Two-Variable K-Map: Identify All Groups Including the All-Ones Case
Logic synthesis tools routinely reduce redundant logic networks down to constant voltage lines to save power and area.
Two distinct 2-variable Karnaugh maps are shown below. Map 1 represents a standard logic function. Map 2 represents a degenerate case where all cells are populated with 1s. The inputs are A and B, where A is the most significant bit.
Map 1 | A \ B | 0 | 1 | |---|---|---| | 0 | 1 | 1 | | 1 | 0 | 0 |
Map 2 | A \ B | 0 | 1 | |---|---|---| | 0 | 1 | 1 | | 1 | 1 | 1 |
Extract the minimal Sum of Products expression for each map. Identify how grouping rules apply when the entire map is covered.
Constraints
- The variables are
AandB. - Expressions must be in minimal Sum of Products (SOP) form.
- Use the tick mark (
') for negation, such asA'.
Topics
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