Assertion (A): The use of K-maps is usually limited to six-variables.
Reason (R): A K-map can not be used for problems involving more than six variables.
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true but R is not the correct explanation of A,
c)
A is true but R is false.
d)
A is false but R is true.
Correct answer is option 'C'. Can you explain this answer?

Question

Assertion (A): The use of K-maps is usually limited to six-variables.
Reason (R): A K-map can not be used for problems involving more than six variables.

a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true but R is not the correct explanation of A,
c)
A is true but R is false.
d)
A is false but R is true.

Correct answer is option 'C'. Can you explain this answer?

Answer

Assertion (A): The use of K-maps is usually limited to six-variables.
Reason (R): A K-map cannot be used for problems involving more than six variables.

Explanation:
Karnaugh maps, also known as K-maps, are a graphical tool used in digital logic design to simplify Boolean algebraic expressions. They provide a visual representation of truth tables and help in minimizing the number of logic gates required to implement a given Boolean function.

Assertion (A): The use of K-maps is usually limited to six-variables.
A K-map is typically used for problems with up to six variables. This limitation arises from the fact that the number of cells in a K-map increases exponentially with the number of variables. For example, a 2-variable K-map has 4 cells, a 3-variable K-map has 8 cells, and so on. As the number of variables increases, the K-map becomes larger and more complex to handle.

While it is possible to create K-maps with more than six variables, it becomes impractical due to the large number of cells required. The size of the K-map grows exponentially with each additional variable, making it difficult to visualize and manipulate.

Reason (R): A K-map cannot be used for problems involving more than six variables.
The reason why K-maps are not commonly used for problems involving more than six variables is that they become unwieldy and difficult to work with. The number of cells in a K-map with n variables is given by 2^n. For example, a 4-variable K-map has 16 cells, a 5-variable K-map has 32 cells, and a 6-variable K-map has 64 cells. As the number of variables increases, the size of the K-map grows exponentially.

Managing such a large number of cells becomes impractical and can lead to errors in analysis and simplification. Other methods, such as algebraic manipulation or computer-based algorithms, are often used for problems with a large number of variables.

Conclusion:
The assertion (A) is true. K-maps are usually limited to problems with up to six variables due to the exponential increase in size and complexity. The reason (R) is false because K-maps can technically be used for problems with more than six variables, but it becomes impractical and difficult to work with.

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