# Converting a boolean expression into simplest product of sums

• Kizaru
In summary, the given Boolean expression can be simplified to a simplest product of sums by using a K-map to see the answer and then making a simplification using perfect induction. The final simplified expression is (B+C)(A+B'+C+D)(A'+B+C')(A'+B').
Kizaru

## Homework Statement

Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.

## The Attempt at a Solution

Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I found the minterm and maxterm list. I then tried to simplify the POS obtained from maxterm list to get
(B+C)(A+B'+C+D)(A'+B+C')(A'+B')

which I'm not sure how to simplify, but seems like it can be simplified.

Kizaru said:

## Homework Statement

Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.

## The Attempt at a Solution

Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I found the minterm and maxterm list. I then tried to simplify the POS obtained from maxterm list to get
(B+C)(A+B'+C+D)(A'+B+C')(A'+B')

which I'm not sure how to simplify, but seems like it can be simplified.

Are you allowed to use a K-map to simplify it, or are you required to do it algebraically in this problem?

berkeman said:
Are you allowed to use a K-map to simplify it, or are you required to do it algebraically in this problem?

Algebraically.

But I just got the answer. I used a K-Map to see the answer and then made a simplification (removing the ABD' term by showing it is irrelevant using perfect induction). It was cake after that. I still appreciate the response though.

## 1. What is a boolean expression?

A boolean expression is a mathematical statement that evaluates to either true or false. It consists of variables, logical operators, and constants.

## 2. What does it mean to convert a boolean expression into simplest product of sums?

Converting a boolean expression into simplest product of sums means simplifying the expression using Boolean algebra rules and reducing it to its most basic form, which is a series of ANDed terms (products) that are ORed together (sums).

## 3. Why is it important to convert a boolean expression into simplest product of sums?

Simplifying a boolean expression into its simplest product of sums form makes it easier to understand and analyze. It also helps in reducing the number of logic gates required to implement the expression, which can save time and resources in digital circuit design.

## 4. What are some common rules used to convert a boolean expression into simplest product of sums?

The most commonly used rules are the distributive law, De Morgan's laws, and the identity and complement laws. These rules can be used to simplify expressions by combining common terms and eliminating double negations.

## 5. Are there any tools or software available to help with converting boolean expressions?

Yes, there are several tools and software available to help with converting boolean expressions into simplest product of sums. Some examples include Boolean Algebra Calculator, Logic Friday, and Espresso Logic Minimizer. These tools can also be used to verify the correctness of the converted expression.

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