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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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4. Example-4 : Minterm = 4,8,10,11,12,15
Minterm = 4,8,10,11,12,15
DontCare =
Variable = a,b,c,d
using Quine-McCluskey
Solution:
Minterm = `sum m(4,8,10,11,12,15)`
Variable = a,b,c,d
1. min terms and their binary representations
Group A1
| | | Group A2
| | | Group A3
| | | Group A4
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2. merging of min term
Group B1
(A1,A2) | | | 4,12 | -100 | ✓ | | 8,10 | 10-0 | ✓ | | 8,12 | 1-00 | ✓ |
| Group B2
(A2,A3) | | | Group B3
(A3,A4) | | |
1. Prime implicant chart (ignore the don't cares)
| PIs\Minterms | 4 | 8 | 10 | 11 | 12 | 15 | a,b,c,d | | 4,12 | X | | | | X | | -100 | | 8,10 | | X | X | | | | 10-0 | | 8,12 | | X | | | X | | 1-00 | | 10,11 | | | X | X | | | 101- | | 11,15 | | | | X | | X | 1-11 |
Column-4 has only single X, so essential PI (4,12) is -100. Now remove this PI Row and corresponding Minterm Column 4,12
Column-15 has only single X, so essential PI (11,15) is 1-11. Now remove this PI Row and corresponding Minterm Column 11,15
Extracted essential prime implicants : -100,1-11
2. Reduced Prime implicant chart
| PIs\Minterms | 8 | 10 | a,b,c,d | | 8,10 | X | X | 10-0 | | 8,12 | X | | 1-00 | | 10,11 | | X | 101- |
(`1^(st)` Row) Row PI 8,10 has maximum(2) X, so essential PI (8,10) is 10-0. Now remove this PI Row and corresponding Minterm Column 8,10
Extracted essential prime implicants : 10-0
All extracted essential prime implicants : -100,1-11,10-0
Minimal Quine-McCluskey Expression = bc'd' + acd + ab'd'
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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