GATE CS 1987 Q1-II — Boolean Algebra

To find the total number of Boolean functions that can be realized with $n$ variables, we can reason as follows:

1. A Boolean function of $n$ variables takes an input of $n$ binary digits. The total number of unique input combinations (or rows in a truth table) is $2^n$.
2. For each of these $2^n$ input combinations, the function can output either $0$ or $1$ (i.e., $2$ choices).
3. Therefore, the total number of distinct Boolean functions of $n$ variables is given by the formula:
   $$\text{Total Functions} = 2^{2^n}$$

Given $n = 4$ variables:

Thus, the correct option is D.