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If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?
1. 65536
2. 16
3. 1
4. 4

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Correct Answer - Option 3 : 1

The correct answer is 1

  • First, we need to understand that when there are no variables, there are two expressions :
    • False=0 and True=1
  • For one variable p, four functions can be constructed. A function maps each input value of a variable to one and only one output value.
    • The False(pfunction maps each value of p to (False).
    • The identity (pfunction maps each value of p to the identical value.
    • The flip (pfunction maps False to True and True to False.
    • The True (p) function maps each value of p to (True).
  • For one variable: 
    • = \(2^{2^1}\)functions can be constructed.This information can be collected into a table: 
    • Input Function
      p False p -p True
      0 0 0 1 1
      1 0 1 0 1
  • For n Variables:
    • Number of Variables Number of Boolean Functions
      0 \(2^{2^0}\) = 20 = 2
      1 \(2^{2^1}\) = 22 = 4
      2 \(2^{2^2}\) = 24 = 16
      3 \(2^{2^3}\) = 28 = 256
      4 \(2^{2^4}\) = 216 = 65536
      n \(2^{2^n}\)
  • Therefore, according to the above table, a maximum of 4 Boolean functions can be generated with 1 variable.

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