Given the boolean function
f(x,y,z) = xyz + xyz' + xy'z + xy'z' + x'yz + x'y'z + x'y'z' (where x' = not x)
In a three variable Karnaugh Map:
yz yz' y'z' y'z
x 1 1 1 1
x' 1 1 1
The goal is to group the adjacent units and simplifying using the distributive law since y+y' would equal one. This is all good, but when it comes to the above Karnaugh map, which one do I group together? The textbook says, it should be the biggest block but I am a bit confused in terms of what that means.
The final answer after simplification would yield:
x + y' + z
Best Answer
I've marked the groups on the image below. As usual, the value of each group is the variable that remains constant in the group.
Red = x
Blue = y'
Green = z
So the answer is x + y' + z