Mastering Combined Operations: Arithmetic, Relational, and Logical Operations | 掌握组合运算：算术、关系与逻辑运算

📚 Mastering Combined Operations: Arithmetic, Relational, and Logical Operations | 掌握组合运算：算术、关系与逻辑运算

In A-Level Edexcel Programming, understanding and correctly applying combined operations is essential. Operations such as arithmetic, relational, logical, and bitwise form the core of decision-making and data manipulation in code. This article provides a thorough exploration of these operations, including their precedence, evaluation, and practical use in Python, the language often used in the Edexcel specification.

在A-Level Edexcel编程中，理解并正确应用组合运算至关重要。算术、关系、逻辑和位运算构成了代码中决策和数据处理的核心。本文全面探讨这些操作，包括它们的优先级、求值方式以及在Edexcel规范中常用的Python语言中的实际应用。

1. Arithmetic Operations | 算术运算

Arithmetic operations perform basic mathematical calculations. In Python, the main arithmetic operators are addition (+), subtraction (-), multiplication (*), division (/), floor division (//), modulus (%), and exponentiation (**). For example, 7 // 2 evaluates to 3, and 2 ** 3 yields 8.

算术运算执行基本的数学计算。在Python中，主要的算术运算符有加法 (+)、减法 (-)、乘法 (*)、除法 (/)、整除 (//)、取模 (%) 和幂运算 (**)。例如，7 // 2 的结果为 3，2 ** 3 得到 8。

Division (/) always returns a float, while floor division (//) truncates towards negative infinity. Modulus (%) gives the remainder of a division, which is extremely useful for tasks like checking divisibility or cycling through arrays.

除法 (/) 始终返回浮点数，而整除 (//) 向负无穷方向截断。取模 (%) 返回除法余数，这在检查整除性或循环遍历数组等任务中非常有用。

In many algorithms, integer arithmetic must be handled with care to avoid overflow, though Python integers have arbitrary precision. However, understanding the difference between true division and floor division is vital for porting code from other languages.

在许多算法中，必须小心处理整数运算以避免溢出，尽管Python整数具有任意精度。然而，理解真除法和整除之间的区别对于从其他语言移植代码至关重要。

2. Relational Operations | 关系运算

Relational operators compare two values and produce a Boolean result (True or False). The standard operators are equal to (==), not equal to (!=), greater than (>), less than (<), greater than or equal to (>=), and less than or equal to (<=). These are fundamental in forming conditions.

关系运算符比较两个值并产生布尔结果（True 或 False）。标准运算符包括等于 (==)、不等于 (!=)、大于 (>)、小于 (<)、大于等于 (>=) 和小于等于 (<=)。它们是构成条件的基础。

When combined with arithmetic operators, relational expressions can test computed values. For instance, (a + b) >= c checks if the sum of a and b is at least c. It is crucial to distinguish = (assignment) from == (equality test) to avoid logical errors.

当与算术运算符结合时，关系表达式可以测试计算出的值。例如，(a + b) >= c 检查 a 与 b 之和是否至少为 c。务必区分 =（赋值）和 ==（相等测试），以避免逻辑错误。

Floating-point comparisons can be tricky due to precision errors. Direct equality of floats is discouraged; instead, check if the absolute difference is within a small tolerance, often using the expression abs(a – b) < 1e-9.

由于精度误差，浮点数比较可能很棘手。不建议直接对浮点数进行相等判断；而应检查绝对差是否在很小的容差范围内，通常使用表达式 abs(a – b) < 1e-9。

3. Logical Operations | 逻辑运算

Logical operators combine Boolean values. In Python, the keywords are and, or, and not. They follow short-circuit evaluation: for a and b, if a is False, b is not evaluated. Similarly, for a or b, if a is True, b is skipped.

逻辑运算符组合布尔值。在Python中，关键词是 and、or 和 not。它们遵循短路求值：对于 a and b，如果 a 为 False，则不计算 b。类似地，对于 a or b，如果 a 为 True，则跳过 b。

Below is the truth table for basic logical operations:

以下是基本逻辑运算的真值表：

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