> For the complete documentation index, see [llms.txt](https://yingshaoxo.gitbook.io/university-notes/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yingshaoxo.gitbook.io/university-notes/digital-electronic-technology/karnaugh-map.md).

# Karnaugh map

> The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions.

For me, I don't think `karnaugh map` is very important at all. (just think about any one of modern programming language, and you will know what I'm feeling)

So I just want to give a picture with a few words. (Chinese book may not the same with what I show you, it's OK, you have to know China usually don't follow the International Standard, it may because of 知识分子素质太差，一叶樟木，井低观天)

![](https://2889346953-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-Le4Kw7maZEabKFjsC7z%2F-Lf5hWWAPXrS6pkg310z%2F-Lf5hl3bKICpG-LQQ2HR%2FKarnaugh_map.png?generation=1558112048577986\&alt=media)

Here if we set $$1$$ as $$A$$, then $$0$$ is $$\overline{A}$$

Here if we set $$1$$ as $$B$$, then $$0$$ is $$\overline{B}$$

Here $$CD$$ or $$AB$$ both connected to the line besides it.

So you can represent $$m7$$ as $$\overline{A}BCD(01 11)$$，$$m13$$ as $$AB\overline{C}D(1101)$$

Google for more information. or if you know Chinese very well, see following.

1. 翻出你的教材对照着看
2. 该表是个球体，x与y是相连的
3. 为了最简，同一个方格最好只被圈一次
4. 0、1同时出现在`一竖或一横`，消去；`一横或一竖`出现相同的`0或1`，保留
5. 先读AB, 竖着；再读CD，横着（反正随你的图而变）
6. `田字四格`化简程度大于`两个相邻格`

update

1. 翻出你的教材对照着看
2. 该表是个“救生圈”，x与y是相连的，四个角也是相连的(可以连成一个田字格)

   ![](https://2889346953-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-Le4Kw7maZEabKFjsC7z%2F-Lf5hWWAPXrS6pkg310z%2F-Lf5hl3eTn5Ov9_I9bWj%2FKarnaugh_circle.png?generation=1558112048515212\&alt=media)
3. 8 > 4 > 2，这里的数字指的是每个圈所圈住的相邻项的个数，尽可能用大圈
4. 为了最简，圈的次数尽量要少
5. 0、1同时出现在`一竖或一横`，消去；`一横或一竖`出现相同的`0或1`，保留
6. 先读AB, 竖着；再读CD，横着（反正随你的图而变）