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For the following function find reduced Boolean equation using Quine McClusky method; F(A,B,C,D)= ?m(1,3,4,6,9,11,12,14)+?d(2,5,8,15)
written 2.9 years ago by gravatar for teamques10 teamques10 ★ 64k •   modified 2.9 years ago
digital electronics
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written 2.9 years ago by gravatar for teamques10 teamques10 ★ 64k

Step 1: Input Grouping the minterms/don't care terms based on number of 1's

Group Minterm/Don’t care terms Binary representation
0 - - - - -
1 1 0 0 0 1
4 0 1 0 0
2 0 0 1 0
8 1 0 0 0
2 3 0 0 1 1
6 0 1 1 0
9 1 0 0 1
12 1 1 0 0
5 0 1 0 1
3 11 1 0 1 1
14 1 1 1 0
4 15 1 1 1 1

Step 2: First Comparison Group the terms in pairs:

Group Pairs Binary representation
0 - - - - -
1 (3,1) 0 0 - 1
(9,1) - 0 0 1
(5,1) 0 - 0 1
(6,4) 0 1 - 0
(12,4) - 1 0 0
(5,4) 0 1 0 -
(3,2) 0 0 1 -
(6,2) 0 - 1 0
(9,8) 1 0 0 -
(12,8) 1 - 0 0
2 (11,3) - 0 1 1
(14,6) - 1 1 0
(11,9) 1 0 - 1
(14,12) 1 1 - 0
3 (15,11) 1 - 1 1
(15,14) 1 1 1 -

Step 3: Second Comparison

Group Pairs Binary representation
0 - - - - -
1 (11,9.3,1) - 0 - 1
(14,12,6,4) - 1 - 0

Step 4: Prime Implicants

(11,9,3,1) - 0 - 1

(14,12,6,4) - 1 - 0

(5,1) 0 - 0 1

(5,4) 0 1 0 -

(3,2) 0 0 1 -

(6,2) 0 - 1 0

(9,8) 1 0 0 -

(12,8) 1 - 0 0

(15,11) 1 - 1 1

(15,14) 1 1 1 -

Step 4: Coverage Table

-0-1 -1-0 0-01 010- 001- 0-10 100- 1-00 1-11 111-
1 x x
3 x x
4 x x
6 x x
9 x x
11 x x
12 x x
14 x x

$F=BD'+B'D$

To verify the output use this handy tool.
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