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).
Shumaila Saeed
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.
Shumaila Saeed
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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Nov 14, 2023
Use in Boolean Functions
Used in Sum of Products (SOP) form
Used in Product of Sums (POS) form
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Nov 14, 2023
Truth Table Representation
Represents rows where output is 1
Represents rows where output is 0
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Nov 14, 2023
Number of Combinations
2^n combinations for n variables
2^n combinations for n variables
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Nov 14, 2023
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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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
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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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
Maxterm
Maxterms are used to simplify Boolean expressions in POS form.
In POS simplification, combining maxterms can lead to simpler expressions.
Shumaila Saeed
Nov 14, 2023
Minterm
Minterms are used to simplify Boolean expressions using Karnaugh maps.
In a Karnaugh map, grouping minterms helps in simplifying expressions.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
Can a minterm represent more than one input combination?
No, each minterm corresponds to exactly one specific input combination.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
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.
Shumaila Saeed
Nov 14, 2023
Can a maxterm represent more than one input combination?
No, each maxterm corresponds to exactly one specific input combination.
Shumaila Saeed
Nov 14, 2023
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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Nov 14, 2023
How are minterms used in Boolean algebra?
Minterms are used to form the Sum of Products (SOP) expression of a Boolean function.
Shumaila Saeed
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).
Shumaila Saeed
Nov 14, 2023
Can minterms be used to simplify POS expressions?
No, minterms are specifically used for simplifying SOP expressions.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
Can maxterms be used to simplify SOP expressions?
No, maxterms are specifically used for simplifying POS expressions.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
Nov 14, 2023
Are minterms and maxterms specific to digital logic design?
Yes, they are fundamental concepts in digital logic design and Boolean algebra.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
Shumaila Saeed
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.
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