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
|
|
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-MapThree Variable Minterm
Minterms for three variables are called three variable minterms.
Three Variable Minterm Table
|
|
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
|
|
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 VariableMinterm for Values
Minterms for values are the minterms obtained by the values of the Boolean variable.
Steps for Obtaining Minterms from Values
- If the Boolean variable is 1 then take the variable as it is without complementing.
- 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 3: Find the SOP for F(A, B, C, D) = ∑m (4, 5, 7, 8, 9, 12, 14)
Solution:
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