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Exercise

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?

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    $\begingroup$ 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. $\endgroup$ Dec 12, 2017 at 17:43
  • $\begingroup$ @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. $\endgroup$
    – O'Niel
    Dec 12, 2017 at 19:51

1 Answer 1

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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. That is the reason why blocks grow in integer powers of two and double their size in every merge step.

A single cell corresponds to a minterm with the full number of input variables.

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