Karnaugh Maps

Introduction to Digital Logic - CPE2210 - 2 February 2018

What is the simplified function for F(w, x, y, z) = Σ(0, 2, 4, 6, 12, 14)?

      yz      
      00 01 11 10
             
wx 00   0 1 3 2
  01   4 5 7 6
  11   12 13 15 14
  10   8 9 11 10

      yz      
      00 01 11 10
             
wx 00   1a 0 0 1a
  01   1ab 0 0 1ab
  11   1b 0 0 1b
  10   0 0 0 0

The simplified function consists of groups a and b, which comprise: w’z’ + xz’

Don’t Care Conditions

Denoted by a hyphen

x y z f
0 0 0 1
0 0 1 0
0 1 0 -
0 1 1 0
1 0 0 1
1 0 1 -
1 1 0 0
1 1 1 0

minterm canonical formula

f(x, y, z) = Σ(0,4) + dc(2, 5)

maxterm canonical formula

f(x, y, z) = Π(1, 3, 6, 7) + dc(2, 5)

Don't Care K-maps

This chart depicts a k-map with Don’t Cares, and since they are there, you can fill them with whatever you want.

Don't Care K-maps

In this case, filling it with 1s which will simplify our equation to y’