# Minterm vs. Maxterm: Know the Difference

By Shumaila Saeed || Updated on December 25, 2023

**Minterms are AND combinations of all variables in a function in either direct or complemented form, producing 1 for a single input combination; Maxterms are OR combinations of all variables, producing 0 for a single input combination.**

## Key Differences

A minterm is a product (AND combination) of all the variables in a function, where each variable is used once in its true or complemented form. It represents a specific combination of inputs that results in the output being 1. Conversely, a maxterm is a sum (OR combination) of all the variables, where each variable appears once in true or complemented form, representing a specific combination of inputs that gives 0 as the output.

Shumaila Saeed

Nov 14, 2023

In the truth table of a Boolean function, each row that yields the output 1 corresponds to a minterm. Minterms collectively represent the function by summing (ORing) all such products. In contrast, each row that yields 0 corresponds to a maxterm, and the function is represented by multiplying (ANDing) all such sums.

Shumaila Saeed

Nov 14, 2023

Minterms are used in the Sum of Products (SOP) form of representing Boolean functions, emphasizing when the output is true (1). Maxterms, on the other hand, are used in the Product of Sums (POS) form, focusing on when the output is false (0).

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Nov 14, 2023

When simplifying Boolean expressions using Karnaugh maps or algebraic methods, minterms help in identifying the minimum conditions for the output to be true. Maxterms are useful in identifying conditions to keep the output false and simplify expressions in POS form.

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Nov 14, 2023

The number of minterms or maxterms in a function depends on the number of variables; with n variables, there are 2^n possible minterms or maxterms. Each minterm corresponds to a unique maxterm, representing a specific input condition from the opposite perspective.

Shumaila Saeed

Nov 14, 2023

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## Comparison Chart

### Output Representation

Produces 1 for a specific input combination

Produces 0 for a specific input combination

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### Use in Boolean Functions

Used in Sum of Products (SOP) form

Used in Product of Sums (POS) form

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### Truth Table Representation

Represents rows where output is 1

Represents rows where output is 0

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### Number of Combinations

2^n combinations for n variables

2^n combinations for n variables

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## Minterm and Maxterm Definitions

#### Minterm

Minterm is an AND combination of all variables in a Boolean function.

In the expression ABC + A'B'C, ABC is a minterm.

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Nov 14, 2023

#### Maxterm

Maxterm represents a specific condition where the function outputs 0.

For the input 101, the maxterm (A + B' + C) corresponds to the output 0.

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Nov 14, 2023

#### Minterm

Minterms are building blocks for the Sum of Products form.

The SOP form A'BC + AB'C is comprised of two minterms.

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Nov 14, 2023

#### Maxterm

Maxterm is an OR combination of all variables in a Boolean function.

In the expression (A + B + C)(A' + B' + C'), (A + B + C) is a maxterm.

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Nov 14, 2023

#### Minterm

Each minterm is associated with a unique row in the truth table.

The minterm AB'C' corresponds to the row with inputs 110 in the truth table.

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#### Maxterm

Maxterms are building blocks for the Product of Sums form.

The POS form (A + B' + C)(A' + B + C') is comprised of two maxterms.

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Nov 14, 2023

#### Minterm

Minterm represents a specific condition where the function outputs 1.

For the input 101, the minterm A'BC corresponds to the output 1.

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Nov 14, 2023

#### Maxterm

Maxterms are used to simplify Boolean expressions in POS form.

In POS simplification, combining maxterms can lead to simpler expressions.

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Nov 14, 2023

#### Minterm

Minterms are used to simplify Boolean expressions using Karnaugh maps.

In a Karnaugh map, grouping minterms helps in simplifying expressions.

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Nov 14, 2023

#### Maxterm

Each maxterm is associated with a unique row in the truth table.

The maxterm (A + B' + C') corresponds to the row with inputs 110 in the truth table.

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Nov 14, 2023

#### Minterm

In Boolean algebra, a product term, with a value of 1, in which each variable appears once (in either its complemented or uncomplemented form, so that the value of the product term becomes 1).

A Boolean function can be expressed, canonically, as a sum of minterms, where each minterm corresponds to a row (of the function's truth table) whose output value is 1.

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Oct 19, 2023

#### Maxterm

(algebra) A sum that is a logical OR of a set of variables where each individual variable only appears once in the sum, either in complemented or uncomplemented form, so that the value of the sum becomes 0.

All the

**maxterms**in a product of maxterms should have the same variables, although each**maxterm**should differ from every other one by the pattern of complementation of those variables.Shumaila Saeed

Oct 19, 2023

## Repeatedly Asked Queries

#### What is a minterm?

A minterm is an AND combination of all variables in a Boolean function, used to represent when the output is 1.

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Nov 14, 2023

#### Can a minterm represent more than one input combination?

No, each minterm corresponds to exactly one specific input combination.

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Nov 14, 2023

#### What is a maxterm?

A maxterm is an OR combination of all variables in a Boolean function, used to represent when the output is 0.

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Nov 14, 2023

#### How are maxterms used in Boolean algebra?

Maxterms are used to form the Product of Sums (POS) expression of a Boolean function.

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#### What is the role of minterms in Karnaugh maps?

Minterms are used in Karnaugh maps to identify and group terms to simplify Boolean expressions in SOP form.

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#### Can a maxterm represent more than one input combination?

No, each maxterm corresponds to exactly one specific input combination.

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#### Can minterms and maxterms be converted into each other?

Yes, each minterm has a corresponding maxterm that represents the same input condition but from the opposite perspective.

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#### How are minterms used in Boolean algebra?

Minterms are used to form the Sum of Products (SOP) expression of a Boolean function.

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Nov 14, 2023

#### How does the number of variables affect minterms and maxterms?

The number of variables directly affects the number of possible minterms and maxterms (2^n for n variables).

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#### Can minterms be used to simplify POS expressions?

No, minterms are specifically used for simplifying SOP expressions.

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Nov 14, 2023

#### What is the role of maxterms in Karnaugh maps?

Maxterms are used in Karnaugh maps to identify and group terms to simplify Boolean expressions in POS form.

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Nov 14, 2023

#### How many minterms are there for a function with n variables?

There are 2^n possible minterms for a function with n variables.

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Nov 14, 2023

#### How many maxterms are there for a function with n variables?

There are 2^n possible maxterms for a function with n variables.

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Nov 14, 2023

#### Can maxterms be used to simplify SOP expressions?

No, maxterms are specifically used for simplifying POS expressions.

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Nov 14, 2023

#### Do maxterms always produce a low output (0)?

Yes, maxterms are designed to produce an output of 0 for their specific input condition.

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Nov 14, 2023

#### How do minterms relate to the truth table of a Boolean function?

Each minterm corresponds to a row in the truth table where the output is 1.

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#### Are minterms and maxterms specific to digital logic design?

Yes, they are fundamental concepts in digital logic design and Boolean algebra.

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Nov 14, 2023

#### Do minterms always produce a high output (1)?

Yes, minterms are designed to produce an output of 1 for their specific input condition.

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Nov 14, 2023

#### Are minterms and maxterms always used together?

No, they are used separately depending on whether the SOP or POS form is needed.

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Nov 14, 2023

#### How do maxterms relate to the truth table of a Boolean function?

Each maxterm corresponds to a row in the truth table where the output is 0.

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Nov 14, 2023

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About Author

Written by

Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.