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

分布式映射与集中式映射

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( 卡诺地图2、3和4-变量 )中，我们已经讨论了K-Map的设计以及基于将它们映射为minterm或maxterm来表示它们的各种形式。

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，我们将研究如何在K-Map上映射这些最小项和最大项表达式，以及如何将它们包围成组？

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，将遵循的约定是映射最小项表达式。由于minterm和maxterm表达式具有互补关系[(F的POS)=(F'的SOP)']，我们还可以使用minterm表达式进行一些操作来解决maxterm问题。
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上映射表达式时，需要注意的一件事是，K-Map的高位LHS字母始终代表MSB位，高位RHS上的字母代表LSB位。对于Ex：如果要在3变量K映射上映射m7 ( 7以二进制表示为111或以最小项表示为ABC)，则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表达式时，我们在K-Map中代表最小项的块中放入1，在其他地方将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表达式时，我们在代表最大项的K-Maps块中放置0，在其他地方放置1。

在K地图中对团体进行包围 (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中映射表达式后，为了简化布尔表达式，在K-Map中将1的对，四边形和八位组圈起来。

a)对 (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变量K映射中，垂直或水平放置的两个相邻1被包围。应当注意，对角相邻的1永远不会被包围。

b)四边形 (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，如果四个1在垂直，水平或正方形的方向上相邻，则将它们围在一起。

c)八位字节 (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中环绕的八个相邻的1被称为八位位组。它们可以垂直或水平存在。

d)重叠组 (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.

环绕1的组时，始终牢记将具有最大1的组一起环绕，即，首先环绕八位字节，然后依次按四边形和对。也可以在一个以上的环绕组中使用相同的1，这些组称为重叠组。

e)滚动组 (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.

制作数量最多的一组1时，可以滚动K-Map。可以按以下方式进行组滚动：K-Map的LHS接触RHS，K-Map的顶部接触K-Map的底部。滚动显示为在组的两侧都将其包围。可以滚动以获得八位位组，四位或四位。

f)冗余组 (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.

在包围组时，某些组的所有1可能被其他组重叠。这样的组称为冗余组，我们需要消除这些冗余组。在下面的给定圆中，带圆圈的圆是多余的圆，因为其所有元素已经被其他组覆盖。

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：将布尔函数F(A，B，C)= ∑(1、2、5、6)映射到三变量K-Map上，并将它们围成适当的组。

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.

从上面给出的布尔函数，我们可以推断出它是最小项的表达式。因此，我们将绘制用于SOP表示的K-Map，并在提供最小项的位置放置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：将布尔函数F(w，x，y，z)= ∑(1、3、5、7、8、9、10、11、12、14)映射到四个变量K-Map上，并对其进行环绕将它们分成适当的组。

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.

从上面给出的布尔函数，我们可以推断出它是最小项的表达式。因此，我们将绘制用于SOP表示的K-Map，并在提供最小项的位置放置1。