Simplifying Boolean Function with Karnaugh Maps

Question

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

Answer 1

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

Answer 2

K-Maps must be grouped in either 1,2,4,8 basically powers of 2.

This K map can be grouped in to 3 groups that have 4 in each group. Then look fro the variables that don't change.

The groups would look like this:

Group 1:

y' z' x'  
y' z' x  
y' z  x'  
y' z  x  

This simplifies to y'.

Group 2:

y  z  x  
y  z' x  
y' z' x  
y' z  x  

This simplifies to x.

Group 3:

y  z  x'  
y' z  x'  
y' z  x
y' z  x    

This simplifies to z.

So the boolean function is: y' + x + z

This is how the final answer is resolved.