## What are minterms and maxterms in Boolean algebra?

Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan’s laws.

### What are minterms and maxterms with examples?

The maxterm is a 0, not a 1 in the Karnaugh map. A maxterm is a sum term, (A+B+C) in our example, not a product term. Thus we place our sole 0 for minterm (A+B+C) in cell A,B,C=000 in the K-map, where the inputs are all 0 .

**What is the difference between minterms and maxterms?**

As nouns the difference between maxterm and minterm is that maxterm is (algebra) a sum that is a logical or of a set of variables while minterm is in boolean algebra, a product term in which each variable appears once (in either its complemented or uncomplemented form).

**How do you write minterms and Maxterms in Boolean algebra?**

Example 1: Maxterm = A+B’

- First, we will write the minterm: Maxterm = A+B’
- Now, we will write 0 in place of complement variable B’.
- We will write 1 in place of non-complement variable A.
- The binary number of the maxterm A+B’ is 10. The decimal point number of (10)2 is 2. So, the shorthand notation of A+B’ is.

## How do you find the product of Maxterms?

The Product of Maxterm is complement of the Sum of Minterm of a function. To obtain the Product of Maxterm, we need two step process. Find those minterms in the Truth Table that gives a 0 as output. Complement those minterms using DeMorgan’s law.

### How are Maxterms calculated?

Example 2: Maxterm = A+B’+C’

- First, we will write the maxterm: Maxterm = A+B’+C’
- Now, we will write 0 in place of complement variables B’ and C’.
- We will write 1 in place of non-complement variable A.
- The binary number of the maxterm A+B’+C’ is 100. The decimal point number of (100)2 is 4.

**What is DNF in boolean algebra?**

In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept. As a normal form, it is useful in automated theorem proving.

**How do you write Maxterms?**

## What is the use of minterms and Maxterms?

In Minterm, we look for the functions where the output results in “1” while in Maxterm we look for function where the output results in “0”. We perform Sum of minterm also known as Sum of products (SOP) . We perform Product of Maxterm also known as Product of sum (POS).

### What is minterm expansion?

Minterm expansion (sometimes called the “minterm expansion principle”) is an algorithm for transforming a truth table into a circuit: For each combination of values that should cause the function to output 1, build a minterm that outputs 1 only for those input values (and 0 for all other input values).

**How do you write Minterms and Maxterms?**