## K-map (What is k-map and examples of it):

(hello friends! Today I will tell you in detail about what is k-map (what is K-map?) In this post. So let's start)

### K-MAP:

The full name of k-map is karnaugh map. It is a graphical method of solving Boolean expressions. With the help of k map we can simplify Boolean expressions with 3, 4 variables without any Boolean expressions theorem.

In this, information from SOP (sum of product) and POS (product of sum) and truth table is displayed.

The k map is displayed like a table, but it provides more information than the truth table.

### k-map and numbering of cells:

The number of cells in the k-map depends on how many variables are there. If the variables are n, then the number of parentheses will be 2n. Gray code is used for numbering brackets. To mark the brackets, a decimal number is given to the brackets which are shown on the top left corner of the brackets.

#### K map with two variable amounts and numbering of its parentheses:

The number of parentheses in it is 22 = 4. Assuming the two variables are A and B, parentheses 3 represents AB (11) obtained by combining A and B. The bracket 2 represents AB à¤•ो (10). A̅B (01) displays bracket 1 and A̅B̅ (00) represents bracket 0. Its picture is given below:

#### K map with three variables and numbering its parentheses:

The number of parentheses in it is 23 = 8. In this, the combination of variable amount A, B and C is displayed. The bracket 0 displays the combination A̅B̅C̅ (000) of the variable amount. Similarly, other combinations are displayed according to their decimal number.

#### K map with four variables and numbering its parentheses:

The number of parentheses in it is 24 = 16. In this, combinations of four variable amounts (A, B, C, D) are displayed. The parentheses are marked based on the decimal equivalent of the combinations.

Either maxterm or minterm can be used to create a k map. minterm is represented by mi and maxterm is represented by Mi.

Wherever '1' is, we have to put them in a rectangular group. It is very important to keep '1's close to the group, only then we will be able to form a rectangular group of 1's bits and the rectangular group can contain only bits as the power of 2. Like - 2,4,8. So in this way we get pair, quads and octets.

**pair**- It consists of taking two 1’s bits into a rectangular group. The bits that are 1's bit horizontally or vertically adjacent to each other are taken into it. To simplify this, a variable amount and its complement becomes extinct. There may be more pairs in the k map. To solve these, a Boolean equation is obtained by "OR" (add) to the simplified equation of each pair.

**Quad-The**quad-quad consists of a rectangular group of four 1’s. It can be adjacent to each other in a line or as a square. To simplify this, two variables and their complement are lost.

**octet**- octet is a group of eight 1’s bits. In simplifying the octet, three variable quantities and their complements become extinct. It can also be simplified as two quad.

**overlapping groups**

In k-map a 1’s bit can be used more than once to create a pair, quad or octet. This means that a 1’s bit can also be used in a pair and can also be used in a quad or octet. Thus the groups that are formed are called overlapping groups.

**map rolling**

There are also groups in the k-map which are created by rolling the map. Suppose a 1’s bit is on the far right of the map and in the same line a 1’s bit is on the far left. Then by rolling the map to make a pair of these two, the right side of the map is merged with the left side, this creates a pair of both 1’s. A quad can also be made using this.

**Steps to solve equation with K-map**

1). The k map is selected according to the number of variables.

2). From the given problem, minterm (SOP) or maxterm (POS) are identified.

3). For SOP, 1 is written in the parentheses of the map and 0 is written in the rest.

4). For POS, 0 is written in the brackets of the map and 1 is written in the rest of the place.

5). Now where there is 1, they are placed in the rectangular group as the power of 2 (2,4,8). In this, as many as 1’s are placed in the group. To be in a group, it is very important for the bits to be side by side.

6). Now the simplified Boolean equation of k map is made by taking product terms and then adding them from the groups that are formed.

**NOTE**: - If this article has been helpful to you, then definitely share it with your friends and if you have any questions about your k-map, then you can tell them in the comment. thanks.