Self dual functions

Question

Number of self-dual binary  functions with 4 variables are:

$A) 16$

$B) 64$

$C) 256$

$D) 512$

Answer 1

Ans: C

https://www.youtube.com/watch?v=uLGIUQc6m1A

Comments

I got it

I'm able to solve this question but when i write anser in the test series i write $2^{2^{(4-1)}} =2^{2^{3}} = 2^{8} = 512$,(silly mistake)

But $2^{8} = 256$

Thanks

Answer 2

Self dual means f(x',y',z',w')=f'(x,y,z,w), which means that since the total combinations with 4 variables are 16, a function if dual, needs to be symmetric which essentially means here that there will be exactly 8 minterms of the function.

Lets try to design a function:- if 0th (0000)minterm is selected to be true, we will automatically select 15th to be false. Likewise if 3th(0011) is selected , 12th (1100)minterm is set to false automatically. So total functions can be computed as-

16*14*12*10*8*6*4*2/8!

(This is permutations divided by total arrangements, to get combinations)

(The numerator is the total choices we have for 8 min terms)

256 is the answer.