Logic Circuits: 3-bit K-map (Karnaugh Map) problem #1

Simplify the following function using K-map: F(x,y,z) = Σ(0,1,4,5)

Solution:
This is a summation of minterms, therefore, 0, 1, 4, and 5 are all 1's. We can group the 4 of them since they form a square in the K-map (see figure). When dealing with minterms, an x is equal to 1 and an x' is equal to 0. Zero's will be listed as x' and one's as x.

Now, we need to list the variables. x has two 0's and two 1's. y has four 0's. And, z has two 0's and two 1's.


We need to simplify. Boolean Algebra Theorems state that x'+x'=x', and x'+x=1