| AB\CD | 00 | 01 | 11 | 10 | |-------|----|----|----|----| | 00 | 1 | 1 | 0 | 1 | | 01 | 0 | 1 | 0 | 0 | | 11 | 0 | 0 | 0 | 0 | | 10 | 1 | 1 | 0 | 1 |
Check if redundant: ( ABCD ) is covered by ( A\overlineD )? No, because D=1 in ABCD, so not covered. Correct. | Group size (cells) | Variables eliminated | Example term | |--------------------|----------------------|--------------| | 1 | 0 | ( ABCD ) | | 2 | 1 | ( ABC ) (D eliminated) | | 4 | 2 | ( AB ) (C, D eliminated) | | 8 | 3 | ( A ) (B, C, D eliminated) | | 16 | 4 | 1 (always true) | 11. Conclusion The 4-variable Karnaugh map is a powerful, intuitive tool for simplifying medium-complexity logic functions. Mastering it requires practice in identifying non-obvious adjacencies (corners, wraparound) and optimally grouping cells. For circuits up to 4 inputs, it is faster and less error-prone than algebraic reduction. Beyond 4 variables, the method extends to 5 and 6 variables using multiple maps, but for larger designs, algorithmic methods become necessary. Nevertheless, the K-map remains an essential conceptual bridge between truth tables and minimal logic circuits.
| | 00 | CD 01 | CD 11 | CD 10 | | :--- | :---: | :---: | :---: | :---: | | AB 00 | m0 (0000) | m1 (0001) | m3 (0011) | m2 (0010) | | AB 01 | m4 (0100) | m5 (0101) | m7 (0111) | m6 (0110) | | AB 11 | m12 (1100)| m13 (1101)| m15 (1111)| m14 (1110)| | AB 10 | m8 (1000) | m9 (1001) | m11 (1011)| m10 (1010)|
When in doubt, draw the 4×4 grid, label axes in Gray code, and look for the biggest symmetrical blocks of 1s (or 0s) — the map will reveal the minimal form visually.