What is Minterm ?

Minterms are the fundamental part of Boolean algebra. Minterm is the product of N literals where each literal occurs exactly once. Minterm is represented by m. The output for the minterm functions is 1. This article explores the minterms in depth in addition to the two-variable, three variable and four variable minterm tables and K-maps. We will also solve some examples based on Minterms.

What is Minterm?

Minterms are the product of various distinct literals in which each literal occurs exactly once. The output result of the minterm function is 1. It is represented by m. To represent a function, we perform the sum of minterms which is called the Sum of Product (SOP).

Example of SOP:

PQ + QR + PR

Two-Variable Minterm

Minterms for two variables are called two-variable minterms.

Two-Variable Minterm Table

Variable		Minterm
A	B	Term	Representation
0	0	A'B'	m0
0	1	A'B	m1
1	0	AB'	m2
1	1	AB	m3

Two-Variable Minterm K-Map

👁 Two variable K-Map

Three Variable Minterm

Minterms for three variables are called three variable minterms.

Three Variable Minterm Table

Variable			Minterm
A	B	C	Term	Representation
0	0	0	A'B'C'	m0
0	0	1	A'B'C	m1
0	1	0	A'BC'	m2
0	1	1	A'BC	m3
1	0	0	AB'C'	m4
1	0	1	AB'C	m5
1	1	0	ABC'	m6
1	1	1	ABC	m7

Three Variable Minterm K-Map

👁 K-Map for three variable

Four Variable Minterm

Minterms for four variables are called four variable minterms.

Four Variable Minterm Table

Variables				Minterms
A	B	C	D	Terms	Representation
0	0	0	0	A'B'C'D'	m0
0	0	0	1	A'B'C'D	m1
0	0	1	0	A'B'CD'	m2
0	0	1	1	A'B'CD	m3
0	1	0	0	A'BC'D'	m4
0	1	0	1	A'BC'D	m5
0	1	1	0	A'BCD'	m6
0	1	1	1	A'BCD	m7
1	0	0	0	AB'C'D'	m8
1	0	0	1	AB'C'D	m9
1	0	1	0	AB'CD'	m10
1	0	1	1	AB'CD	m11
1	1	0	0	ABC'D'	m12
1	1	0	1	ABC'D	m13
1	1	1	0	ABCD'	m14
1	1	1	1	ABCD	m15

Four Variable Minterm K-Map

👁 K-Map for 4 Variable

Minterm for Values

Minterms for values are the minterms obtained by the values of the Boolean variable.

Steps for Obtaining Minterms from Values

1. If the Boolean variable is 1 then take the variable as it is without complementing.
2. If the Boolean variable is 0 then take the complement of the variable.

Solved Examples on Minterms

Example 1: If there are three Boolean variables A = 0, B = 0 and C = 1 then find the minterms for the given values.

Solution:

Given the values of the Boolean variables

A = 0, B = 0, C = 1

The required minterm is given by = A'B'C

We complemented A and B as its value is 0.

Example 2: Simplify SOP and find the result in SOP only.

F(A, B, C, D) = A'BC'D' +A'BC'D +A'BCD + AB'C'D' + AB'C'D + ABC'D' + ABCD'

Solution:

We draw a K-map to simplify SOP

👁 Example 2

Example 3: Find the SOP for F(A, B, C, D) = ∑m (4, 5, 7, 8, 9, 12, 14)

Solution:

👁 Example 3