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分布式映射与集中式映射_K映射上的表达式映射和组包围

發布時間：2025/3/11 编程问答 42 豆豆

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分布式映射與集中式映射

In the previous article (Karnaugh Map 2, 3 and 4- variable) we have already discussed the designing of K-Map and various forms in which they are represented based on either they are being mapped for minterm or maxterm.

在上一篇文章( 卡諾地圖2、3和4-變量 )中，我們已經討論了K-Map的設計以及基于將它們映射為minterm或maxterm來表示它們的各種形式。

In this article, we will be studying about, how do we map these minterm and maxterm expressions on the K-Map and how to encircle them into groups?

在本文中，我們將研究如何在K-Map上映射這些最小項和最大項表達式，以及如何將它們包圍成組？

In this article, the convention that will be followed is for mapping minterm expressions. Since minterm and maxterm expressions have a complementary relationship [ (POS of F) = (SOP of F')' ] we can also use minterm expressions to solve maxterm problems doing some manipulations.

在本文中，將遵循的約定是映射最小項表達式。由于minterm和maxterm表達式具有互補關系[(F的POS)=(F'的SOP)']，我們還可以使用minterm表達式進行一些操作來解決maxterm問題。

During mapping of expressions on K-Map, one thing to be kept in the notice is that the upper LHS alphabet of K-Map always represents the MSB bits and the alphabets on the upper RHS denote LSB bits. For Ex: If we want to map m7 (7 is represented as 111 in Binary or in terms of minterms as ABC) on 3-variable K-Map, then A bit is the MSB bit and C is the LSB bit.

在K-Map上映射表達式時，需要注意的一件事是，K-Map的高位LHS字母始終代表MSB位，高位RHS上的字母代表LSB位。對于Ex：如果要在3變量K映射上映射m7 ( 7以二進制表示為111或以最小項表示為ABC)，則A位是MSB位， C位是LSB位。

While mapping SOP expression, we put 1's in the blocks representing minterms in the K-Maps and 0's elsewhere.

在映射SOP表達式時，我們在K-Map中代表最小項的塊中放入1，在其他地方將0放入。

While mapping POS expression, we put 0's in the blocks representing max terms in the K-Maps and 1's elsewhere.

在映射POS表達式時，我們在代表最大項的K-Maps塊中放置0，在其他地方放置1。

在K地圖中對團體進行包圍 (Encircling of Groups in a K-Map)

After we map expressions in the K-Map, we encircle pairs, quads, and octets of 1's in the K-Map for the purpose of simplification of Boolean expressions.

在K-Map中映射表達式后，為了簡化布爾表達式，在K-Map中將1的對，四邊形和八位組圈起來。

a)對 (a) Pairs)

In 2, 3 and 4-variable K-Map, two adjacent 1's placed either vertically or horizontally are encircled. It is to be noted that diagonally adjacent 1's are never encircled.

在2、3和4變量K映射中，垂直或水平放置的兩個相鄰1被包圍。應當注意，對角相鄰的1永遠不會被包圍。

b)四邊形 (b) Quads)

In the K-Map, if four 1's are adjacent either vertically, horizontally or in the shape of a square, then these are encircled together.

在K-Map中，如果四個1在垂直，水平或正方形的方向上相鄰，則將它們圍在一起。

c)八位字節 (c) Octets)

The eight adjacent 1's are encircled in a K-Map are known as octets. They can be present either vertically or horizontally.

在K-Map中環繞的八個相鄰的1被稱為八位位組。它們可以垂直或水平存在。

d)重疊組 (d) Overlapping Groups)

While circling the group of 1's, it is always kept in mind to encircle the group which has the largest number of 1's together, i.e., Octets are encircled first, then quads and pairs follow in the order. It is also possible that the same 1 may be used in more than one encircled group, these groups are known as overlapped groups.

環繞1的組時，始終牢記將具有最大1的組一起環繞，即，首先環繞八位字節，然后依次按四邊形和對。也可以在一個以上的環繞組中使用相同的1，這些組稱為重疊組。

e)滾動組 (e) Rolling Groups)

While making a group of the largest number of 1's, it is possible to roll the K-Map. Rolling of groups can be made in such a way that LHS of the K-Map touches the RHS and top of the K-Map touches the bottom of the K-Map. Rolling is shown by half encircling the group on both sides. Rolling can be done to make obtain octet, quad or pair.

制作數量最多的一組1時，可以滾動K-Map。可以按以下方式進行組滾動：K-Map的LHS接觸RHS，K-Map的頂部接觸K-Map的底部。滾動顯示為在組的兩側都將其包圍。可以滾動以獲得八位位組，四位或四位。

f)冗余組 (f) Redundant Groups)

While encircling the groups there may be a possibility that all the 1's of some group/groups are overlapped by other groups. Such a group is known as redundant groups, we need to eliminate these redundant groups. In the following given circle, the dotted encircled circle is the redundant circle, since all its elements are already covered in other groups.

在包圍組時，某些組的所有1可能被其他組重疊。這樣的組稱為冗余組，我們需要消除這些冗余組。在下面的給定圓中，帶圓圈的圓是多余的圓，因為其所有元素已經被其他組覆蓋。

Example 1: Map the Boolean function, F (A, B, C) = ∑ (1, 2, 5, 6) on three- variable K-Map and also encircle them into proper groups.

示例1：將布爾函數F(A，B，C)= ∑(1、2、5、6)映射到三變量K-Map上，并將它們圍成適當的組。

Solution:

解：

From the above given Boolean function, we can infer that it is an expression for minterms. So, we will draw a K-Map used for SOP representation and place 1's where minterms are provided.

從上面給出的布爾函數，我們可以推斷出它是最小項的表達式。因此，我們將繪制用于SOP表示的K-Map，并在提供最小項的位置放置1。

Example 2: Map the Boolean function, F (w, x, y, z) = ∑ (1, 3, 5, 7, 8, 9, 10, 11, 12, 14) on four variable K-Map and also encircle them into proper groups.

示例2：將布爾函數F(w，x，y，z)= ∑(1、3、5、7、8、9、10、11、12、14)映射到四個變量K-Map上，并對其進行環繞將它們分成適當的組。