End of Unit 1: Exam-style Case Study Questions | 单元一结束：考试风格案例研究题

📚 End of Unit 1: Exam-style Case Study Questions | 单元一结束：考试风格案例研究题

Case study questions in Cambridge A Level Computer Science Unit 1 often combine several topics, such as data representation, file size calculations, compression and error detection, into one realistic scenario. This article gives you a complete set of exam-style practice questions based on the SmartSurvey platform, with worked solutions, mark schemes and revision tips.

剑桥 A Level 计算机科学单元一的案例研究题通常将多个主题（如数据表示、文件大小计算、压缩和错误检测）整合到一个真实场景中。本文以 SmartSurvey 平台为背景，提供一套完整的考试风格练习题，并附详细解答、评分标准和复习技巧。

1. Understanding the Case Study | 理解案例研究背景

Read the scenario carefully and underline the key technical facts: the exact image resolution and colour depth, the audio sampling rate and duration, the text encoding method, and the data transmission requirements. These numbers drive most of the calculations.

仔细阅读场景并划出关键技术事实：精确的图像分辨率和颜色深度、音频采样率和时长、文本编码方法以及数据传输要求。这些数字将驱动大部分计算。

The SmartSurvey case study is described below. Use it for all the questions that follow.

SmartSurvey 案例研究如下。后续所有问题均以此为基础。

SmartSurvey is an online platform that allows users to create surveys and collect responses. Survey creators can upload a logo image with a maximum size of 1024 × 768 pixels and 24-bit colour depth. They can also record a 20-second audio welcome message sampled at 44.1 kHz with a 16-bit sample resolution in mono. Survey responses are stored as text using Unicode. The platform must transmit data over the internet and verify data integrity using checksums. A junior developer has asked for help with several tasks.

SmartSurvey 是一个在线平台，允许用户创建调查并收集回复。调查创建者可以上传最大尺寸为 1024 × 768 像素、颜色深度为 24 位的标志图像。他们还可以录制 20 秒的音频欢迎信息，采样率为 44.1 kHz，样本分辨率为 16 位，单声道。调查回复使用 Unicode 以文本形式存储。该平台必须通过互联网传输数据，并使用校验和验证数据完整性。一位初级开发人员需要帮助完成几项任务。

2. Question Types in Unit 1 | 单元一常见问题类型

Unit 1 case study questions usually test four skill areas: direct conversion and calculation, explanation of concepts, comparison and choice of methods, and evaluation of errors or limitations. You should be ready to show your working and quote units in every answer.

单元一案例研究题通常测试四个技能领域：直接转换与计算、概念解释、方法比较与选择，以及错误或局限性的评估。你应该准备好展示解题步骤并在每个答案中写出单位。

Binary, denary and hexadecimal conversions with a given number of bits.

具有指定位数的二进制、十进制和十六进制转换。
File size estimation for images and sound using sample rate, resolution and duration.

使用采样率、分辨率和时长进行图像和声音的文件大小估算。
Choosing between lossless and lossy compression for different media types.

为不同媒体类型选择无损或有损压缩。
Explaining how error detection methods such as parity and checksums work.

解释奇偶校验和校验和等错误检测方法的工作原理。

3. Binary and Hexadecimal Conversions | 二进制与十六进制转换

Question: Convert the decimal value 2025 into an 11-bit binary number and then into hexadecimal. Show your working.

问题：将十进制数 2025 转换为 11 位二进制数，然后再转换为十六进制。请展示你的计算过程。

Solution: Use the place-value method. The largest power of 2 not exceeding 2025 is 2¹⁰ = 1024. Subtract the powers in order: 2025 − 1024 = 1001; 1001 − 512 = 489; 489 − 256 = 233; 233 − 128 = 105; 105 − 64 = 41; 41 − 32 = 9; 9 − 8 = 1; 1 − 1 = 0. This gives the binary digits from 2¹⁰ to 2⁰: 11111101001₂.

解答：使用位权法。不超过 2025 的最大 2 的幂是 2¹⁰ = 1024。按顺序减去各位权：2025 − 1024 = 1001；1001 − 512 = 489；489 − 256 = 233；233 − 128 = 105；105 − 64 = 41；41 − 32 = 9；9 − 8 = 1；1 − 1 = 0。由此得到从 2¹⁰ 到 2⁰ 的二进制位：11111101001₂。

To convert binary to hexadecimal, group the binary digits in fours from the right: 0111 1110 1001. Each group converts to 7, E and 9. Therefore the hexadecimal value is 7E9₁₆.

若要将二进制转换为十六进制，从右向左每四位分组：0111 1110 1001。每组分别转换为 7、E 和 9。因此十六进制值为 7E9₁₆。

2025₁₀ = 11111101001₂ = 7E9₁₆

Marking points: 1 mark for the correct binary value, 1 mark for the correct hexadecimal value, and 1 mark for showing the grouping or subtraction method. A common error is to write the binary digits in the wrong order after subtracting powers.

评分点：正确的二进制值得 1 分，正确的十六进制值得 1 分，展示分组或减法过程得 1 分。一个常见错误是在减去各位权后把二进制位写反。

4. Text Representation and Encoding | 文本表示与编码

Question: Survey responses contain names in Chinese and emoji characters. Explain why Unicode is used instead of ASCII and give one advantage and one drawback of using Unicode.

问题：调查回复包含中文姓名和表情符号。解释为什么使用 Unicode 而不是 ASCII，并给出使用 Unicode 的一个优点和一个缺点。

Answer: ASCII uses 7 bits and can represent only 128 characters, which is enough for basic English letters, digits and punctuation. Unicode can represent over 143,000 characters using 8, 16 or 32 bits per character, so it supports Chinese, emoji and many other writing systems.

答案：ASCII 使用 7 位，只能表示 128 个字符，这足够基本的英文字母、数字和标点使用。Unicode 每个字符可使用 8、16 或 32 位，能够表示超过 143,000 个字符，因此支持中文、表情符号和许多其他书写系统。

Advantage: Unicode allows a single encoding scheme to handle multiple languages and symbols, so survey data can be global. Drawback: Unicode often uses more bits per character than ASCII, so text files may be larger and require more storage or bandwidth.

优点：Unicode 允许单一编码方案处理多种语言和符号，因此调查数据可以面向全球。缺点：Unicode 每字符使用的位数通常比 ASCII 多，因此文本文件可能更大，并且需要更多的存储空间或带宽。

ASCII = 7 bits → 128 characters; Unicode = 8/16/32 bits → 143,000+ characters

ASCII = 7 位 → 128 个字符；Unicode = 8/16/32 位 → 143,000+ 个字符

Marking points: 1 mark for stating the limited range of ASCII, 1 mark for explaining Unicode’s wider range, and 1 mark for giving a valid advantage and drawback. Avoid saying Unicode uses ‘7 bits’ or ‘ASCII supports Chinese’.

评分点：说明 ASCII 范围有限得 1 分，解释 Unicode 范围更广得 1 分，给出一个有效的优点和缺点得 1 分。避免说 Unicode 使用 ‘7 位’ 或 ‘ASCII 支持中文’。

5. Image File Size Calculations | 图像文件大小计算

Question: Calculate the uncompressed file size of the SmartSurvey logo image stored at 1024 × 768 pixels with 24-bit colour depth. Give your answer in MiB, rounded to two decimal places.

问题：计算以 1024 × 768 像素、24 位颜色深度存储的 SmartSurvey 标志图像的未压缩文件大小。答案以 MiB 为单位，四舍五入到两位小数。

Solution: First calculate the total number of pixels: 1024 × 768 = 786,432 pixels. Then multiply by the colour depth: 786,432 × 24 = 18,874,368 bits. Convert bits to bytes by dividing by 8: 18,874,368 ÷ 8 = 2,359,296 bytes. Finally divide by 1024 twice to convert to MiB: 2,359,296 ÷ 1024 ÷ 1024 = 2.25 MiB.

解答：首先计算像素总数：1024 × 768 = 786,432 像素。然后乘以颜色深度：786,432 × 24 = 18,874,368 位。将位转换为字节需除以 8：18,874,368 ÷ 8 = 2,359,296 字节。最后除以 1024 两次转换为 MiB：2,359,296 ÷ 1024 ÷ 1024 = 2.25 MiB。

File size (bytes) = (width × height × colour depth) ÷ 8

文件大小（字节）=（宽度 × 高度 × 颜色深度）÷ 8

Marking points: 1 mark for correct total pixels, 1 mark for converting bits to bytes, and 1 mark for the correct MiB answer. A very common error is to forget the ÷ 8 step and give the answer in bits, or to use 1024 × 768 × 24 and call it bytes directly.

评分点：正确的像素总数得 1 分，正确将位转换为字节得 1 分，正确的 MiB 答案得 1 分。一个非常常见的错误是忘记 ÷ 8 这一步，直接把答案写成位，或者把 1024 × 768 × 24 的结果直接称为字节。

6. Sound Sampling and Data Rate | 声音采样与数据速率

Question: Calculate the uncompressed file size of the 20-second mono audio welcome message sampled at 44.1 kHz with a 16-bit sample resolution. Give your answer in MiB, rounded to two decimal places.

问题：计算 20 秒单声道音频欢迎信息的未压缩文件大小，该音频采样率为 44.1 kHz，样本分辨率为 16 位。答案以 MiB 为单位，四舍五入到两位小数。

Solution: Total number of samples = sample rate × duration = 44,100 × 20 = 882,000 samples. Each sample uses 16 bits in mono, so total bits = 882,000 × 16 × 1 = 14,112,000 bits. Convert to bytes: 14,112,000 ÷ 8 = 1,764,000 bytes. Convert to MiB: 1,764,000 ÷ 1024 ÷ 1024 ≈ 1.68 MiB.

解答：样本总数 = 采样率 × 时长 = 44,100 × 20 = 882,000 个样本。每个样本在单声道中使用 16 位，因此总位数 = 882,000 × 16 × 1 = 14,112,000 位。转换为字节：14,112,000 ÷ 8 = 1,764,000 字节。转换为 MiB：1,764,000 ÷ 1024 ÷ 1024 ≈ 1.68 MiB。

File size (bits) = sample rate × sample resolution × channels × time

文件大小（位）= 采样率 × 样本分辨率 × 通道数 × 时间

Marking points: 1 mark for total samples, 1 mark for total bits, 1 mark for converting to MiB. Common errors include forgetting to multiply by the number of channels, using 20 seconds as 20 ms, or mixing up 44.1 kHz with 44.1 Hz.

评分点：样本总数得 1 分，总位数得 1 分，转换为 MiB 得 1 分。常见错误包括忘记乘以通道数，把 20 秒当作 20 毫秒，或者把 44.1 kHz 与 44.1 Hz 混淆。

7. Lossless vs Lossy Compression | 无损与有损压缩

Question: The platform wants to reduce upload time. Compare lossless and lossy compression for the logo image and the audio welcome message. Which compression type should be used for each and why?

问题：该平台希望减少上传时间。比较无损压缩和有损压缩在标志图像和音频欢迎信息上的应用。每种媒体应使用哪种压缩类型？为什么？

Answer: Lossless compression reduces file size without losing any original data, so it can be fully reconstructed. It is suitable for the logo image because logos contain sharp edges, text and flat colours, and any pixel loss would be visible. Lossy compression permanently removes less important data, achieving much smaller files, but some quality is lost. It is suitable for the audio welcome message because a small loss of audio quality is usually acceptable for human speech, and the file size reduction is large.

答案：无损压缩在不丢失任何原始数据的情况下减小

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End of Unit 1: Exam-style Case Study Questions | 单元一结束：考试风格案例研究题