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Self-dual Boolean function

by mathwo
Tags: boolean, function, selfdual
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mathwo
#1
Nov18-12, 09:18 AM
P: 1
A Boolean function of n variables is a mapping f : {0, 1}^n to {0, 1}. . Determine the number of Boolean functions f of n variables such that
(i) f is not self-dual and f(0, 0, . . . , 0) = f(1, 1, . . . , 1),
(ii) f is self-dual and f(0, 0, . . . , 0) = 1.
I think for the first part, i need to find the number of functions that is not self-dual, then find the number of functions i need from it? For the second part,i absolutely have no clue, please help me with this question.
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mfb
#2
Nov18-12, 02:14 PM
Mentor
P: 11,815
For the first part, I would calculate the number of self-dual functions, and the number of functions where f(0, 0, . . . , 0) = f(1, 1, . . . , 1). As all self-dual functions satisfy that condition, both numbers are sufficient to get the answer.

For the second part: Well, you know f(1, 1, . . . , 1) as well. How many independent function values are left which you can choose?


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