|
2. Quine-McCluskey method example
( Enter your problem )
|
- 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
|
Other related methods
- Karnaugh Map method (Kmap)
- Quine-McCluskey method
|
|
1. Example-1 : Minterm = 0,1,2,5,6,7,8,9,10,14
1. Minterm = 0,1,2,5,6,7,8,9,10,14
DontCare =
Variable = a,b,c,d
using Quine-McCluskey
Solution:
Minterm = `sum m(0,1,2,5,6,7,8,9,10,14)`
Variable = a,b,c,d
1. min terms and their binary representations
Group A1
| | | Group A2
| | | 1 | 0001 | `->` | | 2 | 0010 | `->` | | 8 | 1000 | `->` |
| Group A3
| | | 5 | 0101 | `->` | | 6 | 0110 | `->` | | 9 | 1001 | `->` | | 10 | 1010 | `->` |
| Group A4
| | |
2. merging of min term
Group B1
(A1,A2) | | | 0,1 | 000- | `->` | | 0,2 | 00-0 | `->` | | 0,8 | -000 | `->` |
| Group B2
(A2,A3) | | | 1,5 | 0-01 | ✓ | | 1,9 | -001 | `->` | | 2,6 | 0-10 | `->` | | 2,10 | -010 | `->` | | 8,9 | 100- | `->` | | 8,10 | 10-0 | `->` |
| Group B3
(A3,A4) | | | 5,7 | 01-1 | ✓ | | 6,7 | 011- | ✓ | | 6,14 | -110 | `->` | | 10,14 | 1-10 | `->` |
|
3. merging of min term pairs
Group C1
(B1,B2) | | | 0,1,8,9 | -00- | ✓ | | 0,2,8,10 | -0-0 | ✓ |
| Group C2
(B2,B3) | | |
1. Prime implicant chart (ignore the don't cares)
| PIs\Minterms | 0 | 1 | 2 | 5 | 6 | 7 | 8 | 9 | 10 | 14 | a,b,c,d | | 1,5 | | X | | X | | | | | | | 0-01 | | 5,7 | | | | X | | X | | | | | 01-1 | | 6,7 | | | | | X | X | | | | | 011- | | 0,1,8,9 | X | X | | | | | X | X | | | -00- | | 0,2,8,10 | X | | X | | | | X | | X | | -0-0 | | 2,6,10,14 | | | X | | X | | | | X | X | --10 |
Column-9 has only single X, so essential PI (0,1,8,9) is -00-. Now remove this PI Row and corresponding Minterm Column 0,1,8,9
Extracted essential prime implicants : -00-
2. Reduced Prime implicant chart
| PIs\Minterms | 2 | 5 | 6 | 7 | 10 | 14 | a,b,c,d | | 1,5 | | X | | | | | 0-01 | | 5,7 | | X | | X | | | 01-1 | | 6,7 | | | X | X | | | 011- | | 0,2,8,10 | X | | | | X | | -0-0 | | 2,6,10,14 | X | | X | | X | X | --10 |
Column-14 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
Extracted essential prime implicants : --10
3. Reduced Prime implicant chart
| PIs\Minterms | 5 | 7 | a,b,c,d | | 1,5 | X | | 0-01 | | 5,7 | X | X | 01-1 | | 6,7 | | X | 011- | | 0,2,8,10 | | | -0-0 |
(`2^(nd)` Row) Row PI 5,7 has maximum(2) X, so essential PI (5,7) is 01-1. Now remove this PI Row and corresponding Minterm Column 5,7
Extracted essential prime implicants : 01-1
All extracted essential prime implicants : -00-,--10,01-1
Minimal Quine-McCluskey Expression = b'c' + cd' + a'bd
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
|
|
