📚 Year 10 Cambridge Computer Science: Quick Reference to Formulae & Theorems | Year 10 剑桥计算机：公式定理速查手册
This handbook brings together the most important formulae, laws, and truth tables needed for the Year 10 Cambridge IGCSE Computer Science course. Whether you are calculating file sizes, estimating transfer times, simplifying Boolean expressions, or checking logic gate behaviour, the concise entries below will help you work quickly and accurately. All material is aligned with the Cambridge 0478 syllabus and presented in bilingual form for clarity.
本手册汇集了 Year 10 剑桥 IGCSE 计算机科学课程所需的最重要的公式、定律与真值表。无论你是在计算文件大小、估算传输时间、化简布尔表达式还是查阅逻辑门行为，下面的简明条目都能帮助你快速而准确地解题。所有内容均与剑桥 0478 教学大纲一致，并以双语对照形式呈现，便于理解。
1. Storage Unit Conversions | 存储单位换算
bytes, 1 MB = 1024 KB, 1 GB = 1024 MB, 1 TB = 1024 GB. When converting, multiply to go from a larger unit to a smaller unit and divide in the opposite direction.
数字存储单位基于 2 的幂。基本关系为 1 字节 = 8 比特。对于更大单位，采用 IEC 定义：1 KB = 1024 字节，1 MB = 1024 KB，1 GB = 1024 MB，1 TB = 1024 GB。转换时，从大单位转为小单位用乘法，反向用除法。
1 byte = 8 bits
1 KB = 2¹⁰ bytes = 1024 bytes
1 MB = 2²⁰ bytes = 1024 KB
1 GB = 2³⁰ bytes = 1024 MB
1 TB = 2⁴⁰ bytes = 1024 GB
8. Always check whether the question requires the answer in bits, bytes, or a larger unit.
若要计算给定字节大小的文件所含的总比特数，使用：总比特数 = 文件字节大小 × 8。解题时务必确认题目要求的单位是比特、字节还是更大单位。
Example: A 5 MB file in bits: 5 × 1024 × 1024 × 8 = 41,943,040 bits.
示例：一个 5 MB 文件的比特数：5 × 1024 × 1024 × 8 = 41,943,040 比特。
2. Image File Size | 图像文件大小
The size of an uncompressed bitmap image depends on its pixel dimensions and colour depth (the number of bits used to store the colour of each pixel). The formula multiplies width, height, and colour depth.
未压缩的位图图像大小取决于其像素尺寸和颜色深度（每个像素颜色所占的比特数）。公式将宽度、高度与颜色深度相乘。
Image file size (bits) = width (pixels) × height (pixels) × colour depth (bits per pixel)
Common colour depths include 1 bit (monochrome), 8 bits (256 colours), and 24 bits (true colour). If the size is required in bytes, first calculate bits and then divide by 8.
常见的颜色深度有 1 位（单色）、8 位（256 色）和 24 位（真彩色）。如果题目要求字节数，先算出比特数再除以 8。
Example: ith 24-bit colour depth uses 800 × 600 × 24 = 11,520,000 bits = 1,440,000 bytes ≈ 1.37 MB.
示例：一幅 800 × 600、24 位色彩深度的图像占用 800 × 600 × 24 = 11,520,000 比特 = 1,440,000 字节 ≈ 1.37 MB。
3. Sound File Size | 音频文件大小
Uncompressed sound file size is determined by the sample rate, sample resolution (bit depth), duration, and the number of channels. Each sample is recorded at a fixed number of bits per channel.
未压缩音频文件的大小由采样率、采样分辨率（位深度）、时长以及声道数决定。每个声道上的每一个采样都以固定比特数记录。
e (bits) = sample rate (Hz) × sample resolution (bits) × duration (s) × number of channels
Typical CD quality uses a sample rate of 44.1 kHz, 16 bits per sample, and 2 channels (stereo). Remember to convert minutes to seconds and to keep all units consistent.
典型的 CD 音质使用 44.1 kHz 采样率、每采样 16 比特、2 声道（立体声）。解题时记得把分钟转换为秒，并保持所有单位一致。
Example: te of stereo audio at 44.1 kHz, 16 bits: 44100 × 16 × 60 × 2 = 84,672,000 bits ≈ 10.09 MB.
示例：1 分钟、44.1 kHz、16 位的立体声音频：44100 × 16 × 60 × 2 = 84,672,000 比特 ≈ 10.09 MB。
4. Video File Size | 视频文件大小
An uncompressed video can be thought of as a sequence of bitmap images (frames) displayed per second. Therefore the file size depends on the frame dimensions, colour depth, frame rate, and duration.
未压缩视频可视为一系列每秒播放的位图图像（帧）。因此文件大小取决于帧尺寸、颜色深度、帧率和时长。
size (bits) = frame width × frame height × colour depth × frame rate (fps) × duration (s)
This formula gives the size for the video component only. In practice, sound is often stored separately and added to the total. The calculation above assumes no compression.
该公式仅计算视频部分的大小。实际中音频通常单独存储并加入总量。以上计算假设无压缩。
Example: resolution, 24-bit colour, at 30 fps: 1920×1080×24×30×10 = 14,929,920,000 bits ≈ 1.74 GB.
示例：一段 10 秒、1920×1080 分辨率、24 位色彩、30 fps 的视频：1920×1080×24×30×10 = 14,929,920,000 比特 ≈ 1.74 GB。
5. Data Transfer Time | 数据传输时间
When sending a file over a network, the transfer time is calculated by dividing the file size by the data transfer rate. Always ensure that both are expressed in the same units (both in bits or both in bytes).
通过网络发送文件时，传输时间等于文件大小除以数据传输速率。务必保证两者的
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