📚 7S Homework Unit 3: Data Representation and Storage | 7S作业 第3单元：数据表示与存储
Welcome to Unit 3. In this unit, you will learn how computers store and process information using binary codes, and how text, images and sound are converted into digital data. By the end of this unit, you should be able to convert between binary and denary, explain how characters and media are represented, and calculate file sizes.
欢迎学习第3单元。本单元将学习计算机如何使用二进制代码存储和处理信息，以及文本、图像和声音如何转换为数字数据。学完本单元后，你应能进行二进制与十进制之间的转换，解释字符和媒体的表示方式，并计算文件大小。
1. What is Data Representation? | 什么是数据表示？
All data inside a computer, including programs, documents, photos and videos, must be stored as patterns of two symbols: 0 and 1. This is called binary representation because it uses base 2.
计算机内部的所有数据（包括程序、文档、照片和视频）都必须存储为两个符号 0 和 1 的组合。这称为二进制表示法，因为它使用基数为 2 的计数系统。
The processor uses millions of tiny switches called transistors to represent these two states: off (0) and on (1). A single binary digit is called a bit.
处理器使用数百万个称为晶体管的微小开关来表示这两种状态：关（0）和开（1）。一个二进制数字称为一个比特（bit）。
2. Binary Basics: 0s and 1s | 二进制基础：0 和 1
In denary, or base 10, we use ten digits from 0 to 9. In binary, or base 2, we use only two digits: 0 and 1. Each position in a binary number has a place value that doubles from right to left.
在十进制（基数为10）中，我们使用 0 到 9 十个数字。在二进制（基数为2）中，我们只使用两个数字：0 和 1。二进制数中每个位置上的位值从右到左依次翻倍。
For example, the binary number 1011 means one 8, zero 4s, one 2 and one 1. The place values are 8, 4, 2 and 1.
例如，二进制数 1011 表示一个 8、零个 4、一个 2 和一个 1。位值分别是 8、4、2 和 1。
8, 4, 2, 1
3. Converting Binary to Denary | 二进制转十进制
To convert a binary number to denary, write down the binary digits above their place values, multiply each digit by its place value, and then add the results.
要将二进制数转换为十进制，先写下二进制数字及其对应的位值，将每个数字乘以它的位值，然后把结果相加。
om left to right are 8, 4, 2 and 1. So we calculate (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1).
例如，将 1011₂ 转换为十进制。从左到右的位值为 8、4、2 和 1。因此我们计算 (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)。
8 + 0 + 2 + 1 = 11
So binary 1011 is equal to 11 in denary, shown as 1011₂ = 11₁₀.
因此二进制 1011 等于十进制 11，表示为 1011₂ = 11₁₀。
4. Converting Denary to Binary | 十进制转二进制
To convert a denary number to binary, find the largest power of 2 that fits into the number, write 1 in that place, subtract it, and continue with the remainder. You can also use repeated division by 2 and read the remainders backwards.
要将十进制数转换为二进制，先找到不超过该数的最大 2 的幂，在该位置写 1，减去该值，然后继续处理余数。你也可以使用连续除以 2 的方法，反向读取余数。
fits is 8, leaving 5. Then 4 fits, leaving 1, and then 1 fits. So we have 8 + 4 + 1 = 13.
例如，将 13 转换为二进制。不超过 13 的最大 2 的幂是 8，余数为 5。然后 4 符合，余数为 1，最后 1 符合。因此我们有 8 + 4 + 1 = 13。
13₁₀ = 1101₂
5. Units of Digital Information | 数字信息单位
Computers measure data using bits and bytes. A byte is made of 8 bits. Larger units are multiples of a byte, but remember that in many cases they are based on powers of 2 rather than powers of 10.
计算机使用比特和字节来度量数据。一个字节由 8 个比特组成。更大的单位是字节的倍数，但要记住，在许多情况下它们基于 2 的幂而不是 10 的幂。
| Unit | 单位 | Abbreviation | 缩写 | Typical size | 通常大小 |
|---|---|---|
| Bit | 比特 | b | 1 binary digit |
| Byte | 字节 | B | 8 bits |
| Kilobyte | 千字节 | KB | 1,000 bytes or 2¹⁰ bytes |
| Megabyte | 兆字节 | MB | 1,000,000 bytes or 2²⁰ bytes |
| Gigabyte | 吉字节 | GB | 1,000,000,000 bytes or 2³⁰ bytes |
6. Representing Characters: ASCII and Unicode | 字符表示：ASCII 与 Unicode
Text is represented by giving each character a unique binary code. The most basic system is ASCII, which originally used 7 bits to represent 128 characters, including English letters, digits and punctuation.
文本通过为每个字符分配唯一的二进制代码来表示。最基本的系统是 ASCII，它最初使用 7 位来表示 128 个字符，包括英文字母、数字和标点符号。
For example, uppercase 'A' has the code 65 in denary, which is 0100 0001 in binary. Lowercase 'a' is 97, or 0110 0001.
例如，大写字母 'A' 的十进制代码是 65，二进制为 0100 0001。小写字母 'a' 是 97，二进制为 0110 0001。
ASCII cannot represent all world languages, so Unicode was developed. Unicode uses up to 32 bits per character and can represent more than one million symbols, emojis and scripts.
ASCII 无法表示世界上所有的语言，因此开发了 Unicode。Unicode 每个字符最多使用 32 位，可以表示超过一百万个符号、表情符号和文字系统。
7. Representing Images: Pixels and Colour Depth | 图像表示：像素与颜色深度
Images are stored as a grid of tiny squares called pixels. Each pixel has a binary value that represents its colour. The number of bits used for each pixel is called the colour depth.
图像以称为像素的微小方格网格形式存储。每个像素都有一个表示其颜色的二进制值。用于每个像素的位数称为颜色深度。
A higher colour depth means more colours can be represented, but the file size becomes larger. A 1-bit image has only two colours, while a 24-bit image can show about 16.7 million colours.
颜色深度越高，可表示的颜色越多，但文件大小也会更大。1 位图像只有两种颜色，而 24 位图像可以显示约 1670 万种颜色。
ixels, usually given as width × height. File size can be estimated with the formula below:
图像的分辨率是像素总数，通常表示为宽 × 高。文件大小可以用下面的公式估算：
File size = width × height × colour depth
8. Representing Sound: Sampling | 声音表示：采样
Sound is an analogue wave, so it must be converted to digital form by taking samples at regular intervals. This process is called sampling.
声音是一种模拟波，因此必须通过定期采样将其转换为数字形式。这个过程称为采样。
The sample rate is how many samples are taken per second, measured in hertz (Hz). The bit depth is how many bits are used for each sample. Higher sample rate and bit depth improve quality but increase file size.
采样率是每秒采集多少个样本，单位为赫兹（Hz）。位深是每个样本使用的位数。采样率和位深越高，音质越好，但文件大小也会增加。
To estimate the size of an uncompressed sound file, use this formula:
要估算未压缩声音文件的大小，请使用以下公式：
File size = sample rate × bit depth × duration
9. Storage and File Sizes | 存储与文件大小
Being able to calculate file sizes helps you choose appropriate storage and understand download times. You should practise converting between bits, bytes, kilobytes, megabytes and gigabytes.
能够计算文件大小有助于你选择合适的存储设备并理解下载时间。你应练习在比特、字节、千字节、兆字节和吉字节之间进行换算。
× 16 × 30 = 21,168,000 bits. Dividing by 8 gives 2,646,000 bytes, which is about 2.65 MB.
例如，一首 30 秒的短歌曲，以 44,100 Hz 的采样率、16 位位深、单声道录制，大小约为 44,100 × 16 × 30 = 21,168,000 比特。除以 8 得到 2,646,000 字节，约为 2.65 MB。
10. Data Compression: Lossy and Lossless | 数据压缩：有损与无损
Compression reduces file size so that data uses less storage and transmits faster. There are two main types: lossy and lossless.
压缩可以减小文件大小，使数据占用更少的存储空间并更快传输。压缩主要有两种类型：有损压缩和无损压缩。
Lossless compression removes redundancy without losing any original data. When the file is decompressed, it is identical to the original. It is used for text files, programs and some image formats like PNG.
无损压缩在不丢失任何原始数据的情况下去除冗余。文件解压后与原始文件完全相同。它用于文本文件、程序以及 PNG 等一些图像格式。
Lossy compression permanently removes some data that is less noticeable to humans. It is used for JPEG images, MP3 audio and video streaming. The file is smaller, but quality cannot be fully restored.
有损压缩会永久性地删除一些人类不易察觉的数据。它用于 JPEG 图像、MP3 音频和视频流。文件更小，但质量无法完全恢复。
11. Check Your Understanding | 检查你的理解
Here are the key points you should be able to do after completing Unit 3:
完成第3单元后，你应该能够做到以下关键点：
- Explain why computers use binary. 解释计算机为什么使用二进制。
- Convert between binary and denary for small numbers. 对较小的数字进行二进制与十进制转换。
- Describe how ASCII and Unicode represent characters. 描述 ASCII 和 Unicode 如何表示字符。
- Explain how images and sound are stored digitally. 解释图像和声音如何以数字方式存储。
- Use the formulas for image and sound file size. 使用图像和声音文件大小的公式。
- Compare lossy and lossless compression. 比较有损压缩和无损压缩。
12. Exam-Style Tips | 考试技巧
When answering data representation questions, always show your working for conversions and calculations. This allows you to earn method marks even if the final answer is wrong.
在回答数据表示问题时，务必写出转换和计算的过程。这样即使最终答案错误，你也能获得方法分。
Remember to write units such as bits, bytes, KB, MB or GB in file size answers. Check whether the question asks for bits or bytes before you divide or multiply by 8.
在文件大小的答案中记得写上比特、字节、KB、MB 或 GB 等单位。在除以或乘以 8 之前，先检查题目要求的是比特还是字节。
For compression questions, use the phrase 'quality cannot be restored' with lossy, and 'no data is lost' with lossless to show precise understanding.
对于压缩问题，使用有损压缩时用“质量无法恢复”，无损压缩时用“没有数据丢失”，以体现准确理解。
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