What is the maximum number of different functions involving n Boolean variables?

2018

What is the maximum number of different functions involving n Boolean variables?

  1. A.

    n2

  2. B.

    2n

  3. C.

    (2n)2

  4. D.

    (22)n

Attempted by 211 students.

Show answer & explanation

Correct answer: D

A Boolean function with n variables takes 2n possible input combinations (each variable can be 0 or 1).

For each input combination, the output can independently be either 0 or 1.
So, the total number of different Boolean functions is:

(22)n

Explore the full course: Up Lt Grade Assistant Teacher 2025