![BBC NW_Tech Facilities_30 Odd Yrs Ago [J].pdf](https://cdn.slidesharecdn.com/ss_thumbnails/bbcnwtechfacilities30oddyrsagoj-250830230619-0d747bd6-thumbnail.jpg?width=560&fit=bounds)
2.karnaugh map
- 1. Karnaugh map By Md. Fazle Rabbi 16CSE057
- 2. 4.2 • The Karnaugh map, also known as the K-map, is a method to simplify Boolean algebra expressions. • The Karnaugh map reduces the need for extensive calculations by taking advantage of humans‘ pattern-recognition capability. Karnaugh map
- 3. 4.3 Rules of Simplification • Groups may not include any cell containing a zero • Groups may be horizontal or vertical, but not diagonal
- 4. 4.4 • Groups must contain 1, 2, 4, 8, or in general 𝟐𝒏 cells. That is if n = 1, a group will contain two 1's since 𝟐𝟏 = 2. If n = 2, a group will contain four 1's since 𝟐𝟐 = 4. Rules of Simplification
- 5. 4.5 Rules of Simplification • Each group should be as large as possible • Each cell containing a one must be in at least one group.
- 6. 4.6 Rules of Simplification • Groups may overlap.
- 7. 4.7 Rules of Simplification • Groups may wrap around the table. The leftmost cell in a row may be grouped with the rightmost cell and the top cell in a column may be grouped with the bottom cell.
- 8. 4.8 • There should be as few groups as possible, as long as this does not contradict any of the previous rules Rules of Simplification
- 9. 4.9 • No zeros allowed. • No diagonals. • Only power of 2 number of cells in each group. • Groups should be as large as possible. • Every one must be in at least one group. • Overlapping allowed. • Wrap around allowed. • Fewest number of groups possible Summary
- 11. 4.11 The 3 Variable K-Map
- 12. 4.12 The 4 Variable K-Map
- 13. 4.13 K-Map SOP Minimization • The K-Map is used for simplifying Boolean expressions to their minimal form. • A minimized SOP expression contains the fewest possible terms with fewest possible variables per term. • Generally, a minimum SOP expression can be implemented with fewer logic gates than a standard expression.
- 14. 4.14 Determining the Minimum SOP Expression from the Map
- 15. 4.15 Don’t Care Conditions • A don’t care condition, marked by (X) in the truth table, indicates a condition where the design doesn’t care if the output is a (0) or a (1). • A don’t care condition can be treated as a (0) or a (1) in a K-Map. • Treating a don’t care as a (0) means that you do not need to group it. • Treating a don’t care as a (1) allows you to make a grouping larger, resulting in a simpler term in the SOP equation.
- 17. 4.17 K-map Simplification of POS Expression