← ProblemsCircuits / Combinational Logic / Karnaugh Map to Circuit
K-map: checkerboard
15%kmapboolean-algebraImplement the circuit described by the Karnaugh map below.
| a'b' | a'b | ab | ab' | |
|---|---|---|---|---|
| c'd' | 0 | 1 | 0 | 1 |
| c'd | 1 | 0 | 1 | 0 |
| cd | 0 | 1 | 0 | 1 |
| cd' | 1 | 0 | 1 | 0 |
This map is a perfect checkerboard: no two 1s are ever adjacent, so no group larger than a single cell exists and a plain sum-of-products needs eight 4-literal minterms. Maps like this are a strong hint that the function has a much simpler non-SOP form — notice that out is 1 exactly when an odd number of the inputs are 1.