If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?
NIMCET PREVIOUS YEAR QUESTION
🎥 Video solution / Text Solution of this question is given below:
Formula: Number of Boolean functions of $n$ variables is:
$
2^{2^n}
$
Condition: We are told the total functions must be ≤ 4:
\[
2^{2^n} \leq 4
\]
✅ Try values of $n$:
- $n = 0$: $2^{2^0} = 2^1 = 2$ ✅
- $n = 1$: $2^{2^1} = 2^2 = 4$ ✅
- $n = 2$: $2^{2^2} = 2^4 = 16$ ❌
Minimum $n$ for which number of Boolean functions ≤ 4 is:
\[
\boxed{1}
\]
✅ Final Answer: $\boxed{1}$
Commented Feb 10, 2020
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