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2. Quine-McCluskey method example
( Enter your problem )
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- Example-1 : Minterm = 0,1,2,5,6,7,8,9,10,14
- Example-2 : Minterm = 2,6,8,9,10,11,14,15
- Example-3 : Minterm = 2,3,5,7,8,10,12,13,15
- Example-4 : Minterm = 4,8,10,11,12,15
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Other related methods
- Karnaugh Map method (Kmap)
- Quine-McCluskey method
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2. Example-2 : Minterm = 2,6,8,9,10,11,14,15
(Previous example) | 4. Example-4 : Minterm = 4,8,10,11,12,15
(Next example) |
3. Example-3 : Minterm = 2,3,5,7,8,10,12,13,15
Minterm = 2,3,5,7,8,10,12,13,15
DontCare =
Variable = a,b,c,d
using Quine-McCluskey
Solution:
Minterm = `sum m(2,3,5,7,8,10,12,13,15)`
Variable = a,b,c,d
1. min terms and their binary representations
Group A1
| | | Group A2
| | | 3 | 0011 | `->` | | 5 | 0101 | `->` | | 10 | 1010 | `->` | | 12 | 1100 | `->` |
| Group A3
| | | Group A4
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2. merging of min term
Group B1
(A1,A2) | | | 2,3 | 001- | ✓ | | 2,10 | -010 | ✓ | | 8,10 | 10-0 | ✓ | | 8,12 | 1-00 | ✓ |
| Group B2
(A2,A3) | | | 3,7 | 0-11 | ✓ | | 5,7 | 01-1 | `->` | | 5,13 | -101 | `->` | | 12,13 | 110- | ✓ |
| Group B3
(A3,A4) | | | 7,15 | -111 | `->` | | 13,15 | 11-1 | `->` |
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3. merging of min term pairs
1. Prime implicant chart (ignore the don't cares)
| PIs\Minterms | 2 | 3 | 5 | 7 | 8 | 10 | 12 | 13 | 15 | a,b,c,d | | 2,3 | X | X | | | | | | | | 001- | | 2,10 | X | | | | | X | | | | -010 | | 8,10 | | | | | X | X | | | | 10-0 | | 8,12 | | | | | X | | X | | | 1-00 | | 3,7 | | X | | X | | | | | | 0-11 | | 12,13 | | | | | | | X | X | | 110- | | 5,7,13,15 | | | X | X | | | | X | X | -1-1 |
Column-5 has only single X, so essential PI (5,7,13,15) is -1-1. Now remove this PI Row and corresponding Minterm Column 5,7,13,15
Extracted essential prime implicants : -1-1
2. Reduced Prime implicant chart
| PIs\Minterms | 2 | 3 | 8 | 10 | 12 | a,b,c,d | | 2,3 | X | X | | | | 001- | | 2,10 | X | | | X | | -010 | | 8,10 | | | X | X | | 10-0 | | 8,12 | | | X | | X | 1-00 | | 3,7 | | X | | | | 0-11 | | 12,13 | | | | | X | 110- |
Row-2,3 is dominated by Row-3,7, so Row-3,7 is eliminated
Row-8,12 is dominated by Row-12,13, so Row-12,13 is eliminated
Reduced Prime implicant chart after Row dominance
| PIs\Minterms | 2 | 3 | 8 | 10 | 12 | a,b,c,d | | 2,3 | X | X | | | | 001- | | 2,10 | X | | | X | | -010 | | 8,10 | | | X | X | | 10-0 | | 8,12 | | | X | | X | 1-00 |
Column dominance
Column-3 is dominated by Column-2, so Column-2 is eliminated
Column-12 is dominated by Column-8, so Column-8 is eliminated
Reduced Prime implicant chart after Column dominance
| PIs\Minterms | 3 | 10 | 12 | a,b,c,d | | 2,3 | X | | | 001- | | 2,10 | | X | | -010 | | 8,10 | | X | | 10-0 | | 8,12 | | | X | 1-00 |
3. Reduced Prime implicant chart
| PIs\Minterms | 3 | 10 | 12 | a,b,c,d | | 2,3 | X | | | 001- | | 2,10 | | X | | -010 | | 8,10 | | X | | 10-0 | | 8,12 | | | X | 1-00 |
Column-3 has only single X, so essential PI (2,3) is 001-. Now remove this PI Row and corresponding Minterm Column 3
Column-12 has only single X, so essential PI (8,12) is 1-00. Now remove this PI Row and corresponding Minterm Column 12
Extracted essential prime implicants : 001-,1-00
4. Reduced Prime implicant chart
| PIs\Minterms | 10 | a,b,c,d | | 2,10 | X | -010 | | 8,10 | X | 10-0 |
(`1^(st)` Row) Row PI 2,10 has maximum(1) X, so essential PI (2,10) is -010. Now remove this PI Row and corresponding Minterm Column 10
Extracted essential prime implicants : -010
All extracted essential prime implicants : -1-1,001-,1-00,-010
Minimal Quine-McCluskey Expression = bd + a'b'c + ac'd' + b'cd'
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
2. Example-2 : Minterm = 2,6,8,9,10,11,14,15
(Previous example) | 4. Example-4 : Minterm = 4,8,10,11,12,15
(Next example) |
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