# What is maxterm and minterm in digital electronics?

## What is maxterm and minterm in digital electronics?

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 and maxterm?**

A maxterm is a Boolean expression resulting in a 0 for the output of a single cell expression, and 1s for all other cells in the Karnaugh map, or truth table. 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 relationship between minterm and maxterm?**

A minterm of n variables is a product term that contains n literals from all the variables. A maxterm of n variables is a sum term that contains n literals from all the variables.

### What are Minterms and Maxterms with examples?

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.

**Why is SOP called minterm?**

because all terms should be zero for F to be zero, whereas any of the terms in POS being one results in F to be one. Thus it is known as MINTERM (minimum one term!)

**How do we convert POS to SOP?**

There are the following steps to convert the POS function F = Π x, y, z (2, 3, 5) = x y’ z’ + x y’ z + x y z’ into SOP form: In the first step, we change the operational sign to Σ. Next, we find the missing indexes of the terms, 000, 110, 001, 100, and 111. Finally, we write the product form of the noted terms.

#### Is Minterm a SOP?

SOP uses minterms. Minterm is product of boolean variables either in normal form or complemented form. POS uses maxterms. Maxterm is sum of boolean variables either in normal form or complemented form.

**What is SOP & POS?**

The SOP (Sum of Product) and POS (Product of Sum) are the methods for deducing a particular logic function. In other words, these are the ways to represent the deduced reduced logic function. Conversely, POS produces a logical expression comprised of the AND of the multiple OR terms.

**Why is SOP called Minterm?**

## How to find the maxterm solution for minterm?

It also looks strange that (A+B+C) is mapped into the cell 000. For the equation Out= (A+B+C)=0, all three variables (A, B, C) must individually be equal to 0. Only (0+0+0)=0 will equal 0. 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 .

**When does minterm n give a true value?**

A given minterm n gives a true value (i.e., 1) for just one combination of the input variables. For example, minterm 5, a b ‘ c, is true only when a and c both are true and b is false—the input arrangement where a = 1, b = 0, c = 1 results in 1.

**Is the maxterm a dual of the minterm idea?**

Thus, a maxterm is a logical expression of n variables that employs only the complement operator and the disjunction operator. Maxterms are a dual of the minterm idea (i.e., exhibiting a complementary symmetry in all respects). Instead of using ANDs and complements, we use ORs and complements and proceed similarly.

### Why are minterms and maxterms called products?

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 .