# Karnaugh's map single dot

I had to create a DNF from table c. Which results in 'p'q'r + 'p'qr + pq'r.

Than I had to create Karnaugh's map from it, resulting in:

+----+----+-----+------+-----+
|    | QR | 'QR | 'Q'R | Q'R |
+----+----+-----+------+-----+
| P  |    |     |      | x   |
+----+----+-----+------+-----+
| 'P |    | x   | x    |     |
+----+----+-----+------+-----+


x is representing a dot.

I can connect the two x's on the bottom row, and I can connect the single x on the top row to itself, because it's still a power of 2. 1 ^ 2 = 1.

But how can I write that down in formula? The two connected x's give: 'p'q, but what does that single dot give? PQ'R? Because it has no 'changing variable' in the Karnaugh map.

tl;dr: Handling single dots in Karnaugh's map?

• Your assumption is correct: PQ'R. Whenever you merge two adjacent cells or blocks, you omit the differentiating variable and get an expression with fewer literals. A single cell corresponds to a minterm with the full number of input variables. Dec 12, 2017 at 17:43
• @AxelKemper Thanks a lot! Your answer was very clear! If you want you can put your comment in an answer and I'll accept it. Dec 12, 2017 at 19:51

Your assumption is correct: PQ'R.