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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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1. Example-1 : Minterm = 0,1,2,5,6,7,8,9,10,14
(Previous example) | 3. Example-3 : Minterm = 2,3,5,7,8,10,12,13,15
(Next example) |
2. Example-2 : Minterm = 2,6,8,9,10,11,14,15
Minterm = 2,6,8,9,10,11,14,15
DontCare =
Variable = a,b,c,d
using Quine-McCluskey
Solution:
Minterm = `sum m(2,6,8,9,10,11,14,15)`
Variable = a,b,c,d
1. min terms and their binary representations
Group A1
| | | Group A2
| | | 6 | 0110 | `->` | | 9 | 1001 | `->` | | 10 | 1010 | `->` |
| Group A3
| | | Group A4
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2. merging of min term
Group B1
(A1,A2) | | | 2,6 | 0-10 | `->` | | 2,10 | -010 | `->` | | 8,9 | 100- | `->` | | 8,10 | 10-0 | `->` |
| Group B2
(A2,A3) | | | 6,14 | -110 | `->` | | 9,11 | 10-1 | `->` | | 10,11 | 101- | `->` | | 10,14 | 1-10 | `->` |
| Group B3
(A3,A4) | | | 11,15 | 1-11 | `->` | | 14,15 | 111- | `->` |
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3. merging of min term pairs
Group C1
(B1,B2) | | | 2,6,10,14 | --10 | ✓ | | 8,9,10,11 | 10-- | ✓ |
| Group C2
(B2,B3) | | |
1. Prime implicant chart (ignore the don't cares)
| PIs\Minterms | 2 | 6 | 8 | 9 | 10 | 11 | 14 | 15 | a,b,c,d | | 2,6,10,14 | X | X | | | X | | X | | --10 | | 8,9,10,11 | | | X | X | X | X | | | 10-- | | 10,11,14,15 | | | | | X | X | X | X | 1-1- |
Column-2 has only single X, so essential PI (2,6,10,14) is --10. Now remove this PI Row and corresponding Minterm Column 2,6,10,14
Column-9 has only single X, so essential PI (8,9,10,11) is 10--. Now remove this PI Row and corresponding Minterm Column 8,9,11
Extracted essential prime implicants : --10,10--
2. Reduced Prime implicant chart
| PIs\Minterms | 15 | a,b,c,d | | 10,11,14,15 | X | 1-1- |
Column-15 has only single X, so essential PI (10,11,14,15) is 1-1-. Now remove this PI Row and corresponding Minterm Column 15
Extracted essential prime implicants : 1-1-
All extracted essential prime implicants : --10,10--,1-1-
Minimal Quine-McCluskey Expression = cd' + ab' + ac
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
1. Example-1 : Minterm = 0,1,2,5,6,7,8,9,10,14
(Previous example) | 3. Example-3 : Minterm = 2,3,5,7,8,10,12,13,15
(Next example) |
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