SQA Computing: Formulas & Theorems Quick Reference | SQA 计算机：公式定理速查手册

📚 SQA Computing: Formulas & Theorems Quick Reference | SQA 计算机：公式定理速查手册

This quick reference handbook gathers the most important formulas, laws and theorems you will meet in Year 10 SQA Computing Science. Mastering these will help you solve numerical problems, simplify logic expressions and understand core computational principles with confidence.

本速查手册汇集了十年级 SQA 计算机科学中最重要的公式、定律和定理。掌握这些内容将帮助你解决数值计算问题、化简逻辑表达式，并自信地理解核心计算原理。

1. Data Unit Conversions | 数据单位转换

Digital data is measured in bits and bytes. Conversions rely on powers of 2 because computers use binary.

数字数据以位和字节为单位度量。转换基于 2 的幂，因为计算机使用二进制。

Key conversion table:

关键转换表：

To convert from a larger unit to a smaller unit, multiply by 1024 for each step. To convert from smaller to larger, divide by 1024 repeatedly.

从较大单位转换为较小单位，每步乘以 1024。从较小单位转换为较大单位，逐次除以 1024。

Total bits = Total bytes × 8

2. Image File Size Formula | 图像文件大小公式

For an uncompressed bitmap image, the file size depends on the resolution (width × height in pixels) and the colour depth (bits per pixel).

对于未压缩的位图图像，文件大小取决于分辨率（以像素表示的宽度 × 高度）和颜色深度（每像素位数）。

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

To obtain the size in bytes, divide the result by 8. For kilobytes, divide by (8 × 1024).

要得到以字节为单位的大小，将结果除以 8；要得到千字节，除以 (8 × 1024)。

Example: A 1920×1080 image with 24-bit colour depth requires 1920 × 1080 × 24 = 49,766,400 bits ≈ 6.22 MB.

示例：一幅 1920×1080、24 位颜色深度的图像需要 1920×1080×24 = 49,766,400 位 ≈ 6.22 MB。

3. Sound File Size Formula | 音频文件大小公式

Uncompressed digital audio file size is determined by sample rate, sample depth, length and channel count.

未压缩的数字音频文件大小取决于采样率、采样深度、时长和声道数。

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

Convert bits to bytes by dividing by 8, then to larger units as needed.

通过除以 8 将位转换为字节，再根据需要转换为更大单位。

Example: CD-quality stereo audio (44,100 Hz, 16 bits, 3 minutes) = 44100 × 16 × 180 × 2 = 254,016,000 bits ≈ 30.3 MB.

示例：CD 质量立体声音频（44,100 Hz、16 位、3 分钟）= 44100×16×180×2 = 254,016,000 位 ≈ 30.3 MB。

4. Boolean Algebra Laws | 布尔代数定律

The following laws allow simplification of logic expressions. Variables A and B can be 0 or 1.

以下定律可用于化简逻辑表达式。变量 A 和 B 可以取值 0 或 1。

Identity: A + 0 = A and A · 1 = A

同一律：A + 0 = A，A · 1 = A

Null: A + 1 = 1 and A · 0 = 0

零一律：A + 1 = 1，A · 0 = 0

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