1. Quine-McClusky Minimization Method
Lecture L5.3
Section 5.3

2. Quine-McCluskey Method
Tabular Representations
Prime Implicants
Essential Prime Implicants

3. Tabular RepresentationsYZ 00 01 11 10
!W & Y & !Z
0-10 WX 00
!W & X
01-- 1 01 1 1 1 1 11 1 1 1
X & Y
-11- 10 1
W & !Y & Z
1-01
F = X & Y # !W & Y & !Z
# W & !Y & Z # !W & X

4. Prime Implicants Each product term is an implicant
F = X & !Y & Z
# !X & !Z
# !X & Y
A product term that cannot have any of its
variables removed and still imply the logic
function is called a prime implicant.

5. Prime Implicants X YZ 00 01 11 10 1
-10 1 1 1 1 1
1--
F = Y & !Z
# X

6. Prime Implicants X YZ 00 01 11 10 1 -10 Minterm X Y Z F 0 O O O 01
-10
Minterm X Y Z F
0 O O O 0
O O 1
1--
F = Y & !Z
# X

7. Finding Prime Implicants
Step 1
Step 2
Step 3
4 1 O 0
(2,6) - 1 0
(4,5,6,7) 1 - -
(4,5) 1 0 -
(4,6,5,7) 1 - -
(4,6) 1 - 0
(5,7) 1 - 1
(6,7) 1 1 -
All unchecked entries are Prime Implicants
-10 Y & !Z
1-- X

8. Prime Implicants X YZ 00 01 11 10 1 -10 Minterm X Y Z F 0 O O O 01
-10
Minterm X Y Z F
0 O O O 0
O O 1
1--
F = Y & !Z
# X

9. Essential Prime ImplicantsYZ 00 01 11 10 WX
Find the essential
prime implicants
using the Q-M
method. 00 1 1 1 1 01 1 1 11 1 1 10 1 1

10. Essential Prime Implicants
minterms YZ 00 01 11 10 WX 00 1 1 1 1 01 1 1 11 1 1 10 1 1

11. Finding Prime Implicants
Step 1
Step 2
Step 3
(0,1) 000-
(0,1,2,3) 00--
(0,2) 00-0
(0,2,1,3) 00--
(0,8) -000
(0,2,8,10) -0-0
(1,3) 00-1
(1,5) 0-01
(0,8,2,10) -0-0
(2,3) 001-
(1,5,3,7) 0--1
(2,10) -010
(1,3,5,7) 0--1
(8,10) 10-0
(3,7) 0-11
6 Prime Implicants
(5,7) 01-1
1-10
-111
111-
00--
-0-0
0--1
(10,14) 1-10
(7,15) -111
(14,15) 111-

12. Find Essential Prime Implicants
Covered
minterms
Minterms
1-10
-111
111-
00--
-0-0
0--1
10,14
7,15
14,15
0,1,2,3
0,2,8,10
1,3,5,7 X X X X * X X X X X X X X X X X X X X

13. 3 Prime Implicants F = !W & Z # W & X & Y # !X & !Z YZ 00 01 11 10 WX
0--1 01 1 1
!W & Z 11 1 1
111- 10 1 1
!X & !Z
W & X & Y
-0-0