📚 Operators and Expressions in Programming | 编程中的运算符与表达式
Operators are the symbols that tell a computer to perform specific mathematical, relational or logical operations. In Edexcel A-Level Computer Science, you must be able to read, write and trace expressions that combine operators and operands.
运算符是告诉计算机执行特定数学、关系或逻辑操作的符号。在 Edexcel A-Level 计算机科学中，你必须能够阅读、编写并追踪结合了运算符和操作数的表达式。
1. Why Operators Matter | 为什么运算符重要
Operators form the core of every executable instruction. Without them, a program could store data but never calculate, compare or decide.
运算符构成了每条可执行指令的核心。没有它们，程序只能存储数据，却无法计算、比较或做出决策。
- Arithmetic operators build formulas for prices, coordinates and counters. 算术运算符用于为价格、坐标和计数器构建公式。
- Comparison operators drive conditional statements such as IF and WHILE. 比较运算符驱动 IF 和 WHILE 等条件语句。
- Logical operators combine multiple true/false conditions in selection. 逻辑运算符在选择结构中组合多个真/假条件。
2. Arithmetic Operators | 算术运算符
The usual arithmetic operators are addition, subtraction, multiplication, division, modulus, integer division and exponentiation. In Python they are written +, -, *, /, %, //, **.
常见的算术运算符包括加、减、乘、除、取模、整除和乘方。在 Python 中它们分别写作 +、-、*、/、%、//、**。
- + addition 加；- subtraction 减；* multiplication 乘
- / division 除；% modulus 取模；// integer division 整除；** exponentiation 乘方
17 % 5 = 2 and 17 // 5 = 3 and 2 ** 3 = 8
Remember that % gives the remainder after division, while // discards the fractional part and returns an integer in Python.
请记住，% 给出除法后的余数，而 // 在 Python 中丢弃小数部分并返回整数。
3. Comparison / Relational Operators | 比较（关系）运算符
Comparison operators compare two values and return a Boolean result: True or False. They are essential in selection and iteration.
比较运算符比较两个值并返回布尔结果：True 或 False。它们在选择和迭代中是必不可少的。
- == means equal to；!= means not equal to. == 表示等于；!= 表示不等于。
- >, <, >=, <= test order relationships. >、<、>=、<= 测试大小关系。
may be written as = or == depending on the context, so always check the question wording.
在 Edexcel 伪代码中，符号可能根据上下文写作 = 或 ==，因此务必核对题目措辞。
4. Logical Operators | 逻辑运算符
Logical operators act on Boolean values. Python uses and, or and not. Many pseudocode specifications show AND, OR, NOT.
逻辑运算符作用于布尔值。Python 使用 and、or 和 not。许多伪代码规范显示 AND、OR、NOT。
- and returns True only if both operands are True. and 仅当两个操作数都为 True 时才返回 True。
- or returns True if at least one operand is True. or 只要有一个操作数为 True 就返回 True。
- not reverses the Boolean value. not 反转布尔值。
(age >= 18) and (country == 'UK')
The expression above is True only when both the age condition and the country condition are True.
上面的表达式仅当年龄条件和国家条件都为 True 时才为 True。
5. Bitwise Operators | 位运算符
Bitwise operators work on binary representations of integers. They are less common in A-Level exams, but you may need to trace bit-level operations such as AND, OR, XOR, NOT, left shift and right shift.
位运算符对整数的二进制表示进行操作。它们在 A-Level 考试中较少出现，但你可能需要追踪位级运算，例如 AND、OR、XOR、NOT、左移和右移。
- & bitwise AND；| bitwise OR；^ bitwise XOR；~ bitwise NOT
- << shifts bits left；>> shifts bits right. << 将位向左移；>> 将位向右移。
Example: 5 & 3 = 1 because 0101 and 0011 produce 0001.
示例：5 & 3 = 1，因为 0101 与 0011 得到 0001。
6. Assignment Operators | 赋值运算符
=. Compound assignment operators combine arithmetic with assignment, which shortens code.
基本赋值运算符是 =。复合赋值运算符将算术与赋值结合起来，可以缩短代码。
- x += 5 is equivalent to x = x + 5. x += 5 等价于 x = x + 5。
- x *= 2 is equivalent to x = x * 2. x *= 2 等价于 x = x * 2。
- x //= 3 and x %= 3 behave similarly for integer division and remainder. x //= 3 和 x %= 3 分别类似地执行整除和取余。
7. Membership and Identity Operators | 成员与身份运算符
Membership operators test whether a value exists in a sequence. Identity operators test whether two references point to the same object in memory.
成员运算符测试一个值是否存在于序列中。身份运算符测试两个引用是否指向内存中的同一个对象。
- in returns True if the element is present in a list, string or tuple. in 如果元素存在于列表、字符串或元组中，则返回 True。
- not in returns True if the element is absent. not in 如果元素不存在，则返回 True。
- is checks identity; == checks equality of value. is 检查身份；== 检查值的相等性。
8. Precedence and Associativity | 优先级与结合性
Operator precedence decides the order in which operations are evaluated. In most languages, brackets have the highest priority, then exponent, then multiplication/division, then addition/subtraction, then comparisons, then logical operators.
运算符优先级决定了运算的求值顺序。在大多数语言中，括号优先级最高，然后是乘方、乘除、加减，再然后是比较运算，最后是逻辑运算。
- Parentheses override all default priority rules. 括号覆盖所有默认优先级规则。
- *, /, //, % are evaluated before + and -. *、/、//、% 在 + 和 - 之前计算。
- and is evaluated after comparisons but before or in Python. 在 Python 中，and 在比较之后、or 之前计算。
Example: 3 + 4 * 2 equals 11, not 14.
示例：3 + 4 * 2 等于 11，而不是 14。
9. Common Pitfalls in A-Level Exam | A-Level 考试常见易错点
nd ==, misuse integer division, or ignore short-circuit evaluation in logical expressions.
学生经常混淆 = 和 ==，误用整除，或忽略逻辑表达式中的短路求值。
- Using = for comparison in Python causes a syntax error or unintended assignment. 在 Python 中误将 = 用作比较会导致语法错误或意外赋值。
- In many languages, / gives a real result while // gives integer division in Python. 在许多语言中，/ 给出实数结果，而 Python 中的 // 给出整除。
- Check whether the question uses pseudocode or Python; operator symbols can differ. 检查题目使用伪代码还是 Python；运算符符号可能不同。
10. Quick Revision Table | 快速复习表
| Operator | Meaning 含义 | Example 示例 |
|---|---|---|
| + | Addition 加 | 3 + 2 = 5 |
| % | Modulus 取模 | 7 % 4 = 3 |
| // | Integer division 整除 | 7 // 4 = 1 |
| == | Equal to 等于 | 5 == 5 → True |
| and | Logical AND 逻辑与 | True and False → False |
| in | Membership 成员 | 'a' in 'cat' → True |
Use this table as a quick check before the exam, but always practise tracing full expressions with mixed operators.
在考试前可以用此表快速自查，但务必练习追踪包含混合运算符的完整表达式。
Published by TutorHao | Programming Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图