Digital-electronics 简明教程
Implementation of AND Gate from NOR Gate
与非门是一种基本逻辑门，执行二进制乘法，即仅当所有输入都为高电平或逻辑 1 状态时，它才会给出高电平或逻辑 1 输出。另一方面，或非门是一种通用逻辑门。因此，或非门可用于实现任何其他类型的逻辑门。
An AND Gate is a basic logic gate that performs the binary multiplication, i.e., it gives a HIGH or Logic 1 output, only when all its inputs are in HIGH or Logic 1 state. On the other hand, a NOR gate is a type of universal logic gate. Therefore, NOR gate can be used to realize any other type of logic gate.
在介绍仅使用或非门实现与非门之前，让我们首先讨论与非门和或非门的基本理论。
Before going into the implementation of AND gate using NOR gates only, let us discuss the basic theory of AND Gate and NOR Gate first.
What is an AND Gate?
一个 AND Gate 是一个基本逻辑门。一个 AND 门可以有两个或两个以上的输入，但只给一个输出。如果 AND 门的任何一个输入是 LOW（逻辑 0）状态，那么 AND 门输出一个 LOW（逻辑 0）；否则，它输出一个 HIGH（逻辑 1）。因此，只有当 AND 门的所有输入都是 HIGH 或逻辑 1 状态时，AND 门的输出才是 HIGH 或逻辑 1 状态。
An AND Gate is a basic logic gate. An AND gate may have two or more than two inputs, but gives only one output. The AND gate gives a LOW (Logic 0) output if any one of its inputs is in the LOW or Logic 0 state, otherwise, it gives a HIGH (Logic 1) state as output. Therefore, the output of the AND gate is HIGH or Logic 1 state, only if all its inputs are HIGH or Logic 1 state.
与非门也称为“AND”门。两个输入与非门的逻辑符号如图 1 所示。
The AND gate is also known as an "all or nothing gate". The logic symbol of a two input AND gate is shown in Figure-1.
如果变量 A 和 B 是与非门的输入，Y 是与非门的输出变量，那么与非门的输出方程式如下：
If variables A and B are inputs to the AND gate and Y is the output variable of the AND gate, then the output equation of the AND gate is given by,
\mathrm{Y \: = \: A\cdot B}
其中，“.”（点）符号表示与运算。它表示为“Y 等于 A 与 B”。
Where, the '.' (dot) symbol represents the AND operation. It is read as "Y is equal to A AND B".
What is a NOR Gate?
NOR Gate 是通用逻辑门的类型，因为此逻辑门可用于实现任何其他类型的逻辑门。
NOR Gate is a type of universal logic gate, because this logic gate can be used for realization of any other type of logic gate.
NOR 表示 NOT + OR。这意味着，或输出被否定或反转。因此，NOR 门是或门和非门的组合，即
NOR means NOT + OR. That means, the OR output is NOTed or inverted. Therefore, the NOR gate is a combination of OR gate and a NOT gate, i.e.,
\mathrm{NOR \: Gate \: = \: OR \: Gate \: + \: NOT \: Gate}
NOR 门是仅当其所有输入都为 LOW（逻辑 0）时输出为 HIGH（逻辑 1）的逻辑门类型，即使其任何输入变为 HIGH（逻辑 1），它也会输出 LOW（逻辑 0）。两个输入 NOR 门的逻辑符号如图 2 所示。
A NOR gate is a type of logic gate whose output is HIGH (Logic 1), only when all its inputs are LOW (Logic 0), and it gives an output LOW (Logic 0), even if any of its inputs become HIGH (Logic 1). The logic symbol of a two input NOR gate is shown in Figure-2.
如果变量 A 和 B 是输入变量，Y 是 NOR 门的输出变量，则 NOR 门的输出由下式给出：
If variables A and B are the input variables and Y is the output variable of the NOR gate, then the output of the NOR gate is given by,
\mathrm{Y \: = \: \overline{A \: + \: B} \: = \: (A \: + \: B)'}
“Y 等于 A 加 B 杠”。
It is read as "Y is equal to A plus B whole bar".
Implementation of AND Gate from NOR Gate
正如上面提到的，NOR 门是逻辑门，因此我们可以用它来实现 AND 门。仅用 NOR 门实现 AND 门如图 3 所示。
As mentioned above that the NOR gate is a logic gate, therefore, we may use it to realize an AND gate. The realization of an AND gate from the NOR gates only is shown Figure-3.
因此，要从 NOR 门实现 AND 门，我们需要 3 个 NOR 门。其中前两个 NOR 门用于对输入变量 A 和 B 进行补码，第三个 NOR 门用于生成等于 AND 运算的输出。
Thus, for the realization of an AND gate from NOR gate, we require 3 NOR gates. Where, the first two NOR gates are used to complement the input variables A and B, and the third NOR gate is used to produce an output equivalent to the AND operation.
Output Equation
前两个 NOR 门的输出是：
The outputs of the first two NOR gates are,
\mathrm{Y_{1} \: = \: \bar{A}}
\mathrm{Y_{2} \: = \: \bar{B}}
第三个 NOR 门的输出是：
The output of the third NOR gate is,
\mathrm{Y \: = \: \overline{\bar{A} \: + \: \bar{B}} \: = \: \bar{\bar{A}} \cdot \bar{\bar{B}} \: = \: A \cdot B}
\mathrm{Y \: = \: \overline{\bar{A} \: + \: \bar{B}} \: = \: \bar{\bar{A}} \cdot \bar{\bar{B}} \: = \: A \cdot B}
这是 AND 门的输出。因此，图 3 所示的用 NOR 门实现的逻辑电路等效于 AND 门。
This is the output of an AND gate. Hence, the logic circuit using NOR gates shown in Figure-3 is equivalent to the AND gate.