Digital-electronics 简明教程
Implementation of XOR Gate from NOR Gate
为了执行许多逻辑过程，逻辑门是设计数字电路时至关重要的元素。当输入彼此不同时产生高输出的一个这样的门是 XOR（异或）门。本教程将讨论使用 NOR 门创建 XOR 门的一种有趣策略。理解这种实现有助于我们更好地理解逻辑门之间的灵活性和关系。
To carry out numerous logical processes, logic gates are crucial elements in the design of digital circuits. One such gate that generates a high output when the inputs are different from one another is the XOR (Exclusive OR) gate. Using NOR gates to create an XOR gate is an intriguing strategy that will be discussed in this tutorial. Understanding this implementation helps us better grasp the flexibility and relationships between logic gates.
What is a XOR Gate?
另一个在数字电路中经常使用的基本逻辑门是 XOR（异或）门。当有奇数个高输入时，它会产生高输出。换句话说，只有当输入彼此不同时，输出才高。
Another fundamental logic gate that is frequently utilised in digital circuits is the XOR (Exclusive OR) gate. When there are an odd number of HIGH inputs, it generates a HIGH output. To put it another way, the output is only HIGH when the inputs are different from one another.
Truth Table of XOR Gate
双输入异或门的真值表如下 −
A two-input XOR gate’s truth table is as follows −
Input A |
Input B |
Output |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
双输入异或门的布尔表达为 −
The Boolean expression for a two-input XOR gate is −
输出 = A ⊕ B
\mathrm{Output \: = \: A \: \oplus \: B}
其中“⊕”表示 XOR 运算。
Where '$\mathrm{\oplus}$' represents the XOR operation.
NOR Gate
NOR 门是一种执行逻辑析取（OR）然后执行逻辑否定（NOT）的逻辑门。它从两个或更多个输入信号生成一个输出信号。只有当 NOR 门的所有输入都为低（0）时，输出才会为高（1），对于所有其他输入配置，输出都将为低（0）。
A NOR gate is a type of logic gate that executes a logical disjunction (OR) and then a logical negation (NOT). It generates a single output signal from two or more input signals. Only when all of a NOR gate’s inputs are LOW (0) will the output be HIGH (1), and for all other input configurations, the output will be LOW (0).
Truth Table of NOR Gate
双输入 NOR 门的真值表如下 −
A two-input NOR gate’s truth table is as follows −
Input A |
Input B |
Output |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
双输入 NOR 门的布尔表达为 −
The Boolean expression for a two-input NOR gate is −
\mathrm{输出 \: = \: \thicksim \: (A \: + \: B)}
\mathrm{Output \: = \: \thicksim \: (A \: + \: B)}
其中“~”表示逻辑否定（NOT），而“+”表示逻辑析取（OR）。
Where '~' represents logical negation (NOT) and '+' represents logical disjunction (OR).
数字电路中经常使用 NOR 门，可以使用 NOR 门来实现更多逻辑门和复杂的数字电路。由于它们被视为通用门，因此只能使用 NOR 门构建任何其他逻辑门或电路。
Numerous more logic gates and intricate digital circuits can be implemented using NOR gates, which are frequently used in digital circuits. Since they are regarded as universal gates, any other logic gate or circuit can be built only out of NOR gates.
Implementation of XOR Gate from NOR Gate
仅使用 NOR 门创建异或门的电路图至少需要五个 NOR 门。五个以上的 NOR 门也可以包含一个异或门。使用五个 NOR 门实现异或门的原理图显示在附图中。
It takes at least five NOR gates to create the circuit diagram for an XOR gate using only NOR gates. More than five NOR gates can also contain an XOR gate. The schematic for an XOR gate employing five NOR gates is shown in the accompanying figure.
\mathrm{Y \: = \: (A \: \overline{B} \: + \: \overline{A} \: B)}
以下是根据上述电路获得异或门输出的方法 −
Here is how to obtain the output of XOR gate from the above circuit −
最左边的 NOR 门的输入为 A 和 B，其输出为 $\mathrm{\overline{A+B}}$
The leftmost NOR gate has inputs A and B and its output is $\mathrm{\overline{A+B}}$
上 NOR 门的输入为 A 和 $\mathrm{\overline{A+B}}$，输出为 $\mathrm{\overline{A \: + \: \overline{A+B}}}$
Inputs for the upper NOR gate are A and $\mathrm{\overline{A+B}}$ and the output is $\mathrm{\overline{A \: + \: \overline{A+B}}}$
同样，下 NOR 门的输入为 B 和 $\mathrm{\overline{A+B}}$，其输出为 $\mathrm{\overline{B \: + \: \overline{A+B}}}$
Again, the inputs for the lower NOR gate are B and $\mathrm{\overline{A+B}}$ and its output is $\mathrm{\overline{B \: + \: \overline{A+B}}}$
第 4 个 NOR 门的输入是上 NOR 门和下 NOR 门的输出，即 $\mathrm{\overline{A \: + \: \overline{A+B}}}$ 和 $\mathrm{\overline{B \: + \: \overline{A+B}}}$
The inputs for the 4th NOR gate are the outputs of the upper and lower NOR gates i.e. $\mathrm{\overline{A \: + \: \overline{A+B}}}$ and $\mathrm{\overline{B \: + \: \overline{A+B}}}$
第 4 个 NOR 门的输出 = $\mathrm{\overline{\overline{A \: + \: \overline{A+B}} \: + \: \overline{B \: + \: \overline{A+B}}}}$
The output of the 4th NOR gate = $\mathrm{\overline{\overline{A \: + \: \overline{A+B}} \: + \: \overline{B \: + \: \overline{A+B}}}}$
$\mathrm{= \: \overline{\overline{A}\cdot \: \overline{(\overline{A \: + \: B})} \: + \: \overline{B}\cdot \: \overline{(\overline{A \: + \: B})}}}$
$\mathrm{\overline{\overline{A}\cdot \: (A \: + \: B) \: + \: \overline{B}\cdot \: (A \: + \: B)}}$
$\mathrm{\overline{\overline{A}\cdot \: A \: + \: \overline{A}\cdot \: B \: + \: \overline{B}\cdot \: A \: + \: \overline{B}\cdot \: B}}$
$\mathrm{\overline{\overline{A}\cdot \: B \: + \: \overline{B}\cdot \: A}}$
现在，这是最后一个或第 5 个 NOR 门的输入。此 NOR 门将输出作为其输入的逆转。因此，上述电路的最终输出为 $\mathrm{\overline{\overline{B\cdot \overline{A} \: + \: \overline{B}\cdot \: A}}}$ 或 $\mathrm{Y \: = \: (A\cdot \overline{B} \: + \: \overline{A}\cdot \: B)}$
Now, this is the input for the last or 5th NOR gate. This NOR gate gives the output as the inversion of its input. Hence the final output of the above circuit is, $\mathrm{\overline{\overline{B\cdot \overline{A} \: + \: \overline{B}\cdot \: A}}}$ or, $\mathrm{Y \: = \: (A\cdot \overline{B} \: + \: \overline{A}\cdot \: B)}$
这是异或门的输出。因此，上述基于 NOR 门的电路是异或门的电路。
This is the output of the XOR gate. Hence the above NOR gate-based circuit is the circuit of XOR gate.
因此，上述电路的输出与异或门的输出相同。因此，上述电路表示使用 NAND 门的异或门的电路图。
Thus the output of the above circuit is the same as the output of an XOR gate. Hence the above circuit represents the circuit diagram of Exclusive OR gate using NAND gates.