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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)
1 Answer
written 2.9 years ago by |
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 |
$F=B'D+A'BD'+BC'D'$
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