If we can generate a maximum of 4 Boolean functions using n Boolean variables...

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Question Id : 4191 | Context :Boolean algebra

Question

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:

Question: If we can generate a maximum of 4 Boolean functions using n Boolean variables, what is the minimum value of n?

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: $\boxed{1}$

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Aspire Study , Admin
Commented Feb 10 , 2020

Total Number of Boolean Function using n Boolean variables = 2^2ⁿ
Number of Boolean Functions = 4 Hence, n=1

17 Upvote 4 Downvote Reply

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Question: If we can generate a maximum of 4 Boolean functions using n Boolean variables, what is the minimum value of n?

✅ Try values of $n$ :

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Question: If we can generate a maximum of 4 Boolean functions using n Boolean variables, what is the minimum value of n?

✅ Try values of nn:

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✅ Try values of $n$ :