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Using Quine McClusky technique, minimize the following function :- F(A,B,C,D) =?m(3,4,5,7,9,13,14,15)
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 4 0 1 0 0
2 3 0 0 1 1
5 0 1 0 1
9 1 0 0 1
3 7 0 1 1 1
13 1 1 0 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 (5,4) 0 1 0 -
2 (7,3) 0 - 1 1
(7,5) 0 1 - 1
(13,5) - 1 0 1
(13,9) 1 - 0 1
3 (15,7) - 1 1 1
(15,13) 1 1 - 1
(15,14) 1 1 1 -

Step 3: Second Comparison Group the terms in pairs:

Group Pairs Binary Representation
0 - - - - -
1 - - - - -
2 (15,13,7,5) - 1 - 1

Step 4: Prime Implicants:

(15,13,7,5) - 1 - 1

(5,4) 0 1 0 -

(7,3) 0 - 1 1

(13,9) 1 - 0 1

(15,14) 1 1 1 -

Step 5: Coverage Table

-1-1 010- 0-11 1-01 111-
3 x
4 x
5 x x
7 x x
9 x
13 x x
14 x
15 x x

$ABC+A\bar CD+\bar ACD+\bar AB\bar C$

Verify the output using this handy tool
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