UPPCL AE 2018:8

Question

How many different Boolean functions of $n$ variables are there?

• A. $2^{2^{n}}$
• B. $n^{n^{2}}$
• C. $n^{2^{n}}$
• D. $2^{n}$

Answer 1

Different Boolean Function with n variables

Input-------------------------------------->Output

n variable                                               0/1

2x2x2....n times Combination            2 Combination

$2^n$ Combination                                    2 Combination

No of way Function value can be assigned to input combination=[(no. of  output) ^ (no. of  input combination)]

=$(2)^(2^n)$

So A is the correct answer.