Digital-electronics 简明教程
AND Gate in Digital Electronics
在数字电子中，有几种不同类型的逻辑门，例如与门、或门、非门等。在本章中，我们将解释 theory of AND gate 。
In digital electronics, there are several different types of logic gates such as AND gate, OR gate, NOT gate, etc. In this chapter, we will explain the theory of AND gate.
与门是一种基本逻辑门，用于实现各种复杂的数字电路和系统。与门对施加在其上的输入执行逻辑乘法，并相应地产生输出。
An AND gate is a basic logic gate used to implement various complex digital circuits and systems. The AND gate performs the logical multiplication of inputs applied to it and produces an output accordingly.
What is an AND Gate?
AND gate 是用于各种数字电路和系统的一种基本逻辑门。它仅当所有输入均为高电平或逻辑 1 或真时才会产生高电平或逻辑 1 或真输出。对于所有其他输入组合，它会产生低电平或逻辑 0 或假输出。
An AND gate is a type of basic logic gate used in various digital circuits and systems. It produces a high or logic 1 or True output, only when all its inputs are high or logic 1 or true. For all other combinations of inputs, it produces a low or logic 0 or False output.
两个和三个输入与门的逻辑符号如下图所示。
The logic symbols for the two and three input AND gates are depicted in the following figure.
此处， A, B 和 C 是输入变量， Y 是输出变量。
Here, A, B, and C are the input variables and Y is the output variable.
在本章中，我们将仅介绍具有三个输入的与门。但是，我们可以针对任何数量的输入变量设计一个与门。
In this chapter, we will cover AND gates having three inputs only. But we can design an AND gate for any number of input variables.
Truth Table of AND Gate
与门的真值表包含输入和输出，并指定它们之间的关系。
The truth table of an AND gate contains inputs and outputs, and specifies the relationship between them.
下面给出两输入与门的真值表 −
The truth table of a two-input AND gate is given below −
Input |
Output |
A |
B |
Y |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
从这个两输入与门的真值表可以看出，只有当两个输入都为逻辑 1 或高时，与门的输出才为逻辑 1 或高。
From this truth table of two-input AND gate, it can be observed that the output of the AND gate is logic 1 or high, only when both inputs are logic 1 or high.
下表表示 three-input AND gate 的真值表 −
The following table represents the truth table of a three-input AND gate −
Input |
Output |
A |
B |
C |
Y |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
此真值表显示，只有当与门的所有三个输入都为高电平或逻辑 1 时，输出才为高电平或逻辑 1。对于其他输入组合，输出为低电平或逻辑 0。
This truth table shows that the output is high or logic 1 only when all the three inputs to the AND gate are high or logic 1. For rest input combinations, the output is low or logic 0.
从这些与门的真值表中，我们可以得出结论，只有当与门的所有输入都为高电平或逻辑 1 时，与门才会产生高电平或逻辑 1 输出，否则输出为低电平或逻辑 0。
From these truth tables of AND gate, we can conclude that an AND gate produces a high or logic 1 output, only when all its inputs are high or logic 1, otherwise the output is low or logic 0.
Working of AND Gate
下面解释了两个输入与门的运作方式 −
The working of a two-input AND gate is explained below −
-
If A = 0 and B = 0, the output is low i.e., Y = 0.
-
If A = 0 and B = 1, the output is low i.e., Y = 0.
-
If A = 1 and B = 0, the output is low i.e., Y = 0.
-
If A = 1 and B = 1, the output is high i.e., Y = 1.
以下是三输入与门的工作原理 −
The working of a three-input AND gate is explained below −
-
If A = 0, B = 0, and C = 0, the output is low i.e., Y = 0.
-
If A = 0, B = 0, and C = 1, the output is low i.e., Y = 0.
-
If A = 0, B = 1, and C = 0, the output is low i.e., Y = 0.
-
If A = 0, B = 1, and C = 1, the output is low i.e., Y = 0.
-
If A = 1, B = 0, and C = 0, the output is low i.e., Y = 0.
-
If A = 1, B = 0, and C = 1, the output is low i.e., Y = 0.
-
If A = 1, B = 1, and C = 0, the output is low i.e., Y = 0.
-
If A = 1, B = 1, and C = 1, the output is high i.e., Y = 1.
以上是两输入和三输入与门的工作原理。
This is all about working of a two-input and a three-input AND gates.
Boolean Expression of AND Gate
布尔表达式是逻辑方程或指定 AND 门输入与输出之间数学关系的逻辑函数。
Boolean expression is a logic equation or a logic function that represents the mathematical relationship between inputs and output of the AND gate.
一个双输入 AND 门的布尔表达式为，
The Boolean expression of a two-input AND gate is given by,
Y = A · B
其中 A 和 B 是输入， Y 是输出。此表达式解读为“Y 等于 A 与 B”。句点 (·) 符号代表 AND 运算。
Where, A and B are inputs and Y is the output. This expression is read as "Y is equal to A AND B." The dot (·) symbol represents the AND operation.
对于三输入 AND 门，布尔表达式为，
For the three-input AND gate, the Boolean expression is given by,
Y = A · B · C
解读为“Y 等于 A 与 B 与 C”。
It is read as "Y is equal to A AND B AND C".
同样，我们可以获得任何数量的输入变量的与门布尔表达式。
In the same way, we can obtain the Boolean expression for an AND gate having any number of input variables.
AND Gate using Transistor
两个输入与门的晶体管电路如下图所示。
The transistor circuit of a two-input AND gate is shown in the following figure.
使用晶体管实现与门需要与输入数量一样多的晶体管。例如，两输入与门需要两个晶体管。
The implementation of AND gate using transistors requires as many transistors as the number of inputs. For example, a two-input AND gate requires two transistors.
Working of Transistor AND Gate
上图所示晶体管与门的工作原理如下解释：
The working the transistor AND gate shown in the above figure is explained below −
@ {s0}，晶体管 Q1 和 Q2 保持关断状态并充当开路开关。因此，输出线 Y 将直接连接到接地电位。因此，输出为低电平或逻辑 0。
When both inputs A and B are low, the transistors Q1 and Q2 remain in off state and act as open switch. Therefore, the output line Y will directly connect to the ground potential. Thus, the output is low or logic 0.
@ {s1}，第一个晶体管 Q1 断开，第二个晶体管 Q2 导通。但电源电压仍然不会连接到输出线，输出线将保持接地电位。因此，输出为低电平或逻辑 0。
When the input A is low and the input B is high, the first transistor Q1 is off and the second transistor Q2 is on. But still the supply voltage will not connect to the output line and the output line will remain at ground potential. Consequently, the output is low or logic 0.
@ {s2}，晶体管 Q1 将导通，晶体管 Q2 将保持关断。在这种情况下，输出线接收不到电源电压，但连接到接地电位。因此，对于此输入组合，输出为低电平或逻辑 0。
When the input A is high and the input B is low, the transistor Q1 will conduct and the transistor Q2 will remain off. In this condition, the output line does not receive the supply voltage but connect to the ground potential. Hence, for this input combination, the output is low or logic 0.
@ {s3}，晶体管 Q1 和 Q2 都将导通并充当闭合开关。在这种情况下，电源电压直接连接到输出线。这使得电路的输出为高电平或逻辑 1。
When both inputs A and B are high, both transistors Q1 and Q2 will turn on and act as closed switches. In this condition, the supply voltage directly connect to the output line. This makes output of the circuit high or logic 1.
这是上文提到的晶体管电路如何充当两输入与门的原因。我们可以添加更多的晶体管来实现高阶与门。
This is how the above transistor circuit acts a two-input AND gate. We can add more transistors to implement a high order AND gate.
AND Gate using Switches
我们还可使用电池、开关和灯或灯泡来实现与非门逻辑。下图显示了使用开关的与门。
We can also implement AND gate logic using a battery, switches, and a lamp or bulb. The following figure shows the AND gate using switches.
在这个与门电路中，我们有一个电压源、两个开关代表与门的两个输入端，还有一个灯代表输出。
In this AND gate circuit, we have a voltage source, two switches representing two input terminals of the AND gate, and a lamp representing the output.
从该电路可以看出，如果开关 A 和 B 都闭合，电流将有一个闭合通路在电路中流动。因此，灯将发光，代表高电平或逻辑 1 输出。
From the circuit, we see that if both switches A and B are closed, there will be a closed for current to flow in the circuit. Hence, the lamp will glow that represents the high or logic 1 output.
如果两个开关中的一个或两个都断开，电流通路将断开，使灯熄灭。这表示与门输出的低电平或逻辑 0 状态。
If both or any of the two switches be open, there will be a break in the current path, making the lamp off. This represents the low or logic 0 state of the output of the AND gate.
通过这种方式，上述开关电路执行与非门操作。通过串联添加更多数量的开关，我们可以实现高阶与非门。
This way, the above depicted switching circuit performs the AND gate operation. By adding more number of switches in series, we can implement a higher order AND gate.
AND Gate IC
在实践中，有一个集成电路，即 IC 7408，它是最常用的与非门 IC。此与非门 IC 在晶体管晶体管逻辑 (TTL) 中实现。与非门 IC 7408 的框图如下图所示。
In practice, there is an integrated circuit namely, IC 7408 which is a most commonly used AND gate IC. This AND gate IC is implemented in transistor-transistor logic (TTL). The block diagram of the AND gate IC 7408 is shown in the following figure.
它是一个四与非门 IC，在一个芯片上集成了四个两输入与非门。它有 14 个引脚。
It is a Quad-2 AND gate IC having four two-input AND gates integrated on a single chip. It has 14 pins.
Conclusion
总之，与非门是一个基本逻辑门，用于数字电路中实现布尔乘法功能。
In conclusion, the AND gate is a fundamental logic gate used in digital circuits to implement the Boolean multiplication function.
只有当与非门的所有输入都为高电平或逻辑 1 时，输出才为高电平或逻辑 1。否则，它会产生低电平或逻辑 0 输出。
The output of the AND gate is high or logic 1 only when all its inputs are high or logic 1. Otherwise, it generates a low or logic 0 output.
与非门在各种数字电子应用中发挥着重要作用，例如数据处理、存储器设备、算术逻辑单元、控制系统等。
AND gate plays an important role in various digital electronic applications such as data processing, memory devices, arithmetic logic units, control systems, and more.