Digital-electronics 简明教程
Difference between NAND Gate and NOR Gate
在数字电子学中，@ {s0} 是作为数字电路中开关器件的所有数字电路的基本构建块。因此，@ {s1} 是用于执行数字器件或系统中多个逻辑运算的数字电路。逻辑门可以接收一个或多个输入，但只能产生一个输出。其中，逻辑门输出由输入信号的组合决定。逻辑门的操作基于@ {s2}。
In digital electronics, logic gates are the basic building blocks of all digital circuits that act as the switching devices in the digital circuits. Therefore, a logic gate is a digital circuit used to perform several logical operations in a digital device or system. A logic gate can accept one or multiple inputs but produces only a single output. Where, the output of a logic gate is determined by the combination of input signals. The operation of the logic gates is based on the Boolean algebra.
如今，逻辑门被用于所有数字电子设备中，例如智能手机、笔记本电脑、计算机、存储器等。有许多类型的逻辑门可用，例如 AND 门、OR 门、NOT 门、NAND 门、NOR 门、XOR 门、XNOR 门等。
These days, logic gates are being used in every digital electronic device such as smartphones, laptops, computers, memories, etc. There are many types logic gates available such as AND gate, OR gate, NOT gate, NAND gate, NOR gate, XOR gate, XNOR gate, etc.
在这里，我们将重点介绍 NAND 门和 NOR 门之间的所有差异。NAND 门和 NOR 门都是@ {s3}，这意味着我们只能使用 NAND 门和 NOR 门来实现任何逻辑表达式。在研究差异之前，让我们从一些基础知识开始。
Here, we will highlight all the differences between NAND gate and NOR gate. Both the NAND gate and the NOR gate are universal logic gates, which means we can implement any logical expression by using the NAND and NOR gates only. Before getting into the differences, let’s start with some basics.
What is a NAND Gate?
NAND 门基本上是NOT 门和 AND 门的组合，即@ {s4}。因此，NAND 门是 AND 门的否定形式。
A NAND gate basically a combination of NOT gate and AND gate, i.e. NOT + AND = NAND. Therefore, the NAND gate is a negated version of AND gate.
对于 NAND 门，当所有输入都为低电平 (0) 或至少有一个输入为低电平时，门输出为高电平 (1)。如果所有输入都为低电平 (0)，则门输出将为高电平 (1)。因此，从解释中可以清楚地看出，NAND 门是 AND 门的完全逆。
For a NAND gate, the output of the gate is high (1), when all of its inputs are low (0) or at least one input is low. If it has all the inputs low (0), then the gate’s output will be high (1). Hence, from the explanation, it is clear that the NAND gate is an exact inverse of the AND gate.
两个输入 NAND 门的逻辑或布尔表达式由下式给出，
The logical or Boolean expression of a two input NAND gate is given by,
\mathrm{Y \: = \: \overline{A \cdot B} \: = \: (A \cdot B)^\prime}
其中，Y 是 NAND 门的输出，而 A 和 B 是二进制输入。
Where, Y is the output of the NAND gate and A and B are the binary inputs.
NAND 门遵循交换律，即
The NAND gate follows the commutative law, i.e.
\mathrm{(A \: \cdot \: B)^\prime \: = \: (B \: \cdot \: A)^\prime}
因此，从 NAND 门的布尔表达式中，我们可以看到，NAND 门的输出是通过将所有输入相乘，然后取乘积的补数来获得的。
Hence, from the Boolean expression of the NAND gate, we can see that the output of the NAND gate is obtained by multiplying all the inputs and then by taking the compliment of the multiplied result.
以下是两个输入 NAND 门的真值表−
The following is the truth table of a two input NAND gate −
Inputs |
AND |
Output |
A |
B |
A·B |
Y = (A·B)' |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
NAND 门用于实现其他逻辑门，制造触发器、寄存器、防盗警报电路、冷冻机报警器等。
NAND gates are used in realizing other logic gates, making flip-flops, registers, burglar alarm circuit, freezer warning buzzer, etc.
What is a NOR Gate?
NOR 门是 NOT 和 OR 门的组合，即@ {s5}。NOR 门由一个 OR 门后跟一个 NOT 门组成。
The NOR gate is a combination of NOT and OR gates, i.e. OR + NOT = NOR. A NOR gate consists of an OR gate followed by a NOT gate.
对于 NOR 门，当所有输入都为低电平 (0) 时，门输出为高电平 (1)。在所有其他情况下，它产生低电平输出。因此，NOR 门只不过是 OR 门的否定形式。
For the NOR gate, the output of the gate is high (1), when all its inputs are low (0). In all other cases, it produces a low output. Thus, the NOR gate is nothing but a negated version of the OR gate.
两个输入 NOR 门的布尔表达式由下式给出，
The Boolean expression of a two input NOR gate is given by,
\mathrm{Y \: = \: \overline{A \: + \: B} \: = \: (A \: + \: B)^\prime}
其中，Y 是门的输出，而 A 和 B 是输入。因此，从 NOR 门的布尔表达式中，可以清楚地看出，门输出可以通过所有输入的逻辑加法获得，然后取加法结果的补数。
Where, Y is the gate’s output and A & B are the inputs. Hence, from the Boolean expression of the NOR gate, it is clear that the gate’s output can be obtained by the logical addition of all the inputs and then taking the complement of the result of addition.
以下是双输入 NOR 门的真值表：
The following is the truth table of a two input NOR gate −
Inputs |
OR |
Output |
A |
B |
A+B |
Y = (A+B)' |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
NOR 门用于实现多个组合式和顺序式数字电路，例如多路复用器、乘法器、计数器等。
The NOR gate is used in the realization of several combinational and sequential digital circuits like multiplexers, multipliers, counters, etc.
Difference between NAND Gate and NOR Gate
NAND 和 NOR 门是通用逻辑门的类型，但是，它们之间存在一些差异，如下表所示：
NAND and NOR gates are types of universal logic gates, however, there are several differences between these that are listed in the following table −
Difference |
NAND Gate |
NOR Gate |
Definition |
A NAND gate is a universal logic gate which performs the negated logical multiplication. |
A NOR gate is a universal logic gate which performs the negated logical addition. |
Implementation |
NAND gate can be implemented by using an AND gate followed by a NOT gate. |
NOR gate can be implemented by using an OR gate followed by a NOT gate. |
Representation |
The operation of NAND gate can be represented by the complimented AND operation, i.e. (·)'. |
The operation of a NOR gate can be represented by the complimented OR operation, i.e. (+)'. |
Boolean Expression |
The Boolean expression of a two input NAND gate is given by, $\mathrm{Y \: = \: \overline{A \cdot B} \: = \: (A \: \cdot \: B)^\prime}$ |
The Boolean expression of a two input NOR gate is given by, $\mathrm{Y \: = \: \overline{A \: + \: B} \: = \: (A \: + \: B)^\prime}$ |
Low Output |
The NAND gate produces a low (0) output, when all its inputs are high. |
The NOR gate produces a low (0) output, when all its inputs or at least one input is high (1). |
High Output |
The NAND gate produces a high (1) output, when all its inputs or at least one input is low (0). |
The NOR gate produces a high (1) output, when all its inputs are low (0). |
Applications |
The NAND gate is used in constructing other logic gates, making flip-flops, registers, implementing burglar alarm circuit, freezer warning buzzer, etc. |
The NOR gate is used in the implementation of various combinational and sequential digital circuits like multiplexers, multipliers, counters, etc. |