In this note, we are going to know that What is Minterm and Maxterm in Digital Electronics with Examples and Truth Table. Welcome to Poly Notes Hub, a leading destination for diploma and polytechnic engineering notes.
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What is Minterm and Maxterm in Digital Electronics? | With Examples and Truth Tables
Define Minterm in Digital Electronics
A minterm is a product term that comprises all K variables of a Boolean function, each of which is either complemented or uncomplemented. A K-variable function has 2ᴷ minterms, each representing a unique combination of input variables.
The AND operation on all of the function’s variables results in a minterm. In a minterm, a variable is in uncomplemented form if its value in the associated input combination is 1, and in complemented form if its value is 0.
For example, a 2-variable function contains four minterms: A̅B̅, A̅B, AB̅, and AB. Similarly, a three-variable function has eight minterms, each representing one row of the truth table whose function output is 1.
Example or Truth Table of Minterm
2-Variable Truth Table of Minterm
| A | B | Minterm | Expression |
|---|---|---|---|
| 0 | 0 | m₀ | A̅B̅ |
| 0 | 1 | m₁ | A̅B |
| 1 | 0 | m₂ | AB̅ |
| 1 | 1 | m₃ | AB |
3-Variable Truth Table of Minterm
| A | B | C | Minterm | Expression |
|---|---|---|---|---|
| 0 | 0 | 0 | m₀ | A̅B̅C̅ |
| 0 | 0 | 1 | m₁ | A̅B̅C |
| 0 | 1 | 0 | m₂ | A̅BC̅ |
| 0 | 1 | 1 | m₃ | A̅BC |
| 1 | 0 | 0 | m₄ | AB̅C̅ |
| 1 | 0 | 1 | m₅ | AB̅C |
| 1 | 1 | 0 | m₆ | ABC̅ |
| 1 | 1 | 1 | m₇ | ABC |
Define Maxterm in Digital Electronics
A maxterm is a total term that includes all K variables of a Boolean function, each of which appears in either complemented or uncomplemented form. For a K-variable function, there are 2ᴷ maxterms, each representing a unique combination of the input variables.
The OR operation on all of the function’s variables yields a maximum term. In a maxterm, a variable is in uncomplemented form if its value in the associated input combination is 0, and in complemented form if its value is 1.
For a two-variable function, there are four maxterms: (A + B), (A + B̅), (A̅ + B), and (A̅ + B̅). Similarly, a three-variable function has eight maxterms, each representing a row of the truth table where the function result is zero.
Example or Truth Table of Maxterm
2-Variable Truth Table of Maxterm
| A | B | Maxterm | Expression |
|---|---|---|---|
| 0 | 0 | M₀ | (A + B) |
| 0 | 1 | M₁ | (A + B̅) |
| 1 | 0 | M₂ | (A̅ + B) |
| 1 | 1 | M₃ | (A̅ + B̅) |
3-Variable Truth Table of Maxterm
| A | B | C | Maxterm | Expression |
|---|---|---|---|---|
| 0 | 0 | 0 | M₀ | (A + B + C) |
| 0 | 0 | 1 | M₁ | (A + B + C̅) |
| 0 | 1 | 0 | M₂ | (A + B̅ + C) |
| 0 | 1 | 1 | M₃ | (A + B̅ + C̅) |
| 1 | 0 | 0 | M₄ | (A̅ + B + C) |
| 1 | 0 | 1 | M₅ | (A̅ + B + C̅) |
| 1 | 1 | 0 | M₆ | (A̅ + B̅ + C) |
| 1 | 1 | 1 | M₇ | (A̅ + B̅ + C̅) |
Minterm Vs Maxterm
Here is the differences between Minterm and Maxterm in Digital Electronics –
| Basis | Minterm | Maxterm |
|---|---|---|
| Definition | A minterm is a product (AND) term containing all variables of a Boolean function, each in complemented or uncomplemented form. | A maxterm is a sum (OR) term containing all variables of a Boolean function, each in complemented or uncomplemented form. |
| Operator used | AND (·) | OR (+) |
| Output value | Produces 1 for only one input combination. | Produces 0 for only one input combination. |
| Representation | Written as Σm | Written as ΠM |
| Variable form | Variable is uncomplemented for 1 and complemented for 0. | Variable is uncomplemented for 0 and complemented for 1. |
| Use in expression | Used to express a function in Sum of Products (SOP) form. | Used to express a function in Product of Sums (POS) form. |
| Truth table relation | Corresponds to rows where F = 1. | Corresponds to rows where F = 0. |
| Number of terms | For n variables, there are 2ⁿ minterms. | For n variables, there are 2ⁿ maxterms. |
| Example (2 variables) | A̅B, AB̅, AB, A̅B̅ | (A + B), (A̅ + B), (A + B̅), (A̅ + B̅) |
| Example notation | m₀, m₁, m₂… | M₀, M₁, M₂… |