Quine-McClusky Minimization Method Discussion D3.2.

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Quine-McClusky Minimization Method Discussion D3.2

Quine-McCluskey Method Tabular Representations Prime Implicants Essential Prime Implicants

Tabular Representations WX YZ F = XY + W'YZ' + WY'Z + W'X W'X 01-- W'YZ' 0-10 XY -11- WY'Z 1-01

Prime Implicants F = XY'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.

Prime Implicants X YZ F = YZ' + X

Prime Implicants F = YZ' + X X YZ Minterm X Y Z F 0 O O O O O

Finding Prime Implicants O Step 1Step 2 (2,6) (4,5) (4,6) (5,7) (6,7) Step 3 (4,5,6,7) (4,6,5,7) All unchecked entries are Prime Implicants -10 YZ' 1-- X

Prime Implicants F = YZ' + X X YZ Minterm X Y Z F 0 O O O O O

Essential Prime Implicants WX YZ Find the essential prime implicants using the Q-M method.

Essential Prime Implicants WX YZ minterms

Finding Prime Implicants 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 (1,3,5,7) 0--1 (1,5,3,7) Prime Implicants

Find Essential Prime Implicants Prime Implicant Covered minterms Minterms ,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 *

3 Prime Implicants WX YZ W'Z WXY X'Z' F = W'Z + WXY + X'Z'

3 Prime Implicants WX YZ W'Z WXY X'Z' F = W'Z + WXY + X'Z'