📚 Year 11 OCR Computer Science: Formula & Theorem Quick Reference Handbook | Year 11 OCR 计算机科学：公式定理速查手册
This quick reference handbook compiles essential formulas, theorems, and calculation methods for the OCR GCSE (Year 11) Computer Science specification. Use it to revise data representation, Boolean logic, and algorithm efficiency, ensuring you can tackle exam questions confidently.
本速查手册汇编了 OCR GCSE（Year 11）计算机科学课程中必备的公式、定理与计算方法。可用于快速复习数据表示、布尔逻辑和算法效率，帮助你在考试中从容应对计算类题目。
1. Data Units and Conversions | 数据单位与换算
TB) = 1000 GB. The smallest unit is a bit; 4 bits form a nibble and 8 bits form a byte. To convert between units, multiply or divide by 1000.
OCR 计算机科学采用十进制单位前缀：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。最小单位是比特；4 比特组成半字节，8 比特组成一字节。单位换算只需乘以或除以 1000。
| Unit | Equivalent | Power of 10 |
| 1 bit | smallest unit | - |
| 1 nibble | 4 bits | - |
| 1 byte (B) | 8 bits | - |
| 1 KB | 1000 bytes | 103 bytes |
| 1 MB | 1000 KB | 106 bytes |
| 1 GB | 1000 MB | 109 bytes |
| 1 TB | 1000 GB | 1012 bytes |
2. Text File Size Calculation | 文本文件大小计算
For a plain text file, the size in bits is calculated as: File size (bits) = number of characters × bits per character. Standard ASCII typically uses 7 or 8 bits per character (often stored as 1 byte). Extended ASCII uses 8 bits. Unicode UTF-16 uses 16 bits per character, while UTF-8 can vary but is often treated as 8 bits for basic characters.
纯文本文件的大小（以比特计）公式为：文件大小（比特）= 字符数 × 每字符比特数。标准 ASCII 通常每字符占 7 或 8 比特（常存为 1 字节）。扩展 ASCII 使用 8 比特。Unicode UTF-16 每字符占 16 比特，而 UTF-8 可变长，但对基本字符仍可视为 8 比特。
with 8 bits per character uses 200 × 8 = 1600 bits, or 200 bytes (since 8 bits = 1 byte).
示例：一份 200 字符的 ASCII 文本，每字符 8 比特，则大小为 200 × 8 = 1600 比特，即 200 字节（因 8 比特 = 1 字节）。
3. Image File Size Calculation | 图像文件大小计算
The fundamental formula for a bitmap image is: Image size (bits) = width (pixels) × height (pixels) × colour depth (bits per pixel). Colour depth (bit depth) indicates how many bits are used to store the colour of one pixel. A 1-bit image supports 21 = 2 colours, 8-bit supports 28 = 256 colours, and 24-bit true colour supports 224 ≈ 16.7 million colours.
位图图像的基本公式为：图像大小（比特）= 宽度（像素） × 高度（像素） × 颜色深度（每像素比特数）。颜色深度表示存储每个像素颜色所用的比特数。1 位图像支持 21=2 种颜色，8 位支持 28=256 种颜色，24 位真彩色支持 224 ≈ 1670 万种颜色。
l = 300 × 200 × 24 = 1,440,000 bits = 180,000 bytes (≈ 175.8 KB, using 1 KB = 1000 bytes).
示例：一张 300 × 200 像素、颜色深度 24 位/像素的图像，大小 = 300 × 200 × 24 = 1,440,000 比特 = 180,000 字节（约 175.8 KB，按 1KB=1000 字节计）。
4. Sound File Size Calculation | 声音文件大小计算
For uncompressed digital audio: s) = sample rate (Hz) × sample resolution (bits) × duration (seconds) × number of channels. Sample rate is the number of samples taken per second, e.g., 44,100 Hz. Sample resolution (bit depth) is the number of bits per sample, e.g., 16-bit. Stereo means 2 channels; mono means 1 channel.
未压缩数字音频的计算：声音大小（比特）= 采样率（Hz）× 采样分辨率（比特）× 时长（秒）× 声道数。采样率是每秒采集的样本数，例如 44,100 Hz。采样分辨率是每个样本的比特数，例如 16 位。立体声为 2 声道，单声道为 1 声道。
ple rate 44,100 Hz, 16-bit resolution): 44,100 × 16 × 60 × 2 = 84,672,000 bits ≈ 10.58 MB.
示例：录制 60 秒 CD 质量立体声（采样率 44,100 Hz，16 位分辨率）：44,100 × 16 × 60 × 2 = 84,672,000 比特 ≈ 10.58 MB。
5. Data Transmission Time | 数据传输时间
The time to transfer a file is given by: Time (seconds) = file size (bits) ÷ data transfer rate (bits per second, bps). If the file size is given in bytes and the speed in bytes per second, the same formula applies without unit conversion. Always ensure consistent units before dividing.
文件传输时间公式为：时间（秒）= 文件大小（比特）÷ 数据传输速率（比特每秒，bps）。如果文件大小以字节给出、速率以字节每秒给出，可直接相除，无需额外换算。计算前务必保持单位一致。
000 bits) transferred over a 4 Mbps connection: time = 16,000,000 / 4,000,000 = 4 seconds.
示例：一个 2 MB 文件（2 × 1000 × 1000 × 8 = 16,000,000 比特）通过 4 Mbps 网络传输，时间 = 16,000,000 / 4,000,000 = 4 秒。
6. Binary and Hexadecimal Conversions | 二进制与十六进制转换
Hexadecimal (base-16) uses digits 0–9 then A (10) to F (15). Each hex digit represents exactly 4 bits (a nibble). Conversion rule: Hex → Binary: replace each hex digit with its 4-bit binary equivalent. Binary → Hex: group bits into nibbles from the right, padding with leading zeros on the left if necessary, then convert each nibble to a hex digit.
十六进制（基数为 16）使用 0–9 和 A(10)–F(15)。每一位十六进制数恰好表示 4 个比特。转换规则：十六→二：将每位十六进制数替换为对应的 4 位二进制。 二→十六：从右向左每 4 位分组，左侧可补零，再将每组转换为一位十六进制数。
| Hex | Binary | Decimal |
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| A | 1010 | 10 |
| B | 1011 | 11 |
