NIMCET 2015 — Computer PYQ

Explanation:

1. Combinations of Inputs: A Boolean function with $n$ binary variables has $2^n$ possible input combinations (rows in a truth table).

2. Possible Outputs: For each of those $2^n$ combinations, the function can result in one of $2$ possible outputs ($0$ or $1$).

3. Total Functions: Therefore, the total number of distinct Boolean functions is calculated as $2$ raised to the power of the number of input combinations:

   $$\text{Total Functions}=2^{(2^n)}$$