Year 11 AQA Computer Science: Formulas & Theorems Quick Reference | AQA 计算机：公式定理速查手册

📚 Year 11 AQA Computer Science: Formulas & Theorems Quick Reference | AQA 计算机：公式定理速查手册

This handbook brings together the essential formulas, conversion rules, and logical theorems you need for the Year 11 AQA Computer Science exam. Use it to quickly revise how to calculate file sizes, network speeds, compression ratios, digital number conversions, and Boolean logic simplifications.

本手册汇集了 Year 11 AQA 计算机科学考试必需的核心公式、转换规则和逻辑定理。用它快速复习如何计算文件大小、网络速度、压缩比、数码转换以及布尔逻辑化简。

1. Data Units & Conversions | 数据单位与换算

All data in a computer is represented in binary. The smallest unit is the bit (binary digit), and 8 bits make 1 byte. Storage size is counted in binary multiples, so each larger unit is 1024 times the previous one rather than 1000.

计算机中所有数据都用二进制表示。最小单位是位（bit），8 位组成 1 字节（byte）。存储容量采用二进制倍数，因此每个更大的单位是前一个单位的 1024 倍，而不是 1000 倍。

To convert a smaller unit to a larger unit, divide by 1024 for each step. To go the other way, multiply by 1024.

较小单位换算为较大单位时，每步除以 1024；较大单位换算为较小单位时，每步乘以 1024。

Number of bytes = Number of larger units × 1024ⁿ

字节数 = 更大的单位数 × 1024ⁿ

2. Image File Size Formula | 图像文件大小公式

Uncompressed bitmap images store each pixel individually. The total file size in bits can be found by multiplying the image width (in pixels), image height (in pixels), and colour depth (bits per pixel).

未压缩的位图图像单独存储每个像素。总文件大小（以比特为单位）可由图像宽度（像素）、图像高度（像素）和色彩深度（每像素比特数）相乘得到。

File Size (bits) = Width (px) × Height (px) × Colour Depth (bpp)

文件大小（比特）= 宽度（px）× 高度（px）× 色彩深度（bpp）

Colour depth defines how many colours can be represented. For example, 1 bpp gives 2 colours, 8 bpp gives 256 colours, and 24 bpp (true colour) gives over 16 million colours. To convert the result to bytes, divide by 8. Meta-data (headers, etc.) may add extra bytes in real file formats, but the basic formula ignores these for exam calculations.

色彩深度决定了可表示的颜色数。例如，1 bpp 可显示 2 种颜色，8 bpp 可显示 256 种颜色，24 bpp（真彩色）可显示超过 1600 万种颜色。要将结果转换为字节，除以 8 即可。实际文件格式中元数据（文件头等）会额外增加字节，但考试计算时通常忽略这些只使用基本公式。

3. Sound File Size Formula | 声音文件大小公式

The size of an uncompressed digital audio file depends on four factors: sample rate (how often the sound is measured per second, in Hz), sample resolution (bits per sample, also called bit depth), duration (in seconds), and the number of channels (1 for mono, 2 for stereo).

未压缩数字音频文件的大小取决于四个因素：采样率（每秒测量声音的次数，单位 Hz）、采样分辨率（每采样的比特数，也称位深）、时长（秒）以及声道数（单声道为 1，立体声为 2）。

File Size (bits) = Sample Rate (Hz) × Sample Resolution (bits) × Duration (s) × Channels

文件大小（比特）= 采样率（Hz）× 采样分辨率（比特）× 时长（s）× 声道数

Higher sample rates and larger sample resolutions improve sound quality but dramatically increase file size. For CD-quality audio, the sample rate is 44,100 Hz with a resolution of 16 bits in stereo, generating about 10 MB per minute of sound.

更高的采样率和更大的采样分辨率能提升音质，但会急剧增加文件大小。CD 品质音频的采样率为 44,100 Hz，分辨率为 16 位，立体声，每分钟约产生 10 MB 的数据。

4. Text Storage Estimation | 文本存储估算

The storage needed for plain text is determined by the number of characters and the encoding scheme. A character set maps each character to a binary code; the number of bits per character defines the minimum storage per letter.

纯文本所需的存储空间由字符数量和编码方案决定。字符集将每个字符映射到一个二进制代码；每个字符的位数决定了每个字母的最低存储量。

Text Size (bits) = Number of Characters × Bits per Character

文本大小（比特）= 字符数 × 每字符位数

• Standard ASCII: 7 bits per character (128 characters)
• Extended ASCII: 8 bits per character (256 characters)
• Unicode (UTF-32): 32 bits per character (covers most global scripts)

• 标准 ASCII：每字符 7 位（128 个字符）
• 扩展 ASCII：每字符 8 位（256 个字符）
• Unicode (UTF-32)：每字符 32 位（覆盖绝大多数文字系统）

For example, a 500-character sentence stored in extended ASCII occupies 500 × 8 = 4000 bits (500 bytes), while the same text in UTF-16 would need 8000 bits (1000 bytes).

例如，一个 500 个字符的句子用扩展 ASCII 存储占用 500 × 8 = 4000 位（500 字节），而同样的文本用 UTF-16

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