Let’s assume instead of 4, there is only one variable, say ‘a’.
for single variables, the number of input combinations will be 2 i.e. 0 and 1.
Function table for one variable
a |
f1 |
f2 |
f3 |
f4 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
so here only 4 functions are possible in the case of one variable.
f1 = 0
f2= a
f3 = a’
f4 = 1
so from here, we can say that the number of functions is $2^{number of rows}$.
Number of rows = $2^{number of variables}$.
In short, the Relation between the number of functions and the number of variables = $2^{2^{number of variables}}$.
{Note: order should be maintained first do $2^{number of variables}$ then what result you will get make that of power of 2}
Now in question, it is given that the number of variables = 4.
so,
= $2^{2^{4}}$
= $2^{16}$.
= 65,536
The correct answer is Option D.