variables or logical operators.

## Why is it important to reduce boolean expressions to two literals?

Reducing boolean expressions to two literals can make them easier to understand and evaluate. It can also help identify any errors in the expression.

## What are the steps to reduce a boolean expression to two literals?

The steps to reduce a boolean expression to two literals include identifying the variables and logical operators in the expression, using logical equivalences to simplify the expression, and rearranging the expression to only include two literals.

## Can all boolean expressions be reduced to two literals?

No, not all boolean expressions can be reduced to two literals. Some expressions may require more than two literals to accurately represent the logical relationship between variables.

## Are there any tools or methods that can help with reducing boolean expressions to two literals?

Yes, there are various tools and methods, such as truth tables and Karnaugh maps, that can aid in reducing boolean expressions to two literals. These tools can help visualize the logical relationships and simplify the expressions.

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