GCSE Edexcel Computer Science: Formula Summary Handbook | GCSE Edexcel 计算机：公式汇总手册

📚 GCSE Edexcel Computer Science: Formula Summary Handbook | GCSE Edexcel 计算机：公式汇总手册

This revision guide brings together all the essential formulas you need for the GCSE Edexcel Computer Science exam. From file size calculations to compression ratios, every equation is explained step by step with both English and Chinese explanations. Keep this handbook handy as a quick reference, and make sure you understand the units and conventions used by the Edexcel specification.

这份复习指南汇集了 GCSE Edexcel 计算机科学考试所需的所有核心公式。从文件大小计算到压缩比，每一个公式都配有中英双语的逐步讲解。请将这本手册作为快速参考资料，并确保你理解 Edexcel 考试大纲中使用的单位和约定。

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1. Storage Unit Conversions | 存储单位换算

Edexcel GCSE Computer Science uses decimal (base‑10) units: 1 kilobyte (KB) = 1000 bytes, 1 megabyte (MB) = 1000 KB, 1 gigabyte (GB) = 1000 MB, 1 terabyte (TB) = 1000 GB. In some contexts, binary (base‑2) units may be mentioned, where 1 KiB = 1024 bytes, but the exam expects the use of the decimal convention unless specified otherwise.

Edexcel GCSE 计算机科学使用十进制单位：1 千字节 (KB) = 1000 字节，1 兆字节 (MB) = 1000 KB，1 吉字节 (GB) = 1000 MB，1 太字节 (TB) = 1000 GB。在某些情境下可能会提及二进制单位 (1 KiB = 1024 字节)，但考试若无特别说明，默认使用十进制。

To convert between units, multiply or divide by 1000 repeatedly. For example, to convert 2,500,000 bytes into megabytes: divide by 1000 twice (first to KB, then to MB).

单位之间换算时，反复乘以或除以 1000。例如，将 2,500,000 字节换算为兆字节：先除以 1000 变成 KB，再除以 1000 变成 MB。

Larger unit to smaller: ×1000 each step. Smaller to larger: ÷1000 each step.

大单位换小单位：每级 ×1000。小单位换大单位：每级 ÷1000。

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2. Text File Size | 文本文件大小

The size of a plain text file depends on the number of characters and the character encoding used. Most exam questions assume ASCII encoding, where each character occupies 8 bits (1 byte). If a text file contains 500 characters, the file size is 500 bytes (or 4000 bits).

纯文本文件的大小取决于字符数量和所用的字符编码。多数考题假设使用 ASCII 编码，每个字符占 8 位（1 字节）。若文本文件包含 500 个字符，则文件大小为 500 字节（即 4000 位）。

Text file size (bytes) = number of characters × 1 byte

文本文件大小（字节）= 字符数 × 1 字节

When characters are encoded with Unicode (e.g., UTF‑8), a single character may occupy more than 1 byte, but for GCSE Edexcel purposes, stick to the 1‑byte‑per‑character rule unless told otherwise.

当字符采用 Unicode（如 UTF‑8）编码时，单个字符可能占用超过 1 字节，但在 GCSE Edexcel 考试中，除非另有说明，请按每字符 1 字节的规则计算。

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3. Image File Size | 图像文件大小

A bitmap image is made up of pixels, and each pixel stores a colour value determined by the colour depth. The total number of bits required for an image is calculated by multiplying the width in pixels, the height in pixels, and the colour depth (bits per pixel). To express the size in bytes, divide by 8; to convert to kilobytes, divide by 8000 (Edexcel uses 1000‑based divisions).

位图图像由像素组成，每个像素储存一个由颜色深度决定的颜色值。图像所需的总位数可通过图像的像素宽度、像素高度和颜色深度（每像素位数）相乘得出。若要以字节表示文件大小，需除以 8；若转为千字节，则除以 8000（Edexcel 采用 1000 进制换算）。

Image file size (bits) = width (pixels) × height (pixels) × colour depth (bits per pixel)

图像文件大小（位）= 宽度（像素）× 高度（像素）× 颜色深度（每像素位数）

Example: A 300×200 pixel photo with 24‑bit colour depth uses 300 × 200 × 24 = 1,440,000 bits, or 180,000 bytes, or 180 KB.

例如：一张 300×200 像素的 24 位色深照片占用 300 × 200 × 24 = 1,440,000 位，即 180,000 字节，或 180 KB。

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4. Sound File Size | 声音文件大小

Digital audio is stored by taking samples of the sound wave at regular intervals. The file size depends on the sample rate (samples per second, in Hz), the bit depth (bits per sample), the duration in seconds, and the number of channels (1 for mono, 2 for stereo). Multiply these four values to get the file size in bits.

数字音频通过对声波进行定期采样来存储。文件大小取决于采样率（每秒采样数，单位 Hz）、位深度（每采样位数）、以秒为单位的时长和声道数（单声道为 1，立体声为 2）。将这四个值相乘即可得到以位为单位的文件大小。

Sound file size (bits) = sample rate × bit depth × duration (s) × number of channels

声音文件大小（位）= 采样率 × 位深度 × 时长（秒）× 声道数

A 10‑second stereo recording at 44.1 kHz with 16‑bit depth: 44,100 × 16 × 10 × 2 = 14,112,000 bits, which is 1,764,000 bytes or about 1.764 MB.

一段 10 秒、44.1 kHz、16 位深度立体声录音：44,100 × 16 × 10 × 2 = 14,112,000 位，即 1,764,000 字节，约 1.764 MB。

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5. Colour Depth and Number of Colours | 颜色深度与颜色数量

Colour depth is the number of bits used to represent the colour of a single pixel. The total number of colours that can be represented is 2 raised to the power of the colour depth. For instance, 1‑bit colour depth gives 2^1 = 2 colours (black and white), 8‑bit gives 2^8 = 256 colours, 24‑bit gives 2^24 ≈ 16.7 million colours.

颜色深度是用来表示单个像素颜色的位数。可表示的颜色总数等于 2 的颜色深度次方。例如，1 位颜色深度给出 2¹ = 2 种颜色（黑与白），8 位深度给出 2⁸ = 256 种颜色，24 位深度给出 2²⁴ ≈ 1670 万种颜色。

Number of colours = 2^(colour depth)

颜色数量 = 2^(颜色深度)

Increasing the colour depth improves image quality but also increases the file size, as shown in the image formula. The relationship between colour depth and file size is direct: doubling the colour depth doubles the number of bits per pixel.

增加颜色深度会提高图像质量，但也会增加文件大小，正如图像公式所示。颜色深度与文件大小成正比：颜色深度每增加一倍，每像素位数也增加一倍。

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6. Sampling Rate, Bit Depth and Sound Quality | 采样率、位深度与音质

In digital audio, the sample rate and bit depth directly influence the quality and size of the file. A higher sample rate captures more detail per second, while a higher bit depth records more precise amplitude values. Both increase the bit rate, which is the number of bits processed per second.

在数字音频中，采样率和位深度直接影响文件的质量和大小。更高的采样率每秒捕捉更多细节，更高的位深度则记录更精确的振幅值。两者都会提高比特率，即每秒处理的位数。

Bit rate (bps) = sample rate × bit depth × number of channels

比特率（bps）= 采样率 × 位深度 × 声道数

Using the bit rate, you can quickly estimate the file size: multiply the bit rate by the duration. For instance, CD‑quality audio (44.1 kHz, 16‑bit, stereo) has a bit rate of 44,100 × 16 × 2 = 1,411,200 bps, which is about 1.4 Mbps.

利用比特率，你可以快速估算文件大小：将比特率乘以时长即可。例如，CD 品质音频（44.1 kHz、16 位、立体声）的比特率为 44,100 × 16 × 2 = 1,411,200 bps，约 1.4 Mbps。

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7. Data Transfer Time | 数据传输时间

When files are sent over a network, the transfer time depends on the file size and the data transfer rate (often called bandwidth or bit rate). To calculate the time, divide the file size by the transfer rate, ensuring both are in the same unit (bits, bytes, or multiples).

文件通过网络传输时，传输时间取决于文件大小和数据传输速率（常称为带宽或比特率）。计算时间时，用文件大小除以传输速率，需保证两者使用相同的单位（位、字节或其倍数）。

Transfer time (seconds) = file size ÷ transfer rate

传输时间（秒）= 文件大小 ÷ 传输速率

Example: To download a 30 MB file over a 12 Mbps connection, first convert 30 MB to megabits: 30 × 8 = 240 Mb. Then divide by 12 Mbps to get 20 seconds.

例如：以 12 Mbps 的连接下载一个 30 MB 的文件，首先将 30 MB 转换为兆位：30 × 8 = 240 Mb，然后除以 12 Mbps 得到 20 秒。

Always check the units carefully: network speeds are usually given in megabits per second (Mbps), while file sizes are often given in megabytes (MB). Multiply bytes by 8 to convert to bits.

务必仔细检查单位：网络速度通常以兆位每秒（Mbps）表示，而文件大小常以兆字节（MB）表示。将字节乘以 8 即可转换为位。

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8. Compression Ratio | 压缩比

Compression reduces file size. The compression ratio compares the original size to the compressed size. A ratio of 5:1 means the original file was five times larger than the compressed version. The formula is:

压缩会减小文件大小。压缩比比较原始大小与压缩后的大小。5:1 的比率表示原始文件是压缩后文件的五倍。公式为：

Compression ratio = original file size ÷ compressed file size

压缩比 = 原始文件大小 ÷ 压缩后文件大小

Sometimes the ratio is expressed as ‘original : compressed’, e.g., 100 KB : 20 KB gives a ratio of 5:1. To calculate the compressed size when the ratio is known, rearrange the formula: compressed size = original size ÷ compression ratio.

有时比率表示为“原始 : 压缩”，例如 100 KB : 20 KB 得到 5:1 的比率。若已知压缩比，可变换公式以计算压缩后大小：压缩后大小 = 原始大小 ÷ 压缩比。

Lossless compression preserves all original data, while lossy compression achieves higher ratios by permanently discarding some information. On an exam, you may be asked to calculate the new file size after compression given a ratio or percentage reduction.

无损压缩保留所有原始数据，而有损压缩通过永久丢弃部分信息来获得更高的压缩比。考试中可能要求你根据给定的压缩比或减少百分比计算压缩后的新文件大小。

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9. File Size After Percentage Reduction | 按百分比缩减后的文件大小

Another way to describe compression is by a percentage reduction in size. For example, ‘compressed by 40%’ means the new file size is 60% of the original. The formula is:

另一种描述压缩的方式是文件大小的缩减百分比。例如，“压缩 40%”表示新文件大小是原始大小的 60%。公式为：

Compressed size = original size × (1 – percentage reduction/100)

压缩后大小 = 原始大小 × (1 – 缩减百分比/100)

If an 800 KB image is compressed by 25%, the compressed size is 800 × (1 – 0.25) = 800 × 0.75 = 600 KB. This is quicker to compute when you only need the result in bytes or kilobytes.

若一张 800 KB 的图片被压缩 25%，压缩后大小为 800 × (1 – 0.25) = 800 × 0.75 = 600 KB。当你只需要以字节或千字节为单位的结果时，这种方法计算起来更快。

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10. Quick‑Reference Formula Summary | 公式快速参考汇总

The table below lists the key formulas you should memorise for the GCSE Edexcel Computer Science exam. Use it alongside practice questions to build your confidence.

下表列出了 GCSE Edexcel 计算机科学考试中应记住的关键公式。搭配练习题使用，以增强信心。

Formula / 公式	Application / 应用
Text size = characters × 1 byte	Plain text files, ASCII encoding
Image size (bits) = width × height × colour depth	Bitmap images
Sound size (bits) = sample rate × bit depth × duration × channels	Digital audio files
Bit rate = sample rate × bit depth × channels	Streaming / audio quality
Number of colours = 2^(colour depth)	Colour range of an image
Transfer time = file size ÷ transfer rate	Network downloads/uploads
Compression ratio = original size ÷ compressed size	File compression
Compressed size = original size × (1 – % reduction/100)	Percentage compression
1 KB = 1000 bytes, 1 MB = 1000 KB, etc.	Unit conversions (Edexcel convention)

Remember to always show your workings in exam questions, check the units, and state the final answer with the correct unit (bits, bytes, KB, MB, etc.).

请记住，在考试答题时务必展示计算过程、检查单位，并用正确的单位（位、字节、KB、MB 等）写出最终答案。

Published by TutorHao | Computer Science Revision Series | aleveler.com

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