Minterms and maxterms of boolean's expression

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In summary, the conversation discusses Minterms and Maxterms of boolean expressions and their definitions. The first method involves adding Boolean terms that are composed of factors of x, y, and z with values of 0 or 1, representing the OR operation. The second method uses a product of factors with each factor being an OR of the inputs.
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desmond iking
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i couldn't find the definition of Minterms and maxterms of boolean's expression on the internet nor my book. Can someone explain it? I was given only this in my book, without any explanation.
 

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The two definitions are right there in the photo you posted 2.3.1

Try reading it again and look at the examples provided.

The first f(x,y,z) adds up a bunch of Boolean terms. Each term is composed of factors of x,y and z. X,y and z can have values of 0 or 1 so each term is an AND of x,y and z. The adding is in reality the OR operation.

The equation is saying f(x,y,z) is true when xyz is true OR x'yz is true OR ... That's a minterm way of defining the f function.

The alternate way to define the f function is to use a product of factors with each factor being an OR of x, y, z inputs.
 

FAQ: Minterms and maxterms of boolean's expression

What are minterms and maxterms in boolean expression?

Minterms and maxterms are two different ways of representing a boolean expression in its simplest form. Minterms are the product of all the variables in a boolean expression, while maxterms are the sum of all the variables.

How are minterms and maxterms used in boolean algebra?

Minterms and maxterms are used as building blocks to simplify boolean expressions and create logic circuits. They help break down complex expressions into simpler forms that can be easily implemented in digital systems.

What is the difference between minterms and maxterms?

The main difference between minterms and maxterms is the way they are written. Minterms are written as the product of all variables, while maxterms are written as the sum of all variables. Additionally, minterms represent the logical AND operation, while maxterms represent the logical OR operation.

How do you convert a boolean expression into minterm or maxterm form?

To convert a boolean expression into minterm or maxterm form, you can use a truth table and identify the rows where the expression evaluates to 1. For minterm form, you would write out the product of the variables in those rows, while for maxterm form, you would write out the sum of the variables.

Are minterms and maxterms unique for a boolean expression?

Yes, minterms and maxterms are unique for a boolean expression. While there may be multiple ways to represent a boolean expression in minterm or maxterm form, the resulting expressions will be equivalent and have the same truth table.

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