📚 Pre-U CAIE Computer Science: Core Knowledge Review | Pre-U CAIE 计算机：核心知识点梳理
The Cambridge Pre-U Computer Science syllabus is a rigorous course that builds deep understanding of how computers work, how data is represented and processed, and how to design and evaluate computational solutions. This article provides a structured review of the core knowledge areas, covering theory and principles essential for success in the examination.
剑桥 Pre-U 计算机科学是一门严谨的课程，旨在深入理解计算机的工作原理、数据的表示与处理，以及如何设计和评估计算解决方案。本文系统地梳理核心知识领域，涵盖考试必备的理论与原理。
1. Data Representation | 数据表示
All data inside a computer is stored and processed as binary digits (bits). A group of 8 bits forms a byte, and memory sizes are measured in kilobytes (2¹⁰ bytes), megabytes (2²⁰), etc. Hexadecimal (base‑16) is widely used to simplify binary notation, as each hex digit corresponds to exactly 4 bits.
计算机中所有数据都以二进制位（0 和 1）形式存储与处理。8 位组成一个字节，内存大小以千字节（2¹⁰ 字节）、兆字节（2²⁰）等为单位。十六进制（基数为 16）被广泛用于简化二进制表示，因为每个十六进制数字恰好对应 4 个二进制位。
Integers can be represented in unsigned, sign‑and‑ e subtraction can be performed by addition, and zero has a unique representation. Floating‑point numbers follow the IEEE 754 standard: a 32‑bit single‑ es 1 sign bit, 8 exponent bits (biased by 127), and 23 mantissa bits, representing value (–1)ˢ × 1.m × 2ᵉ⁻¹²⁷.
整数可用无符号、原码或二进制补码形式表示。补码是带符号整数的标准表示，因为减法可通过加法实现，且零的表示唯一。浮点数遵循 IEEE 754 标准：32 位单精度数使用 1 位符号位、8 位阶码（偏移量 127）和 23 位尾数，表示的值为 (–1)ˢ × 1.m × 2ᵉ⁻¹²⁷。
Characters are encoded using standards such as ASCII (7‑bit) and Unicode. Unicode can be implemented as UTF‑8, UTF‑16 or UTF‑32, supporting virtually all writing systems. Images can be stored as bitmaps (pixels with colour depth) or vectors (mathematical descriptions of shapes). Sound is digitised through sampling: the sampling rate and bit depth determine fidelity and file size.
字符通过编码标准表示，例如 ASCII（7 位）和 Unicode。Unicode 可通过 UTF‑8、UTF‑16 或 UTF‑32 实现，支持几乎所有书写系统。图像可以位图（带有颜色深度的像素）或矢量图（形状的数学描述）存储。声音通过采样数字化：采样率和位深度决定保真度与文件大小。
2. Computer Architecture | 计算机体系结构
The Von Neumann architecture stores data and instructions in a shared memory, using a single set of address and data buses. Its central processing unit (CPU) comprises an arithmetic logic unit (ALU), a control unit (CU), and a set of registers such as the program counter (PC), memory address register (MAR), memory buffer register (MBR), and accumulator (ACC).
冯·诺依曼架构将数据和指令存放在共享内存中，使用一套地址总线和数据总线。它的中央处理器（CPU）由算术逻辑单元（ALU）、控制单元（CU）和一组寄存器组成，如程序计数器（PC）、内存地址寄存器（MAR）、内存缓冲寄存器（MBR）和累加器（ACC）。
The fetch–decode–execute cycle is repeated endlessly: the processor fetches an instruction from memory (address in PC), decodes it via the CU, and then executes it, often involving data transfer and ALU operations. Pipelining improves throughput by overlapping the stages of multiple instructions; however, hazards (data, control, structural) must be managed.
取指－译码－执行周期不断重复：处理器从内存取出指令（地址在 PC 中），经控制单元译码后执行，常涉及数据传输和 ALU 操作。流水线通过重叠多条指令的不同阶段来提高吞吐量；但必须处理数据冒险、控制冒险和结构冒险。
Cache memory exploits temporal and spatial locality to reduce average access time. Levels L1, L2 and L3 provide a hierarchy of speed vs. size. In contrast, Harvard architecture uses physically separate memories for instructions and data, enabling simultaneous access and potentially higher performance in embedded systems.
高速缓存利用时间局部性和空间局部性来降低平均访问时间。L1、L2、L3 级缓存构成了速度与容量之间的层次结构。相比之下，哈佛架构使用物理上独立的指令存储器和数据存储器，可同时访问，在嵌入式系统中可能提供更高性能。
3. Operating Systems | 操作系统
An operating system (OS) acts as an interface between hardware and user applications, managing resources and providing abstraction. Its main functions include process management, memory management, file system management, and I/O handling. The OS schedules processes using algorithms such as round‑robin, shortest job first, or priority‑based scheduling, aiming to maximise throughput and responsiveness.
操作系统充当硬件与用户应用程序之间的接口，管理资源并提供抽象。其主要功能包括进程管理、内存管理、文件系统管理和 I/O 处理。操作系统使用轮转法、最短作业优先或基于优先级的调度算法来调度进程，以最大化吞吐量和响应速度。
Memory management uses techniques like paging and segmentation to allow processes to run in separate logical address spaces. Virtual memory extends RAM using disk storage, enabling the execution of larger programs. Interrupts (hardware, software) allow the CPU to respond to events asynchronously; an interrupt service routine (ISR) handles each event, after which the original context is restored.
内存管理采用分页和分段等技术，让进程在独立的逻辑地址空间中运行。虚拟内存利用磁盘存储扩展 RAM，使更大程序的执行成为可能。中断（硬件中断、软件中断）使 CPU 能异步响应事件；中断服务程序（ISR）处理每个事件，之后恢复原上下文。
4. Networks | 计算机网络
Modern networks are described by protocol stacks, most commonly the TCP/IP model with layers: application, transport, internet, and network access. The application layer supports protocols like HTTP, FTP, SMTP, and DNS. The transport layer provides end‑to‑end communication using TCP (reliable, connection‑oriented) or UDP (connectionless, low overhead).
现代网络通过协议栈描述，最常见的是 TCP/IP 模型，其分层为：应用层、传输层、互联网层和网络接入层。应用层支持 HTTP、FTP、SMTP 和 DNS 等协议。传输层使用 TCP（可靠的、面向连接）或 UDP（无连接、低开销）提供端到端通信。
At the internet layer, the Internet Protocol (IP) routes packets between hosts. IPv4 uses 32‑bit addresses (dotted decimal), while IPv6 uses 128‑bit hexadecimal addresses to solve address exhaustion. Subnetting divides a network into smaller logical segments using a subnet mask. The Domain Name System (DNS) translates human‑readable domain names into IP addresses through a hierarchical, distributed database.
在互联网层，互联网协议（IP）在主机之间路由数据包。IPv4 使用 32 位地址（点分十进制），而 IPv6 使用 128 位十六进制地址以解决地址耗尽问题。子网划分通过子网掩码将网络分割成更小的逻辑网段。域名系统（DNS）通过层次化分布式数据库将人类可读的域名转换为 IP 地址。
Network security relies on firewalls that filter traffic based on rules, and on encryption protocols like TLS for securing web traffic. Symmetric encryption (same key) and asymmetric encryption (public/private key pairs) both play crucial roles in confidentiality and authentication.
网络安全依赖于基于规则过滤流量的防火墙，以及像 TLS 这样的加密协议来保护 Web 通信。对称加密（相同密钥）和非对称加密（公钥/私钥对）在机密性和身份认证中都起着关键作用。
5. Databases | 数据库
A database is an organised collection of data, often modelled using the relational model. Data is stored in tables (relations) with rows (tuples) and columns (attributes). Each table typically has a primary key that uniquely identifies each row; foreign keys implement relationships between tables.
数据库是有组织的数据集合，常使用关系模型建模。数据存储在表（关系）中，包含行（元组）和列（属性）。每个表通常有一个主键，唯一标识每一行；外键实现表之间关系。
Entity‑relationship (ER) diagrams model the structure of a database: entities (rectangles), attributes (ovals), and relationships (diamonds), with cardinality notations such as one‑to‑many. Structured Query Language (SQL) is used to define and manipulate data with commands like SELECT, INSERT, UPDATE, DELETE; filtering (WHERE), joining tables (JOIN), and grouping (GROUP BY) are fundamental operations.
实体关系图（ER 图）对数据库结构建模：实体（矩形）、属性（椭圆）和联系（菱形），并带有基数表示，如一对多。结构化查询语言（SQL）用于定义和操作数据，常用命令如 SELECT、INSERT、UPDATE、DELETE；过滤（WHERE）、表连接（JOIN）和分组（GROUP BY）是基本操作。
Normalisation is the process of reducing data redundancy and unwanted anomalies by decomposing tables. First normal form (1NF) requires atomic values; second normal form (2NF) removes partial dependencies; third normal form (3NF) eliminates transitive dependencies. Well‑designed databases balance normalisation with performance requirements.
规范化是通过分解表来减少数据冗余和异常的过程。第一范式（1NF）要求原子值；第二范式（2NF）消除部分依赖；第三范式（3NF）消除传递依赖。设计良好的数据库在规范化与性能需求之间取得平衡。
6. Data Structures & Algorithms | 数据结构与算法
Arrays store elements of the same type in contiguous memory, allowing O(1) indexed access. Linked lists use nodes with data and pointers, enabling efficient insertion/deletion but O(n) access. Stacks (LIFO) and queues (FIFO) are abstract data types implemented with arrays or linked lists; they support operations like push, pop, enqueue, dequeue.
数组将同类型元素存储在连续内存中，支持 O(1) 的索引访问。链表使用带有数据和指针的节点，插入和删除高效，但访问时间为 O(n)。栈（后进先出）和队列（先进先出）是抽象数据类型，可用数组或链表实现；它们支持压入、弹出、入队、出队等操作。
Trees, especially binary search trees (BST), arrange data hierarchically: for any node, left subtree values are smaller and right subtree values are larger, supporting O(log n) search on average. Balanced trees (e.g. AVL) avoid degradation to O(n). Graphs consist of vertices and edges; they can be represented by adjacency matrices or adjacency lists. Traversal algorithms include depth‑first and breadth‑first search.
树，特别是二叉搜索树（BST），以层次结构安排数据：对于任意节点，左子树值较小，右子树值较大，平均查找时间为 O(log n)。平衡树（如 AVL 树）可避免退化到 O(n)。图由顶点和边组成，可用邻接矩阵或邻接表表示。遍历算法包括深度优先搜索和广度优先搜索。
Sorting algorithms include bubble sort (O(n²)), merge sort (O(n log n)), and quick sort (average O(n log n)). Searching includes linear search (O(n)) and binary search (O(log n) on sorted data). Algorithm efficiency is analysed using Big‑O notation, focusing on worst‑case time and space complexity.
排序算法包括冒泡排序 (O(n²))、归并排序 (O(n log n)) 和快速排序（平均 O(n log n)）。查找包括线性查找 (O(n)) 和二分查找（对已排序数据为 O(log n)）。算法效率使用大 O 记号分析，关注最坏情况下的时间复杂度和空间复杂度。
7. Programming & Software Development | 编程与软件开发
Programming paradigms provide different approaches to writing code. Procedural programming (e.g. C, Python) organises code into procedures or functions that operate on data. Object‑oriented programming (e.g. Java, C++) models real‑world entities as objects with attributes and methods, supporting encapsulation, inheritance, and polymorphism. Functional programming (e.g. Haskell) treats computation as the evaluation of mathematical functions, avoiding mutable state.
编程范型提供了不同的代码编写方式。过程式编程（如 C、Python）将代码组织成对数据进行操作的过程或函数。面向对象编程（如 Java、C++）将现实世界实体建模为具有属性和方法的对象，支持封装、继承和多态。函数式编程（如 Haskell）将计算视为数学函数的求值，避免可变状态。
The software development life cycle (SDLC) often includes stages: analysis, design, implementation, testing, deployment, and maintenance. Methodologies such as waterfall (linear, sequential) and agile (iterative, incremental) guide the process. Testing strategies involve unit testing, integration testing, acceptance testing; debugging methods include desk checking and using trace tables.
软件开发生命周期通常包括分析、设计、实现、测试、部署和维护等阶段。瀑布模型（线性的、顺序的）和敏捷方法（迭代的、增量的）等方法论指导该过程。测试策略包括单元测试、集成测试、验收测试；调试方法包括桌面检查和跟踪表。
8. Boolean Algebra & Logic | 布尔代数与逻辑
Boolean algebra operates on binary variables with values 0 and 1, using operators AND (·), OR (+), and NOT (overbar). Basic laws include identity, complement, commutative, associative, and distributive laws. Boolean expressions can be simplified using algebraic manipulation or Karnaugh maps (K‑maps) for up to 4 variables, which provide a visual method for minimisation.
布尔代数
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