UPPCL AE 2018:31

Question

How many different Boolean circuits of $n$ variables are there?

• A. None of the above
• B. $n^{2^{n}}$
• C. $2^{2^{n}}$
• D. $2^{n}$

Comments

i think it 2^n.

Answer 1

The total number of boolean circuits formed will be equal to the total number of operation formed by that function.

Binary operation on set A is a function F: A  x  A $\rightarrow$ A.

the domain, i.e AxA has n X n elements, each of this n$ ^ {2}$ elements can be mapped to one of the elements of A.

so total $^{n^{n^{2}}}$ binary operation possible.

Hence the total boolean circuit  = $^{n^{n^{2}}}$

Answer 2

thus option C is correct