Simplifying a Boolean function from a Kernaugh Map Given the three variable Karnaugh Map: x\yz 00 01 11 10 \___________________ 0 | 0 1 1 0 1 | 1 0 0 1 I am supposed to write a simplified expression for the Boolean function. Based on this KMap, I figured there should be 2 terms after simplified. I can't figure out how to simplify them though. Here is what I'm stuck at: F(xyz) = x(yz)' + x'(yz) + (xy)'z + (xy)z'

The products that are adjacent on the Karnaugh map are $(100,110)$ and $(001,011)$. In the first pair, $x$ and $z$ are set, but $y$ can take either value. So, the pair of products $xy'z' + xyz'$ can be "factored" into $xz'$.

Similarly, the other pair can be simplified into $x'z$.

So, we find $$ F(x,y,z) = x'z + xz' $$ (which is to say, $x$ XOR $z$).