Computer Science Key Topics | 计算机科学核心考点

📚 Computer Science Key Topics | 计算机科学核心考点

Mastering computer science requires a solid understanding of key theoretical concepts and practical skills. This revision guide covers the essential topics examined in high school and college-level computer science courses, including algorithms, data representation, computer architecture, programming, networks, databases, and the societal impacts of technology. Each section provides concise explanations in both English and Chinese to support bilingual learners.

掌握计算机科学需要扎实的理论概念与实践技能。本复习指南涵盖高中及大学预科计算机科学课程的核心考点，包括算法、数据表示、计算机体系结构、编程、网络、数据库以及科技的社会影响。每个部分提供中英双语简明解释，助力双语学习者。

1. Algorithms and Problem Solving | 算法与问题求解

An algorithm is a step-by-step procedure for solving a problem. All algorithms must be unambiguous, have a defined input and output, be finite (terminate after a finite number of steps), and be feasible given available resources. Common examples include searching and sorting algorithms.

算法是解决问题的分步过程。所有算法必须无歧义、有明确的输入和输出、有限性（在有限步内终止）并且在给定资源下可行。常见的例子包括搜索和排序算法。

Linear search checks each element in a list sequentially until the target is found, with a worst-case time complexity of O(n). Binary search works on sorted arrays by repeatedly dividing the search interval in half, achieving O(log n). Bubble sort repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order, resulting in O(n²) in the worst case.

线性搜索按顺序检查列表中的每个元素直到找到目标，最坏时间复杂度为 O(n)。二分搜索适用于有序数组，通过不断将搜索区间减半，达到 O(log n)。冒泡排序重复遍历列表，比较相邻元素并交换顺序错误者，最坏情况为 O(n²)。

Flowcharts use standard symbols: a rectangle for processing, a rhombus for decision, a parallelogram for input/output, and an arrow for flow direction. Pseudocode bridges the gap between human language and actual code, helping programmers plan logic before implementation.

流程图使用标准符号：矩形表示处理，菱形表示判断，平行四边形表示输入/输出，箭头表示流程方向。伪代码弥合了人类语言与实际代码之间的鸿沟，帮助程序员在实现之前规划逻辑。

2. Data Representation | 数据表示

Computers store data as binary digits (bits): 0 or 1. A group of 8 bits is a byte. Denary (base-10) numbers can be converted to binary by successive division by 2. Hexadecimal (base-16) uses digits 0-9 and letters A-F, making it more compact for representing binary values. For example, 1100 1011₂ equals CB₁₆.

计算机以二进制数字（位）存储数据：0 或 1。8 位一组称为一个字节。十进制（基数为10）数可以通过不断除以2转换为二进制。十六进制（基数为16）使用数字 0-9 和字母 A-F，更紧凑地表示二进制值。例如，1100 1011₂ 等于 CB₁₆。

When adding binary numbers, overflow occurs if the result exceeds the bit width, often flagged by a status register. Negative numbers can be represented using two’s complement: invert all bits and add 1 to the least significant bit.

二进制加法时，如果结果超出位宽会发生溢出，通常由状态寄存器标志。负数可以使用二进制补码表示：将所有位取反后加1。

Characters are encoded using standards like ASCII (7 bits, 128 characters) and Unicode (variable length, over 1 million code points). Images are represented as bitmaps of pixels, where colour depth determines bits per pixel; resolution affects clarity. Sound is sampled at a rate (e.g., 44.1 kHz) with a given bit depth; file size = sample rate × bit depth × duration (in seconds) ÷ 8 for bytes.

字符使用 ASCII（7 位，128 个字符）和 Unicode（可变长度，超过 100 万个码点）等标准编码。图像以像素位图表示，颜色深度决定每像素位数；分辨率影响清晰度。声音以采样率（如 44.1 kHz）和给定位深度采样；文件大小 = 采样率 × 位深度 × 时长（秒）÷ 8 得到字节数。

3. Computer Architecture | 计算机体系结构

The von Neumann architecture stores both program instructions and data in the same memory. The CPU contains the control unit (CU), arithmetic logic unit (ALU), and registers such as the program counter (PC), memory address register (MAR), memory data register (MDR), and accumulator (ACC). The fetch-decode-execute cycle continuously retrieves an instruction, decodes it in the CU, and executes it via the ALU.

冯·诺依曼架构将程序指令和数据存储在同一内存中。CPU 包含控制单元 (CU)、算术逻辑单元 (ALU) 以及程序计数器 (PC)、存储器地址寄存器 (MAR)、存储器数据寄存器 (MDR) 和累加器 (ACC) 等寄存器。取值-解码-执行周期不断取指令、在 CU 中解码并通过 AL

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