Question

Number of duals of distinct boolean expressions of 4 variables is ?

Comments

$2^{n-1}=2^{3}=8$

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Answer is 256 and I think 256 is number of self dual functions.

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yes you are right,

number distinct boolean expression will be $2^{n-1}$ and for each of these expressions we can assign $0$ or $1$

i.e $2$ chioce,

hence number of boolean function =$2^{2^{n-1}}=2^{8}=256$

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Number of boolean functions is 2^2^n and not 2^2^(n-1)

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@xylene i am talking about Number of duals of distinct boolean  function

Answer 1

Dual functions : 2^n

Self dual functions : 2^2^(n-1)

Note:

2^(n-1) beacuse we have total 2^n  functions , each of which will have 2 values True, or False. So distinct values: (2^n)/2 = 2^(n-1)

 

In this case: 2^2^3 or 2^8 or 256

Comments

How are dual functions 2ⁿ ?

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No of distinct Dule function =2^2^n-1

Because we have 2^n total terms each have to choice but when we do dule of a term it convert into other so half of 2^n =2^n-1 each have two choice so 2^2^n-1

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Question asks No of duals and not no of self duals? Why have you calculated no of self duals?