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Quine-McClusky Minimization Method Module M4.3 Section 5.3.

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Presentation on theme: "Quine-McClusky Minimization Method Module M4.3 Section 5.3."— Presentation transcript:

1 Quine-McClusky Minimization Method Module M4.3 Section 5.3

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

3 Tabular Representations 111 1 1 WX YZ 00011110 00 01 11 10 111 1 F = X & Y # !W & Y & !Z # W & !Y & Z # !W & X !W & X 01-- !W & Y & !Z 0-10 X & Y -11- W & !Y & Z 1-01

4 Prime Implicants F = X & !Y & Z # !X & !Z # !X & Y Each product term is an implicant 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 00011110 0 1 1 1 11 F = Y & !Z # X 1 -10 1--

6 Prime Implicants F = Y & !Z # X X YZ 00011110 0 11 1 111 Minterm X Y Z F 0 O O O 0 10 0 1 0 20 1 0 1 31 1 1 0 4 1 O O 1 51 0 1 1 61 1 0 1 71 1 1 1 -10 1--

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

8 Prime Implicants F = Y & !Z # X X YZ 00011110 0 11 1 111 Minterm X Y Z F 0 O O O 0 10 0 1 0 20 1 0 1 31 1 1 0 4 1 O O 1 51 0 1 1 61 1 0 1 71 1 1 1 -10 1--

9 Essential Prime Implicants 11 11 1 WX YZ 00011110 00 01 11 10 11 1 11 Find the essential prime implicants using the Q-M method.

10 Essential Prime Implicants 11 11 1 WX YZ 00011110 00 01 11 10 11 1 11 minterms 0 0000 1 0001 2 0010 8 1000 3 0011 5 0101 10 1010 7 0111 14 1110 15 1111

11 Finding Prime Implicants 0 0000 1 0001 2 0010 8 1000 3 0011 5 0101 10 1010 7 0111 14 1110 15 1111 Step 1Step 2 (0,1) 000- (0,2) 00-0 (0,8) -000 (1,3) 00-1 (1,5) 0-01 (2,3) 001- (2,10) -010 (8,10) 10-0 (3,7) 0-11 (5,7) 01-1 (10,14) 1-10 (7,15) -111 (14,15) 111- Step 3 (0,1,2,3) 00-- (0,2,1,3) 00-- (0,2,8,10) -0-0 (0,8,2,10) -0-0 (1,5,3,7) 0--1 (1,3,5,7) 0--1 6 Prime Implicants 1-10 -111 111- 00-- -0-0 0--1

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

13 3 Prime Implicants 11 11 1 WX YZ 00011110 00 01 11 10 11 1 11 0--1 -0-0 111- !W & Z W & X & Y !X & !Z F = !W & Z # W & X & Y # !X & !Z

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