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For the following function find the reduced Boolean equations using Quine McClusky method; F(A,B,C,D)=?m(1,3,4,6,9,11,12)+?d(5,8,15)
written 4.5 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 4.5 years ago
digital electronics
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written 4.5 years ago by gravatar for teamques10 teamques10 ★ 70k

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

Group Minterm/Don’t care terms Binary Representation
1 1 0 0 0 1
4 0 1 0 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
4 15 1 1 1 1

 

Step 2: First Comparison Group the terms in pairs:

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

Step 3: Second Comparison

Group Pairs Binary Representation
0 (1,3,9,11) - 0 - 1

Step 4: Prime Implicants:

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

(1,5) 0 - 0 1

(4,6) 0 1 - 0

(4,12) - 1 0 0

(4,5) 0 1 0 -

(8,9) 1 0 0 -

(8,12) 1 - 0 0

(11,15) 1 - 1 1

Step 4: Coverage Table

-0-1 0-01 01-0 -100 010- 100- 1-00 1-11
1 x x
3 x
4 x x x
6 x
9 x x
11 x x
12 x x

$F=B'D+A'BD'+BC'D'$

Verify the output using this handy tool
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