📚 Logic Circuits, Logic Expressions, Truth Tables and Problem Statements | 逻辑电路、逻辑表达式、真值表与问题陈述
Logic circuits form the foundation of digital electronics. They process binary signals (0 and 1) using basic building blocks called logic gates. Understanding how to represent these circuits through logic expressions and truth tables, and how to translate real-world problem statements into gate combinations, is essential for IGCSE Science (Physics).
逻辑电路是数字电子学的基础。它们使用称为逻辑门的基本构件来处理二进制信号（0 和 1）。理解如何通过逻辑表达式和真值表来表示这些电路，以及如何将现实世界的问题陈述转化为门的组合，对于 IGCSE 科学（物理）至关重要。
1. Introduction to Logic Gates | 逻辑门简介
Logic gates are electronic devices that perform a logical operation on one or more binary inputs to produce a single binary output. The two possible states are typically represented as 0 (low voltage, false) and 1 (high voltage, true). The most basic gates are NOT, AND, and OR, from which more complex gates like NAND, NOR, and XOR are derived.
逻辑门是电子器件，对一个或多个二进制输入执行逻辑运算，产生单个二进制输出。两种可能的状态通常表示为 0（低电压，假）和 1（高电压，真）。最基本的门是非门、与门和或门，由此衍生出与非门、或非门和异或门等更复杂的门。
Each gate has a unique symbol, a Boolean expression, and a truth table that defines its behaviour for all possible input combinations. In IGCSE Physics, you will be expected to recognise these symbols, write truth tables, and combine gates to solve simple problems.
每种门都有独特的符号、布尔表达式以及定义其所有可能输入组合行为的真值表。在 IGCSE 物理中，你需要识别这些符号、写出真值表，并组合各种门来解决简单问题。
2. The NOT Gate | 非门
put A is 0, the output Q is 1; if A is 1, Q is 0. The logic expression is written as Q = A' or Q = ¬A, pronounced "Q equals NOT A". Its symbol is a triangle pointing right with a small circle (bubble) at the output end.
非门，也称为反相器，有一个输入和一个输出。它产生的输出是输入的逻辑相反值。如果输入 A 为 0，输出 Q 为 1；如果 A 为 1，Q 为 0。逻辑表达式写为 Q = A' 或 Q = ¬A，读作“Q 等于非 A”。其符号是一个指向右方的三角形，输出端有一个小圆圈（表示反相）。
| Input A | Output Q |
|---|---|
| 0 | 1 |
| 1 | 0 |
The truth table above confirms that the output is always the inverse of the input. The NOT gate is often used to change the sense of a signal, for example, to activate an alarm when a sensor gives a low reading.
上面的真值表证实输出始终是输入的反相。非门常用于改变信号的含义，例如当传感器给出低读数时激活警报。
3. The AND Gate | 与门
ut is 0. The Boolean expression is Q = A AND B, which can be written as Q = A · B or Q = A ∧ B. The dot (·) is the symbol for logical AND in Boolean algebra.
与门可以有两个或更多输入；在最简单的形式中，它有两个输入 A 和 B。仅当所有输入均为 1 时，输出 Q 才为 1。如果任一输入为 0，则输出为 0。布尔表达式为 Q = A AND B，可写作 Q = A · B 或 Q = A ∧ B。点（·）是布尔代数中逻辑与的符号。
| A | B | Q = A · B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The AND gate behaves like a series circuit: all conditions must be true for the output to be active. A practical example is a safety interlock that allows a machine to start only if two safety guards are both closed.
与门的行为类似于串联电路：必须满足所有条件输出才有效。一个实际的例子是安全联锁，只有当两个安全护罩都关闭时才允许机器启动。
4. The OR Gate | 或门
when all inputs are 0. The Boolean expression is Q = A OR B, written as Q = A + B or Q = A ∨ B. In Boolean algebra, the plus sign (+) denotes logical OR, not arithmetic addition.
或门也有两个或更多输入。如果至少一个输入为 1，则输出 Q 为 1。仅当所有输入均为 0 时，输出才为 0。布尔表达式为 Q = A OR B，写作 Q = A + B 或 Q = A ∨ B。在布尔代数中，加号（+）表示逻辑或，而不是算术加法。
| A | B | Q = A + B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
An OR gate is like a parallel circuit: if either switch is closed, the circuit is complete. A typical use is a warning light that turns on if any one of several sensors detects a fault.
或门类似于并联电路：如果任一开关闭合，电路就导通。一个典型的用途是警告灯，如果多个传感器中的任何一个检测到故障就点亮。
5. The NAND Gate | 与非门
1. For all other input combinations the output is 1. The Boolean expression is Q = (A · B)' or Q = ¬(A ∧ B). The prime (') or overbar indicates negation.
与非门等效于一个与门后接一个非门。它的输出是与功能的取反：仅当所有输入均为 1 时输出 0。对于其他所有输入组合，输出均为 1。布尔表达式为 Q = (A · B)' 或 Q = ¬(A ∧ B)。撇号（'）或上划线表示取反。
| A | B | Q = (A · B)' |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The NAND gate is called a universal gate because you can build any other type of gate—NOT, AND, OR—using only NAND gates. This makes it very important in digital circuit design.
与非门被称为通用门，因为你仅用与非门就可以构建任何其他类型的门——非门、与门和或门。这使得它在数字电路设计中非常重要。
6. The NOR Gate | 或非门
puts are 0. If any input is 1, the output becomes 0. Its Boolean expression is Q = (A + B)' or Q = ¬(A ∨ universal gate, meaning any logic function can be implemented exclusively with NOR gates.
或非门是或门后接一个非门。仅当所有输入均为 0 时输出 1。如果任一输入为 1，则输出变为 0。它的布尔表达式为 Q = (A + B)' 或 Q = ¬(A ∨ B)。与非门一样，或非门也是一种通用门，这意味着任何逻辑功能都可以仅用或非门实现。
| A | B | Q = (A + B)' |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
A practical use of a NOR gate is in a system that should be active only when no sensor is triggered—such as a "system OK" indicator that lights up when all monitored parameters are normal (logic 0 for fault-free).
或非门的一个实际用途是在一个仅当没有传感器被触发时才应激活的系统中——例如“系统正常”指示灯，当所有监控参数都正常（无故障为逻辑 0）时亮起。
7. The XOR Gate |
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