| 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 |
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. mapa de karnaugh 4 variables
| | 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)| | AB\CD | 00 | 01 | 11
1. Introduction: Why a 4-Variable K-Map? Boolean algebra is powerful, but algebraic simplification becomes error-prone and time-consuming with 4 or more variables. The Karnaugh Map (K-map) provides a visual, graphical method to simplify logic expressions. For 4 variables (typically labeled A, B, C, D ), the K-map is a 4×4 grid of 16 cells, each representing a unique minterm (product term) or maxterm (sum term). Its core power lies in exploiting adjacency to eliminate variables via the Boolean law: ( X + \overlineX = 1 ). 2. Structure of the 4-Variable K-Map 2.1 The Grid Layout Unlike a simple 2D matrix, the K-map uses Gray code ordering (only one bit changes between adjacent cells). This ensures that moving to any adjacent cell horizontally or vertically changes exactly one variable. Its core power lies in exploiting adjacency to
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.