Question

Which of the following is true for a 5-variable Karnaugh map?

A. It has 16 cells.
B. It can represent up to 32 different binary values.
C. It can eliminate up to 4 variables from the output expression.
D. It is typically used for simplifying expressions with 3 variables.

Answer 1

A 5-variable Karnaugh map has 32 cells and can represent up to 32 different binary values. It is used for simplifying boolean expressions with five variables, not three.

Step-by-step explanation:

A 5-variable Karnaugh map is a tool used in digital logic design for simplifying boolean expressions with five input variables. When we talk about a 5-variable K-map, it's important to clarify the following:

• Option A states that it has 16 cells, which is incorrect. A 5-variable K-map actually has 32 cells to represent all possible combinations of the five variables.
• Option B is true because with 5 variables, there are 25 different binary values, which equals 32. So, a 5-variable K-map can indeed represent up to 32 different binary values.
• Option C suggests it can eliminate up to 4 variables from the output expression, which is not accurate. The purpose of a K-map is to simplify boolean expressions, and while it may reduce the number of terms, it doesn't necessarily eliminate variables completely.
• Option D is incorrect because the 5-variable K-map is typically used for simplifying expressions with 5 variables, not 3.

Therefore, the correct answer is B. A 5-variable Karnaugh map can represent up to 32 different binary values.