📚 GCSE OCR Computer Science: Data Representation Exam Essentials | GCSE OCR 计算机：数据表示 考点精讲
Data representation is a core topic in GCSE OCR Computer Science, covering how computers store and manipulate numbers, text, images, and sound. Understanding binary, hexadecimal, and compression techniques is essential for the exam and for grasping how digital systems work at the most fundamental level.
数据表示是 GCSE OCR 计算机科学的核心主题，涵盖计算机如何存储和处理数字、文本、图像及声音。理解二进制、十六进制和压缩技术对考试至关重要，也有助于从最基础的层面把握数字系统的工作原理。
1. Why Data Representation Matters | 为什么数据表示如此重要
All digital data inside a computer is represented using binary (0s and 1s) because the underlying hardware uses transistors that act as switches — either off (0) or on (1). By combining these binary values, we can represent numbers, letters, colours, sound waves and any other form of information.
计算机内部的所有数字数据都使用二进制（0 和 1）表示，因为底层硬件使用晶体管作为开关——要么关（0）要么开（1）。通过组合这些二进制值，我们可以表示数字、字母、颜色、声波以及任何其他形式的信息。
In the OCR exam, you need to convert between number systems, calculate file sizes, understand how text, images and sound are digitised, and explain the trade-offs between storage space and quality. This topic builds the foundation for understanding memory, storage and networking in later units.
在 OCR 考试中，你需要在不同数制之间转换、计算文件大小、理解文本、图像和声音如何数字化，并解释存储空间与质量之间的权衡。本主题为后续单元理解内存、存储和网络奠定基础。
2. Storage Units: Bits and Bytes | 存储单位：比特与字节
The smallest unit of data is a bit (binary digit), which can be either 0 or 1. Eight bits form a byte. A byte can represent 256 different values (from 0 to 255) because 2⁸ = 256.
最小的数据单位是比特（二进制位），可以是 0 或 1。八个比特组成一个字节。一个字节可以表示 256 种不同的值（从 0 到 255），因为 2⁸ = 256。
Larger units follow powers of 2: 1 kilobyte (KB) = 1024 bytes, 1 megabyte (MB) = 1024 KB, 1 gigabyte (GB) = 1024 MB, 1 terabyte (TB) = 1024 GB. Note that storage manufacturers sometimes use decimal definitions (e.g., 1 GB = 1000 MB), but in the exam you must use binary definitions unless told otherwise.
更大的单位遵循 2 的幂：1 千字节 (KB) = 1024 字节，1 兆字节 (MB) = 1024 KB，1 千兆字节 (GB) = 1024 MB，1 太字节 (TB) = 1024 GB。请注意，存储制造商有时使用十进制定义（例如 1 GB = 1000 MB），但在考试中除非另有说明，你必须使用二进制定义。
3. Binary and Denary Conversion | 二进制与十进制转换
To convert a binary number to denary (decimal), write the column headings as powers of 2 from right to left: … 128, 64, 32, 16, 8, 4, 2, 1. For each column, if the bit is 1, add the column value; if 0, ignore it. For example, 1011₂ = 8 + 2 + 1 = 11 in denary.
要将二进制数转换为十进制，请从右向左写出以 2 为幂的列标题：…… 128, 64, 32, 16, 8, 4, 2, 1。对每一列，如果该位是 1，则加上列值；如果是 0 则忽略。例如 1011₂ = 8 + 2 + 1 = 11（十进制）。
To convert denary to binary, repeatedly divide the denary number by 2 and note the remainder. Read the remainders from bottom to top. For 13: 13 ÷ 2 = 6 r1; 6 ÷ 2 = 3 r0; 3 ÷ 2 = 1 r1; 1 ÷ 2 = 0 r1. Reading upwards gives 1101₂.
要将十进制转换为二进制，反复将十进制数除以 2 并记录余数。从下往上读取余数。以 13 为例：13 ÷ 2 = 6 余 1；6 ÷ 2 = 3 余 0；3 ÷ 2 = 1 余 1；1 ÷ 2 = 0 余 1。从下往上读得到 1101₂。
4. Hexadecimal Numbers | 十六进制数
Hexadecimal (base-16) is a compact way to represent binary values. It uses digits 0–9 and letters A–F, where A=10, B=11, C=12, D=13, E=14, F=15. Each hex digit represents exactly 4 bits (a nibble). For example, 1010₂ = A₁₆ and 1111₂ = F₁₆.
十六进制（基数为 16）是表示二进制值的一种紧凑方式。它使用数字 0–9 和字母 A–F，其中 A=10, B=11, C=12, D=13, E=14, F=15。每个十六进制位恰好代表 4 位（一个半字节）。例如 1010₂ = A₁₆，1111₂ = F₁₆。
To convert binary to hex, split the binary number into groups of 4 bits from the right, then convert each group. For 11010110₂: split into 1101 0110. 1101 = D, 0110 = 6, so hex is D6₁₆. When converting between hex and denary, go through binary or use column values of 16ⁿ.
要将二进制转换为十六进制，从右开始将二进制数分成 4 位一组，然后转换每组。对于 11010110₂：拆分为 1101 0110。1101 = D，0110 = 6，因此十六进制为 D6₁₆。在十六进制与十进制之间转换时，可通过二进制进行，或使用 16ⁿ 的列值。
5. Binary Arithmetic and Overflow |
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