📚 Year 9 AQA Computer Science: Formula & Theorem Quick Reference Handbook | 九年级 AQA 计算机科学：公式定理速查手册
This handbook gathers the key formulas, conversion rules and Boolean theorems required for the Year 9 AQA Computer Science course. Keep it handy when you revise data representation, file size calculations, network speeds and logic circuits.
本手册汇集了九年级 AQA 计算机科学课程所需的关键公式、转换规则与布尔定理，适合在复习数据表示、文件大小计算、网络速率和逻辑电路时随时查阅。
1. Data Units & Conversions | 数据单位与换算
All digital data is stored as bits. A group of 8 bits makes one byte, while a nibble is 4 bits. Larger units are powers of 1024 (binary prefixes).
所有数字数据以位的形式存储。8 个位组成一个字节，而半字节是 4 个位。更大的单位使用 1024 的幂（二进制前缀）。
| Unit | Abbreviation | Value in bytes |
|---|---|---|
| Bit | b | 1/8 byte |
| Nibble | — | 4 bits = 0.5 B |
| Byte | B | 1 B = 8 b |
| Kilobyte | KB | 1024 B |
| Megabyte | MB | 1024 KB = 1,048,576 B |
| Gigabyte | GB | 1024 MB |
| Terabyte | TB | 1024 GB |
The relationship between bits and bytes is given by the conversion formula:
Number of bits = Number of bytes × 8
位与字节的关系为：位数 = 字节数 × 8
2. Binary & Denary Conversions | 二进制与十进制转换
Binary numbers use base‑2 with digits 0 and 1. Each position has a place value that doubles from right to left (… 2³, 2², 2¹, 2⁰).
二进制使用基数为 2，数字为 0 和 1。每个位置的位值从右向左加倍（… 2³, 2², 2¹, 2⁰）。
To convert a binary number to denary, multiply each bit by its place value and sum the products. The leftmost bit is the most significant bit (MSB), the rightmost the least significant bit (LSB).
将二进制转换为十进制时，将每一位乘以它的位值并求和。最左边的位是最高有效位 (MSB)，最右边的是最低有效位 (LSB)。
Denary value = Σ (binary digit × 2^position)
十进制值 = Σ（二进制数字 × 2^位权）
Example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀
示例：1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀
To convert denary to binary, repeatedly divide the denary number by 2 and record the remainders (reading upwards).
将十进制转换为二进制时，反复将十进制数除以 2 并记录余数（自下而上读取）。
3. Hexadecimal System | 十六进制系统
Hexadecimal (hex) uses base‑16 with digits 0–9 and letters A–F, where A=10, B=11, … F=15.
十六进制使用基数为 16，数字为 0–9 和字母 A–F，其中 A=10, B=11, …, F=15。
| Denary | 0 | 1 | … | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|
| Hex | 0 | 1 | … | A | B | C | D | E | F |
One hex digit represents exactly 4 bits (a nibble). To convert binary to hex, group bits in fours from the right and replace each group with its hex equivalent.
一个十六进制数字正好代表 4 个位（一个半字节）。将二进制转换为十六进制时，从右开始将位按四个一组分组，并将每组替换为对应的十六进制数字。
Example: 1101 0110₂ = D6₁₆. To go from hex to binary, expand each hex digit to a 4‑bit binary nibble.
示例：1101 0110₂ = D6₁₆。从十六进制转为二进制时，将每个十六进制数字扩展为 4 位二进制半字节。
4. Character Encoding – ASCII & Unicode | 字符编码 – ASCII 与 Unicode
Characters are represented by numeric codes stored in binary. Standard ASCII uses 7 bits, giving 2⁷ = 128 characters. Extended ASCII uses 8 bits (2⁸ = 256 characters).
字符用二进制存储的数字编码表示。标准 ASCII 使用 7 位，可表示 2⁷ = 128 个字符。扩展 ASCII 使用 8 位（2⁸ = 256 个字符）。
Unicode uses a much larger code space (up to 32 bits per character) and can represent characters from all major writing systems. The number of representable characters depends on the number of bits:
Unicode 使用更大的编码空间（每个字符最多 32 位），可以表示所有主要书写系统的字符。可表示的字符数由位数决定：
Number of representable characters = 2^number of bits
可表示的字符数 = 2^位数
5. Image Representation – Pixels & Colour Depth | 图像表示 – 像素与色深
A bitmap image is made of a grid of pixels. The image resolution is width × height in pixels. The colour depth (bit depth) tells how many bits are used to store the colour of each pixel.
位图图像由像素网格构成。图像分辨率为宽度 × 高度（像素）。色深（位深度）表示每个像素的颜色用多少位存储。
The number of possible colours per pixel = 2^colour
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