# What is Quine-McCluskey method and how is it implemented to simplify combinational circuits?

## What is Quine-McCluskey method and how is it implemented to simplify combinational circuits?

The Quine-McCluskey algorithm uses a given function , which contains the sum of minterms or the sum of the products (SOP) to determine a simplified and reduced equivalent. If the expression does not have minterms then we need to evaluate the corresponding minterms before proceeding further.

## What is Quine McCluskey minimization technique?

Quine McCluskey minimization method, is a technique for reducing for minimizing the expression in their SOP (sum of product) or POS (product of sum) form. Also called a tabular method, this method has advantages over the K Map method, in case the number of input variables is large.

What is dont care combination?

A Don’t Care cell can be represented by a cross(X) or minus(-) or phi(Φ) in K-Maps representing an invalid combination. For example, in the Excess-3 code system, the states 0000, 0001, 0010, 1101, 1110, and 1111 are invalid or unspecified. These states are called don’t cares.

### What is don’t care condition in digital electronics explain with relevant example?

The “Don’t care” condition says that we can use the blank cells of a K-map to make a group of the variables. The “don’t care” in excess-3 code are 0000, 0001, 0010, 1101, 1110, and 1111 because they are invalid combinations.

### How Quine-McCluskey method overcome K-map?

Quine–McCluskey method is a tabular method that has an advantage over Karnaugh maps when a large number of inputs are present. With more inputs, pattern recognition in Karnaugh maps can be tedious or sometimes even impossible. The Quine–McCluskey method does not require pattern recognition.

What are differences between K-map and Quine McCluskey?

Karnaugh map (K-map) and Quine-McCluskey (QM) methods are well known methods to simplify Boolean expression. K-map method becomes complex beyond five variable Boolean expression. Quine-McCluskey method is computer based technique for minimization of Boolean function and it is faster than K-map method.

#### What are don’t care conditions discuss how they are handled with the help of an example?

The combinations for which we don’t have any output expression specified are called don’t care combination. For Example, in 8421 code, input states 1001, 1010, 1011, 1100, 1101, 1110 and 1111 are invalid and the corresponding output is the don’t care.

#### What is the utility of using dont care conditions in combinational circuit design?

Don’t care conditions are a set of inputs which never occurs or which is not a valid combination for digital circuit. we use these conditions for further simplification of boolean expression so that the circuit can be implemented with less no. Of gates.

What is the advantage of using Quine-McCluskey method in simplify Boolean function?

The Q-M technique is capable of minimizing logic relationships for any number of inputs. The main advantage of this method is that it can be implemented in the software in an algorithmic fashion.

## What is the advantage of simplifying the Boolean function using Quine-McCluskey method?

The VLSI designers can use minimization methods to produce high speed, inexpensive and energy-efficient integrated circuits with increased complexity. Quine-McCluskey (Q-M) is an attractive algorithm for simplifying Boolean expressions because it can handle any number of variables.

## What are the disadvantages of K-map?

The disadvantage of k map :

• It is not suitable for computer reduction.
• It is not suitable when the number of variables involved exceed four.
• Care must be taken to field in every cell with the relevant entry, such as a 0, 1 (or) don’t care terms.