• **Simplification of Boolean algebra** is the process of reducing a Boolean expression to its simplest form.

## Map methods

**Map methods **are a graphical way to simplify Boolean expressions. The most common map methods are the **Karnaugh map **and the **Quine**–**McCluskey method**.

## Karnaugh map

The **K-map** is a systematic way of simplifying Boolean expressions. With the help of the K-map method, we can find the simplest POS and SOP expression, which is known as the minimum expression. The K-map provides a cookbook for simplification.

• **A k-map is similar to a truth table** because it presents all of the possible values of input variables and the resulting output for each value.

• In K-map, the number of cells is similar to the total number of variable input combinations. **For example**, if the number of variables is three, the number of cells is 2^{3}=8, and if the number of variables is four, the number of cells is 2^{4}.

• The K-map takes the **SOP **and **POS **forms.

• The K-map grid is filled using **0’s** and **1’s**. The K-map is solved by making groups.

**Note:
Cell Adjacency:** **The cells that differ by only one bit are called as cell adjacency.**

## 2 Variable K-map

A **2-variable Karnaugh map (K-map)** is a table with 4 cells, each representing a different combination of the two input variables, **A **and **B**. The value of each cell is the value of the output variable, F, for that combination of input variables.

## 3-variable K-map

A **3-variable Karnaugh map (K-map) **is a table with 8 cells, each representing a different combination of the three input variables, **A**, **B**, and **C**. The value of each cell is the value of the output variable, F, for that combination of input variables.

## 4-variable k-map

A **4-variable Karnaugh map (K-map)** is a table with 16 cells, each representing a different combination of the four input variables, **A**, **B**, **C**, and **D**. The value of each cell is the value of the output variable, F, for that combination of input variables.

## 5-variable K-map:

A **5-variable Karnaugh map (K-map)** is a graphical method for simplifying Boolean expressions with five variables.

• A K-map for five variables (ABCDE) can be constructed using two 4-variable maps. Each map contains 16 cells with all combinations of variables B, C, D, and E. One map is for A = 0, and the other is for A = 1).