📚 End of Unit 1: Exam-style Case Study Questions | 单元1末尾：考试风格案例研究题
In Cambridge A-Level Computer Science, Unit 1 covers the fundamental concepts of data representation, communication, hardware, processor architecture, and system software. To truly assess your understanding, examiners often present a scenario-based case study that weaves together multiple topics. This article provides a comprehensive example of such a case study, complete with exam-style questions and detailed, model answers. Work through each section carefully – attempt the questions yourself before studying the solutions – and you will gain confidence in applying theoretical knowledge to practical, integrated problems.
在剑桥 A-Level 计算机科学中，单元 1 涵盖了数据表示、通信、硬件、处理器架构和系统软件的基本概念。为了真正评估你的理解，考官通常会给出一个基于情境的案例研究，将多个主题交织在一起。本文提供了一份全面的案例研究示例，包括考试风格的问题和详细的参考答案。请仔细完成每个部分——在查看解答之前先自己尝试回答问题——你将获得将理论知识应用于实际综合性问题的信心。
1. Case Study Scenario: EduStream Online Learning Platform | 案例场景：EduStream在线学习平台
EduStream is a rapidly growing company that provides on-demand educational video content to students worldwide. Their current IT infrastructure consists of a single server, a few workstations, and a consumer-grade Internet connection. As the technical consultant, you have been asked to propose an upgraded system that can store thousands of hours of high-definition video, stream it efficiently to users, manage user accounts, and ensure data security. The management has provided specific requirements: videos must be available in both HD and SD versions, the platform must support up to 10,000 concurrent viewers, and all personal data must be handled in compliance with international data protection regulations. Throughout this case study, you will answer questions drawn directly from the Unit 1 syllabus, including number representation, compression algorithms, networking hardware, processor functionality, operating system roles, and ethical implications.
EduStream 是一家快速发展的公司，为全球学生提供按需教育视频内容。他们现有的 IT 基础设施包括一台服务器、几台工作站和一个消费者级别的互联网连接。作为技术顾问，你受邀提出一个升级系统，可以存储数千小时的高清视频，将其高效地流式传输给用户，管理用户账户，并确保数据安全。管理层提出了具体要求：视频必须提供高清和标清两种版本，平台必须支持多达 1 万名并发观众，并且所有个人数据必须按照国际数据保护法规进行处理。在整个案例研究中，你将回答直接源于单元 1 教学大纲的问题，包括数字表示、压缩算法、网络硬件、处理器功能、操作系统角色和伦理意义。
2. Question 1: Data Representation – Image Thumbnails | 问题1：数据表示 – 图像缩略图
he file size of one such thumbnail in kilobytes (KB), assuming 1 KB = 1024 bytes. The design team suggests using an 8-bit indexed colour palette to save storage. By calculating the new file size, explain the trade-off involved in switching to indexed colour. (6 marks)
EduStream 将视频缩略图存储为分辨率 320 × 240 像素、色深 24 位的未压缩位图文件。计算一个这样的缩略图文件大小（千字节 KB），假设 1 KB = 1024 字节。设计团队建议使用 8 位索引调色板以节省存储空间。通过计算新的文件大小，解释切换到索引颜色所涉及的权衡。(6 分)
. Dividing by 1024 gives 225 KB. With an 8-bit palette, each pixel stores a 1-byte index, so the size becomes 76,800 bytes or 75 KB. This is a reduction of about two-thirds. However, the palette is limited to 256 colours. For photographic thumbnails this may lead to visible colour banding or loss of detail unless dithering is applied, which itself adds processing overhead. The trade-off is between storage space and image fidelity.
使用 24 位颜色，每个像素需要 3 字节。总像素数为 320 × 240 = 76,800。因此，文件大小 = 76,800 × 3 = 230,400 字节。除以 1024 得到 225 KB。使用 8 位调色板，每个像素存储 1 字节索引，因此大小变为 76,800 字节，即 75 KB。这减少了大约三分之二。然而，调色板限制为 256 种颜色。对于照片缩略图，这可能导致明显的色彩断层或细节丢失，除非应用抖动技术，而这本身会增加处理开销。这一权衡涉及存储空间与图像保真度之间的选择。
3. Question 2: Sound Sampling and File Size | 问题2：声音采样与文件大小
EduStream records voice-over narration using the following parameters: sampling rate 44.1 kHz, sample resolution 16 bits, stereo channels. Calculate the uncompressed file size in megabytes (MB) for a 5-minute recording. The audio engineer wants to double the sample rate to 88.2 kHz. Discuss how this change affects file size and the perceived audio quality, explaining the underlying principles of sampling theory. (8 marks)
EduStream 使用以下参数录制旁白：采样率 44.1 kHz，采样分辨率 16 位，立体声通道。计算一段 5 分钟录音的未压缩文件大小，单位为兆字节 (MB)。音频工程师希望将采样率翻倍至 88.2 kHz。讨论这一变化如何影响文件大小和感知音频质量，并解释采样理论的基本原理。(8 分)
00 = 423,360,000 bits. In bytes: 423,360,000 ÷ 8 = 52,920,000 bytes. In MB: 52,920,000 ÷ (1024 × 1024) ≈ 50.45 MB. Doubling the sample rate to 88.2 kHz doubles the bit rate, so the file size also doubles to approximately 100.9 MB. According to the Nyquist theorem, the highest frequency that can be accurately captured is half the sampling rate. The original 44.1 kHz captures up to 22.05 kHz, already beyond human hearing range (which is about 20 kHz). Increasing the sample rate to 88.2 kHz extends the reproducible frequency to 44.1 kHz, which may be useful for professional mastering or for preserving ultrasonic information, but for typical voice narration the improvement in perceived quality is negligible, while the storage cost increases dramatically.
首先，将录音时间转换为秒：5 × 60 = 300 秒。每秒比特数 = 44,100 × 16 × 2（立体声）= 1,411,200 比特/秒。总比特数 = 1,411,200 × 300 = 423,360,000 比特。字节数：423,360,000 ÷ 8 = 52,920,000 字节。兆字节数：52,920,000 ÷ (1024 × 1024) ≈ 50.45 MB。将采样率翻倍至 88.2 kHz 会使比特率翻倍，因此文件大小也大约翻倍至 100.9 MB。根据奈奎斯特定理，能够准确捕获的最高频率是采样率的一半。原来的 44.1 kHz 捕获高达 22.05 kHz，已经超出人类听觉范围（约 20 kHz）。将采样率提高到 88.2 kHz 将可重现频率扩展至 44.1 kHz，这可能对专业母带处理或保留超声波信息有用，但对于典型的语音旁白而言，感知质量的提升微乎其微，而存储成本却大幅增加。
4. Question 3: Compression for Video and Documents | 问题3：视频与文档的压缩
EduStream must deliver video efficiently while also distributing supplementary PDF documents and text-based transcripts. Compare lossy and lossless compression, giving one concrete example of an algorithm for each type. Explain why the company should use lossy compression for its video streams and lossless compression for its text documents. In your answer, refer to how each technique exploits different types of redundancy. (7 marks)
EduStream 需要高效地分发视频，同时还要分发补充的 PDF 文档和文本转录稿。比较有损压缩和无损压缩，各举一种具体的算法为例。解释为什么公司应该对视频流使用有损压缩，而对文本文档使用无损压缩。在你的回答中，要提及每种技术如何利用不同类型的冗余。(7 分)
Lossless compression algorithms, such as Run-Length Encoding (RLE) or Huffman coding, reduce file size without losing any information. They work by identifying and eliminating statistical redundancy, for example by replacing repeated patterns with shorter codes. The original data can be perfectly reconstructed. Lossy compression, such as JPEG for still images or MPEG for video, permanently discards some data that the human sensory system is less likely to notice. It exploits perceptual redundancy, like removing high-frequency colour variations the eye is not sensitive to. For streaming video, lossy compression is essential because the bandwidth savings are enormous (often 95% or more reduction), and the slight quality loss is acceptable to viewers. For text documents such as transcripts, even a single changed byte could alter meaning, so lossless compression (e.g., DEFLATE used in ZIP) is mandatory. A PDF can contain both lossless text and lossy images.
无损压缩算法，如游程编码 (RLE) 或霍夫曼编码，在不丢失任何信息的情况下减小文件大小。它们通过识别和消除统计冗余来工作，例如用更短的代码替换重复模式。原始数据可以完美重建。有损压缩，如用于静态图像的 JPEG 或用于视频的 MPEG，会永久丢弃人类感官系统不太可能注意到的部分数据。它利用感知冗余，例如去除人眼不敏感的高频颜色变化。对于流媒体视频，有损压缩至关重要，因为节省的带宽巨大（通常减少 95% 或更多），而轻微的质量损失观众是可以接受的。对于如转录稿这样的文本文档，即使一个字节的改变也可能改变含义，因此必须使用无损压缩（例如 ZIP 中使用的 DEFLATE）。一个 PDF 文件可以同时包含无损文本和有损图像。
5. Question 4: Network Topology and Transmission Media | 问题4：网络拓扑与传输介质
EduStream's main office is being redesigned. They need a LAN to connect 80 workstations, three file servers, and several network printers. Evaluate the star and bus topologies, making a reasoned recommendation. Additionally, the office spans two floors with a total cable run length of up to 120 metres. Suggest an appropriate wired transmission medium, giving two advantages of your choice over a basic coaxial cable. (8 marks)
EduStream 的主办公室正在重新设计。他们需要一个局域网来连接 80 台工作站、三台文件服务器和若干网络打印机。评估星型拓扑和总线拓扑，提出合理的建议。此外，办公室跨越两层楼，总布线长度可达 120 米。建议一种合适的有线传输介质，并给出其相较于基本同轴电缆的两个优点。(8 分)
In a bus topology, all devices share a single backbone cable. It uses less cable and is simple to set up, but a break in the backbone can bring down the entire network, and performance degrades as more devices are added because of data collisions. A star topology connects each device to a central switch. If one cable fails, only that node is affected, making fault isolation straightforward. Adding new devices is easy and does not disrupt the network. For 80 devices, a star topology using a modern Ethernet switch is the clear recommendation because it offers higher reliability, easier maintenance, and dedicated bandwidth to each node thanks to the switch's ability to create collision domains. With a cable run of up to 120 metres, Category 6a (Cat6a) Unshielded Twisted Pair (UTP) cable is a strong choice; alternatively, fibre optic cable could be used for the backbone between floors. Cat6a supports up to 10 Gbps and is far more resistant to electromagnetic interference than coaxial cable, and it has a higher bandwidth-distance product.
在总线拓扑中，所有设备共享同一条主干电缆。它使用较少的电缆，安装简单，但主干中的一处断裂就可能导致整个网络瘫痪，并且随着设备增多，由于数据冲突，性能会下降。星型拓扑将每台设备连接到一个中央交换机。如果一条电缆出现故障，只有该节点会受影响，从而便于故障隔离。添加新设备也很容易，且不会中断网络。对于 80 台设备，使用现代以太网交换机的星型拓扑是明确的推荐选择，因为它提供更高的可靠性、更易维护，并且由于交换机能够创建碰撞域，能为每个节点提供专属带宽。对于长达 120 米的布线长度，六类增强型非屏蔽双绞线 (Cat6a UTP) 是一个很好的选择；或者，楼层之间的主干可以使用光纤电缆。Cat6a 支持高达 10 Gbps 的速率，比同轴电缆更能抵抗电磁干扰，并且具有更高的带宽-距离乘积。
6. Question 5: IP Addressing and Subnetting | 问题5：IP地址与子网划分
The ISP assigns EduStream the public network 203.178.45.0/24. The company needs to divide this into four separate subnets for the departments: Administration, Content Management, Streaming Engineering, and Guest Wi‑Fi. Explain the concept of subnetting, showing clearly how you derive the new subnet mask, the number of usable host addresses per subnet, and the complete range (network address, first usable, last usable, broadcast) for the Content Management subnet. (8 marks)
ISP 向 EduStream 分配了公有网络 203.178.45.0/24。公司需要将其划分为四个独立的子网，分别用于：行政部、内容管理部、流媒体工程部和访客 Wi‑Fi。解释子网划分的概念，清晰地展示如何得出新的子网掩码、每个子网的可用主机地址数量，以及内容管理子网的完整范围（网络地址、第一个可用地址、最后一个可用地址、广播地址）。(8 分)
8 host bits. To create 4 subnets, we need to borrow 2 bits (2² = 4). The new prefix length is /26, i.e. subnet mask 255.255.255.192. This leaves 6 bits for hosts, so each subnet has 2⁶ – 2 = 62 usable addresses. The subnets are:
