Digital-electronics 简明教程
Implementation of XNOR Gate using NOR Gate
NOR 门是一种通用逻辑门类型，因此我们可以仅仅利用 NOR 门来实现 XNOR 逻辑函数。
The NOR gate is a type of universal logic gate, hence we can use only NOR gates to realize the XNOR logic function.
Designing an XNOR Gate using NOR Gate
为了利用 NOR 门设计 XNOR 门，我们首先根据 NOR 逻辑以如下形式导出 XNOR 逻辑函数：
To design an XNOR gate using NOR gate, we first derive the XNOR logic function in terms of NOR logic as follows.
XNOR 门的输出由下式给出：
The output of XNOR gate is given by,
\mathrm{Y \: = \: AB \: + \: \bar{A} \: \bar{B}}
为了利用 NOR 门实现 XNOR 门逻辑，我们至少需要 4 个 NOR 门。NOR 门的 XNOR 门电路图描述如下图：
To implement an XNOR gate logic using NOR gate, we require a minimum of 4 NOR gates. The circuit diagram of XNOR gate from NOR gate is depicted in the following figure:
在此电路中，输出为
In this circuit, the output is
\mathrm{Y \: = \: \overline{\overline{A \: + \: \overline{(A \: + \: B)}} \: + \: \overline{B \: + \: \overline{(A \: + \: B)}}}}
\mathrm{Y \: = \: \overline{\overline{A \: + \: \overline{(A \: + \: B)}}} \: \cdot \: \overline{ \overline{B \: + \: \overline{(A \: + \: B)}}}}
\mathrm{Y \: = \: (A \: + \: \overline{(A \: + \: B)}) \: \cdot \: (B \: + \: \overline{(A \: + \: B)})}
\mathrm{Y \: = \: (A \: + \: (\bar{A} \: \cdot \: \bar{B})) \: (B \: + \: (\bar{A} \: \cdot \: \bar{B}))}
\mathrm{Y \: = \: (A \: + \: \bar{A}) \: (A \: + \: \bar{B}) \: (\bar{A} \: + \: B) \: (B \: + \: \bar{B})}
\mathrm{Y \: = \: (A \: + \: \bar{B}) \: (\bar{A} \: + \: B)}
\mathrm{Y \: = \: A\cdot\bar{A} \: + \: \bar{A}\cdot\bar{B} \: + \: A\cdot B \: + \: B\cdot\bar{B}}
\mathrm{\therefore \: Y \: = \: A\cdot B \: + \: \bar{A}\cdot\bar{B}}
这是 XNOR 门的预期输出。因此，上面所示的 NOR 逻辑电路执行 XNOR 操作。
This is the desired output of the XNOR gate. Thus, the above shown NOR logic circuit performs the XNOR operation.