Question

Derive a Boolean function f(x, y, z) that yields a 1 when exactly two of the three input variables are 0.

Answer 1

The notation from analyzing the Karnaugh map is:

F(X,Y,Z) = X'Y'Z + X'Z'Y + Y'Z'X

With logical functions would be:

F(X,Y,Z) = (NOT(X AND Y) AND Z) OR ((NOT Z) AND (X XOR Y))

Explanation:

You can reduce the logical function with a Karnaugh map, like the attached, notice the gray coding notation, to assure only one variable change at each cell.