为什么将乘积称为最小项，而总和称为最大项? [英] Why are products called minterms and sums called maxterms?

问题描述

他们有这样做的理由吗?我的意思是，在最小项的总和中，您寻找输出为1的项；我不明白为什么他们称其为"minterms".为什么不使用maxterms，因为1远大于0?

Do they have a reason for doing so? I mean, in the sum of minterms, you look for the terms with the output 1; I don't get why they call it "minterms." Why not maxterms because 1 is well bigger than 0?

背后有我不知道的原因吗?还是我应该接受它而不问为什么?

Is there a reason behind this that I don't know? Or should I just accept it without asking why?

推荐答案

将这些术语称为"minterms"和"maxterms"的约定并不等于1大于0.例如:

The convention for calling these terms "minterms" and "maxterms" does not correspond to 1 being greater than 0. I think the best way to answer is with an example:

假设您有电路，并且由X̄YZ̄ + XȲZ描述.

Say that you have a circuit and it is described by X̄YZ̄ + XȲZ.

此形式由两组组成，每组三个，每组三个是一个'minterm'.minterm表达式的含义是暗示表达式中的每三个组仅具有1的值X，Y和Z的八种可能组合之一以及它们的逆数." http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Logic /Logic2.html

"This form is composed of two groups of three. Each group of three is a 'minterm'. What the expression minterm is intended to imply it that each of the groups of three in the expression takes on a value of 1 only for one of the eight possible combinations of X, Y and Z and their inverses." http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Logic/Logic2.html

因此，最小"是指以下事实:这些术语是构建特定功能所需的最小"术语.如果您想了解更多信息，请在所提供的链接中在更多上下文中解释以上示例.

So what the "min" refers to is the fact that these terms are the "minimal" terms you need in order to build a certain function. If you would like more information, the example above is explained in more context in the link provided.

他们将MIN用于AND，而MAX用于OR的原因是:

在产品总和(您称为AND)中，只有一个最小项必须为true才能使表达式为true. 在和的乘积(您称为OR)中，所有maxterm都必须为true才能使表达式为true.

The "reason they used MIN for ANDs, and MAX for ORs" is that:

In Sum of Products (what you call ANDs) only one of the minterms must be true for the expression to be true. In Product of Sums (what you call ORs) all the maxterms must be true for the expression to be true.

这篇关于为什么将乘积称为最小项，而总和称为最大项?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！