I would just like to clarify if I am on the right track or not. I have these questions:
Consider the Boolean functions $f(x,y,z)$ in three variables such that the table of values of $f$ contains exactly four $1$’s.
- Calculate the total number of such functions.
- We apply the Karnaugh map method to such a function $f$. Suppose that the map does not contain any blocks of four $1$’s, and all four $1$’s are covered by three blocks of two $1$’s. Moreover, we find that it is not possible to cover all $1$’s by fewer than three blocks. Calculate the number of the functions with this property.
1a: I have answered $70 = \binom{8}{4}$.
1b: I have manually drawn up Karnaugh maps and have obtained the answer $12$, but my friend has $24$. Is there another way to do this?
Thank you