A 3-variable K-map has 2³ = 8 cells, arranged as 2 rows by 4 columns. Rows are A; columns are BC in gray code order:
- A = 0:
m0m1m3m2 - A = 1:
m4m5m7m6
Notice m3 comes before m2, and m7 before m6. That is the Gray order of the columns, 00, 01, 11, 10. To place a minterm, write it in binary: the first bit picks the row and the last two pick the column. m3 = 011 sits in row A = 0, column BC = 11.
Every cell has exactly three neighbors: one above or below, and one on each side, counting the wrap between the first and last columns.
Group sizes and term lengths:
- 1 cell → 3 literals
- 2 cells → 2 literals
- 4 cells → 1 literal (a full row, a 2×2 square, or the four end cells)
- 8 cells → the constant 1
Some books draw this map tall instead, with BC down the side and A across the top. The groups and answers come out the same; only cell positions differ (see k map layout).
| A\BC | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 0 | 1m0 | 0m1 | 0m3 | 1m2 |
| 1 | 0m4 | 1m5 | 1m7 | 0m6 |