Digital-electronics 简明教程

Digital Electronics - Comparators

在数字电子学中， comparator 是一种组合逻辑电路，用于比较两个二进制数的大小。比较器用于多种不同的电子电路，例如模数转换器、电压电平检测器、过零检测器等。

In digital electronics, a comparator is a combinational logic circuit that is used to compare the magnitudes of two binary numbers. Comparators are used in several different electronic circuits like analog to digital converters, voltage level detectors, zero-crossing detectors, etc.

比较器最基本的示例是 XNOR 门，它仅在两个输入相等时产生高电平或逻辑 1 输出。

The most basic example of a comparator is an XNOR gate which produces a high or logic 1 output only when both its inputs are equal.

在本章中，我们将学习数字电子学中比较器的基础知识、类型和应用。那么，让我们从比较器的基本定义开始。

In this chapter, we will learn about the basics, types, and applications of comparators in digital electronics. So, let’s start with the basic definition of a comparator.

What is a Comparator?

用于比较两个二进制数字的大小以确定相等或不等的数字组合电路称为比较器。

A digital combinational circuit used to compare the magnitude of two binary numbers to determine the equality or non-equality is called a comparator.

因此，比较器的主要功能是比较输入数字的值并产生输出，指出这些数字是否相等或指定哪个数字更大。

Therefore, the main function of a comparator is to compare the values of input numbers and produce an output indicating whether the numbers are equal or specifies which of the numbers is greater.

借助一个示例，让我们了解比较器的运作方式。

Let us understand the working of a comparator with the help of an example.

考虑两个 3 位二进制数 A2A1A0 和 B2B1B0。如果它们的对应位都重合，则这两个二进制数就被认为相等。换句话说，当 A2 = B2、A1 = B1 和 A0 = B0 时，这两个二进制数相等。

Consider two 3-bit binary numbers A2A1A0 and B2B1B0. These two binary numbers are said to be equal if all their corresponding bits coincide. In other words, these two binary numbers are equal if A2 = B2, A1 = B1, and A0 = B0.

block diagram of a typical comparator 显示在以下图中 −

The block diagram of a typical comparator is shown in the following figure −

这里，A 和 B 是输入位，L、E 和 G 是输出线，其中 L 指示哪个数字较小，E 指示相等，G 指示较大数字。

Here, A and B are the input bits, and L, E, and G are the output lines, where L indicates which number is smaller, E indicates equality, and G indicates the greater number.

Types of Comparators

根据位数，以下是一些数字电路中使用的主要类型比较器 −

Depending on the number of bits, the following are some main types of comparators used in digital circuits −

1-Bit Magnitude Comparator
2-Bit Magnitude Comparator
4-Bit Magnitude Comparator

让我们详细讨论每种类型的比较器。

Let us discuss each type of comparator in detail.

1-Bit Magnitude Comparator

1-bit magnitude comparator 是一种可以比较两个各为一位的二进制数的逻辑电路。它产生的输出指示两个输入数字之间的关系。

A 1-bit magnitude comparator is a logic circuit which can compare two binary numbers of one bit each. It produces an output that indicates the relationship between the two input numbers.

换句话说，1 位幅度比较器就是比较两个 1 位二进制数字并生成一个输出，显示一个数字是否等于或大于或小于另一个。

In other words, a 1-bit magnitude comparator is one that compares two 1-bit binary numbers and generates an output showing whether one number is equal to or greater than or less than the other.

1 位幅度比较器的框图如图所示

The block diagram of a 1-bit magnitude comparator is shown in the following figure −

这里，A 和 B 是 1 位输入数字，L、E 和 G 是输出线路，分别表示 A 和 B 之间小于或等于或大于的关系。

Here, A and B are the 1-bit input numbers, and L, E, and G are the output lines indicating less than or equal to or greater than relationship between A and B respectively.

让我们了解这种类型的比较器的原理。

Let us understand the working this type of comparator.

如果 A = 0 和 B = 0 或 A = 1 和 B = 1，则 A = B。这表示两个二进制数字相等。因此，

If A = 0 and B = 0 or if A = 1 and B = 1, then A = B. It indicates that the two binary numbers are equal. Therefore,

\mathrm{E \: = \: \overline{A} \: \cdot \: \overline{B} \: + \: A \: \cdot \: B \: = \: A \: \odot \: B}

如果 A = 0 和 B = 1，则 A < B。这表示二进制数 A 小于二进制数 B。因此，

If A = 0 and B = 1, then A < B. This indicates that the binary number A is less than the binary number B. Therefore,

\mathrm{L \: = \: \overline{A} \: B}

如果 A = 1 和 B = 0，则 A > B。这表示二进制数 A 大于二进制数 B。因此，

If A = 1 and B = 0, then A > B. It indicates that the binary number A is greater than the binary number B. Therefore,

\mathrm{G \: = \: A \: \overline{B}}

1 位幅度比较器比较输入数字 A 和 B 的相应位。为此，它使用不同类型的逻辑门。

The 1-bit magnitude comparator compares the corresponding bits of the input numbers A and B. For this, it uses different types of logic gates.

1 位幅度比较器的真值表如下所示

The truth table of the 1-bit magnitude comparators is given below −

Inputs	Outputs
A	B
L (A < B)	E (A = B)
G (A > B)	0
0	0
1	0
0	1
1	0
0	1
0	0
0	1
1	1
0	1

我们可以使用此真值表获取 1 位幅度比较器的布尔表达式。

We can use this truth table to obtain the Boolean expression of the 1-bit magnitude comparator.

\mathrm{L \: = \: \overline{A} \: B}

\mathrm{E \: = \: \overline{A} \: \cdot \: \overline{B} \: + \: A \: \cdot \: B \: = \: A \: \odot \: B}

\mathrm{G \: = \: A \: \overline{B}}

1 位幅度比较器的逻辑电路图如图所示。

The logic circuit diagram of the 1-bit magnitude comparator is shown in the following figure.

它包括两个与门、两个非门和一个异或非门。

It consists of two AND gates, two NOT gate, and an XNOR gate.

2-Bit Magnitude Comparator

用于比较两个 2 位二进制数的幅度并确定它们之间关系的数字组合电路称为 2-bit magnitude comparator 。

A digital combinational circuit used to compare the magnitudes of two 2-bit binary numbers and determine the relationship between them is called a 2-bit magnitude comparator.

因此，2 位幅度比较器将两个 2 位二进制数表示的值进行比较，然后生成一个输出，表示一个数字是否等于或大于或小于另一个数字。

Hence, the 2-bit magnitude comparator compares the values represented by two 2-bit binary numbers and then generates an output that indicates whether one number is equal to or greater than or less than the other.

典型的 2 位幅度比较器的框图如图所示

The block diagram of a typical 2-bit magnitude comparator is shown in the following figure −

这里，线路 A0A1 和 B0B1 表示两个 2 位二进制数输入，线路 L、E 和 G 表示小于、等于和大于输出线。

Here, the lines A0A1 and B0B1 represents two 2-bit binary number inputs and the lines L, E, and G represents the less than, equal to, and greater than output lines.

借助以下真值表，我们可以了解 2 位大小比较器的操作 −

We can understand the operation of the 2-bit magnitude comparator with the help of its truth table given below −

Inputs	Outputs
A1	A0
B1	B0
L (A < B)	E (A = B)
G (A > B)	0
0	0
0	0
1	0
0	0
0	1
1	0
0	0
0	1
0	1
0	0
0	0
1	1
1	0
0	0
1	0
0	0
0	1
0	1
0	1
0	1
0	0
1	1
0	1
0	0
0	1
1	1
1	0
0	1
0	0
0	0
0	1
1	0
0	1
0	0
1	1
0	1
0	0
1	0
1	0
1	1
1	0
0	1
1	0
0	0
0	1
1	1
0	1
0	0
1	1
1	1
0	0
0	1
1	1
1	1
0	1

现在，让我们推导出输出 L、E 和 G 的布尔表达式。

Let us now derive the Boolean expression for the outputs L, E, and G.

如果 A0 = B0 且 A1 = B1，则比较器产生输出 A = B 为 E。因此，输出 E 的布尔表达式为，

The comparator produces an output A = B which is E, if A0 = B0 and A1 = B1. Therefore, the Boolean expression for the output E will be,

\mathrm{E \: = \: (A_{0} \: \odot \: B_{0}) \: (A_{1} \: \odot \: B_{1})}

如果满足以下条件，则比较器产生输出 A < B 为 L：

The comparator produces an output A < B which is L, if

A1 = 0 and B1 = 1, OR
A1 = B1 and A0 = 0 and B0 = 1.

从这些陈述中，可以写出输出 L 的布尔表达式如下 −

From these statements, we can write the Boolean expression for the output L as follows −

\mathrm{L \: = \: \overline{A_{1}} \: B_{1} \: + \: (A_{1} \: \odot \: B_{1}) \: \overline{A_{0}} \: B_{0}}

如果满足以下条件，则比较器的输出将为 A > B，即 G：

The output of the comparator will be A > B i.e., G, if

A1 = 1 and B1 = 0, OR
A1 = B1 and A0 = 1 and B0 = 0.

从这些陈述中，输出 G 的布尔表达式为，

From these statements, the Boolean expression for the output G will be,

\mathrm{G \: = \: A_{1} \: \overline{B_{1}} \: + \: (A_{1} \: \odot \: B_{1}) \: A_{0} \: \overline{B_{0}}}

下图显示了 2 位大小比较器的逻辑电路图 −

The following figure shows the logic circuit diagram of the 2-bit magnitude comparator −

4-Bit Magnitude Comparator

4 位大小比较器用于微处理器、微控制器和许多更多复杂的数字电路中。

The 4-bit magnitude comparator is used in more complex digital circuits like microprocessors, microcontrollers, and many more.

它是一种可以比较两个 4 位二进制数的值或大小的比较器，并产生一个输出指示一个数是否等于、小于或大于另一个数。

It is a type of comparator that can compare the values or magnitudes of two 4-bit binary numbers and produce an output indicating whether one number is equal to or less than or greater than the other.

4 位大小比较器的框图示于下图中 −

The block diagram of the 4-bit magnitude comparator is shown in the following figure −

现在，让我们了解这个 4 位大小比较器的原理。为此，设 A = A3A2A1A0 是第一个 4 位二进制数，B = B3B2B1B0 是第二个 4 位二进制数。

Let us now understand the working of this 4-bit magnitude comparator. For that consider A = A3A2A1A0 is the first 4-bit binary number and B = B3B2B1B0 is the second 4-bit binary number.

比较器将显示如下结果 −

The comparator will show the results as follows −

如果两个数字中的所有对应位相等，即 A3 = B3，A2 = B2，A1 = B1 和 A0 = B0，那么比较器会生成输出 A = B，即 E。

The comparator will produce an output A = B which is E, if all the corresponding bits in the two numbers are equal i.e., A3 = B3 and A2 = B2 and A1 = B1 and A0 = B0.

在这种情况下，输出的布尔表达式将是，

In this case, the Boolean expression of the output will be,

\mathrm{E \: = \: (A_{3} \: \odot \: B_{3}) \: (A_{2} \: \odot \: B_{2}) \: (A_{1} \: \odot \: B_{1}) \: (A_{0} \: \odot \: B_{0})}

当满足以下条件时，比较器将生成一个输出 A < B，为 L：

The comparator will produce an output A < B which is L, if

A3 = 0 and B3 = 1, OR
A3 = B3 and if A2 = 0 and B2 = 1, OR
A3 = B3 and if A2 = B2 and if A1 = 0 and B1 = 1, OR
A3 = B3 and if A2 = B2 and if A1 = B1 and if A0 = 0 and B0 = 1.

根据这些陈述，我们可以得到输出 L 的布尔表达式，如下所示：

From these statements, we can derive the Boolean expression for the output L, which is given below.

\mathrm{L \: = \: \overline{A_{3}} \: B_{3} \: + \: (A_{3} \: \odot \: B_{3}) \: \overline{A_{2}} \: B_{2} \: + \: (A_{3} \: \odot \: B_{3}) \: (A_{2} \: \odot \: B_{2}) \: \overline{A_{1}} \: B_{1} \: + \: (A_{3} \: \odot \: B_{3}) \: (A_{2} \: \odot \: B_{2}) \: (A_{1} \: \odot \: B_{1}) \: \overline{A_{0}} \: B_{0}}

当满足以下条件时，比较器将生成一个输出 A > B，为 G：

The comparator produces an output A > B which is G, if

A3 = 1 and B3 = 0, OR
A3 = B3 and if A2 = 1 and B2 = 0, OR
A3 = B3 and if A2 = B2 and if A1 = 1 and B1 = 0, OR
A3 = B3 and if A2 = B2 and if A1 = B1 and if A0 = 1 and B0 = 0.

因此，从这些语句中，我们可以写出输出 G 的布尔表达式，即：

Hence, from these statements, we can write the Boolean expression for the output G which is,

\mathrm{G \: = \: A_{3} \: \overline{B_{3}} \: + \: (A_{3} \: \odot \: B_{3}) \: A_{2} \: \overline{B_{2}} \: + \: (A_{3} \: \odot \: B_{3}) \: (A_{2} \: \odot \: B_{2}) \: A_{1} \: \overline{B_{1}} \: + \: (A_{3} \: \odot \: B_{3}) \: (A_{2} \: \odot \: B_{2}) \: (A_{1} \: \odot \: B_{1}) \: A_{0} \: \overline{B_{0}}}

4 位幅度比较器的逻辑电路实现如下图所示 −

The logic circuit implementation of the 4-bit magnitude comparator is shown in the following figure −

Comparator IC

比较器 IC 是一种集成的电路，它可比较两个二进制数，并根据比较结果生成输出。

A comparator IC is an integrated circuit which is designed to compare two binary numbers and produce an output based on the comparison results.

常用的比较器 IC 是 IC 7485，它是一个 4 位幅度比较器 IC。它广泛用于数字电子应用，用于比较两个 4 位二进制数。

A commonly used comparator IC is IC 7485 which is a 4-bit magnitude comparator IC. It is widely in digital electronic applications to compare two 4-bit binary numbers.

IC 7485 比较两个输入数字的相应位，并确定一个数字是否等于、大于或小于另一个数字。IC 7485 的管脚图显示在下图中。

The IC 7485 compares corresponding bits of the two input numbers and determines whether one number is equal to or greater than or less than the other. The pin diagram of the IC 7485 is depicted in the following figure.

该 IC 广泛用于各种数字电路中，例如微处理器、微控制器、控制系统和算术逻辑单元。

This IC is widely used in various digital circuits such as microprocessors, microcontrollers, control systems, and arithmetic logic units.

Applications of Comparators

比较器是各种数字电路中的基本组件。它们具有比较电压电平和做出决定的能力。

The comparators are fundamental components in various digital circuits. They provide capabilities to compare voltage levels and make decisions.

在数字电子领域中，比较器的一些关键应用如下所列 −

Some of the key applications of comparators in the field of digital electronics are listed below −

Comparators are used to detect changes in voltage levels in electronic circuits.
Comparators are also used temperature monitoring systems.
Comparators are used as zero-crossing detector in various power circuits like phase control circuits, motor and power control circuits, etc.
Comparators are key components in analog to digital converters (ADCs).
In signal conditioning circuits, the comparators are used for amplification and filtering of signals before processing.

Conclusion

总而言之，比较器是一种组合逻辑电路，用于在各种数字电子应用中比较两个类似的数量，例如两个 2 位二进制数或两个电压电平，等等。

In conclusion, a comparator is a combinational logic circuit used in various digital electronic applications to compare two similar quantities like two 2-bit binary numbers or two voltage levels, etc.

比较器帮助我们根据两个输入值的比较做出决策。它们广泛用于几种不同的电子设备和系统中，例如算术逻辑单元、基于微处理器的系统、控制系统、自动化系统和电信系统。

Comparators help us to make decisions based on a comparison of two input values. They are widely used in several different electronic devices and systems such as arithmetic logic units, microprocessor-based systems, control systems, automation systems, and telecommunication systems.

根据特定应用所需的输入位数，我们可以设计 1 位、2 位或 4 位比较器。此外，比较器以集成电路的形式提供。最常用的 IC 比较器是 IC 7485，它是一个 4 位幅度比较器。

Depending on the number of input bits required for a particular application, we can design a 1-bit, 2-bit, or 4-bit comparator. Also, comparators are available in the form of integrated circuit. The most commonly used IC comparator is IC 7485 which is a 4-bit magnitude comparator.