K Map in Boolean Algebra is a graphical representation used in Boolean algebra and digital circuit design. It provides a systematic way to simplify and minimize Boolean expressions. K map simplify the boolean expression in pictorial format without using boolean laws or theorems. It is generally used for solving the complex Boolean expressions and get the minimum number of logic gets in our circuit.
Instead of Boolean algebra, there is one more way through we simplify the Boolean expression and we find minimum number of logic gets. That is “k Map In Boolean Algebra”.
The map itself is a grid-like structure where each cell corresponds to a unique combination of input variables in a truth table. So k – Map In Boolean Algebra relay on grids or cells, we use it to solve or understand the combination of various inputs. we will understand deeply k Map In Boolean Algebra , in just few lines next.
Truth Table In Boolean Algebra
A truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It lists all possible input combinations and the output that results from those combinations. Means, when we put two different types of input in truth table than , truth table gives us a new or unique out puts. as we can see that in bellow picture.
Example: The truth table for the logical AND operator (2-input AND gate).
Note:- K map is developed by Karnaugh in the year 1953.
When we solve any Boolean expression than we generally use simple formula that is :-
In K -Map in Boolean Algebra number of variable can be 2 , 3 or more. let’s see ,one by one in detail.
Example :-
Let suppose we have two variable than according to formula …
In this picture A and B are variables and 0 ,1 , 2 , 3 are number of cell or boxes. Generally in k-Map counting of cells are started from 0.
Let suppose we have Three variable than according to formula …
Here the most important thing is to notice that , counting of cells are quite different as you can see in both (two and three variable cells). Numbers are not continuous, there is something twist means after 1 we expect 2 but it is not as per out expectation instead it has started from 0 . So we have to remember these sequence of numbers. It is not too tough to remember.
One more thing, you have to observe the sequence of binary number means , if we talk about the last cell in three variable table (It is 6 and it’s binary number is ‘110’), we write from left to write means A → B → C’ that is why we found binary number 110 that is equals to 6.
Same as this, if we talk about forth cell ( It is 2 and binary number is ‘010’ ) we write from left to write means A’ → B → C’ that is why we found binary number 010, that is equals to 2.
Key Points Of K – Map
- k – Map is nothing but it is just a representation that represent values in tabular format but it gives more information than any truth table.
- Through K-Map we can minimize the Boolean expression (2,3,4 variables) easily, without using any postulates of Boolean Algebra.
- We can easily find out the SOP (sum of product ) and POS (product of sum) form of any given Boolean expression using K-Map.
- It is basically Graphical representation of Truth Table.
- K-Map is basically consists of cells arranged in a grids , where each cells corresponds to a unique combinations.
How To Make Pairs in K-Map 👈
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