📚 Formula & Theorem Quick Reference for Year 7 SQA Computing | SQA Year 7 计算机公式定理速查手册
This quick reference handbook collates the essential formulas, theorems, and key facts required for Year 7 SQA Computing. It covers data representation, Boolean logic, digital storage, and simple networking concepts to help you revise efficiently.
本速查手册整理了 SQA Year 7 计算机课程所需的公式、定理和关键事实。涵盖数据表示、布尔逻辑、数字存储和简单网络概念，助你高效复习。
1. Binary Number Basics | 二进制数基础
All data in a computer is processed using the binary number system, which uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 20 on the right.
计算机中的所有数据都使用二进制数系统处理，该系统只使用两个数字：0 和 1。二进制数的每一位代表 2 的幂，从右边的 20 开始。
| Place value | 23 = 8 | 22 = 4 | 21 = 2 | 20 = 1 |
|---|---|---|---|---|
| Binary digit | 1 | 0 | 1 | 1 |
The value of the binary number 10112 is (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 11 in denary. The subscript ‘2’ denotes the base.
二进制数 10112 的值为 (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 11（十进制）。下标 ‘2’ 表示基数。
2. Denary to Binary Conversion | 十进制转二进制
To convert a denary number to binary, repeatedly divide the number by 2 and record the remainders. The binary number is the sequence of remainders read from the last remainder obtained to the first.
将十进制数转换为二进制，可反复除以 2 并记录余数。从下往上读取余数序列，即得二进制数。
Example: Convert 13 to binary.
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders upwards gives 11012.
示例：将 13 转换为二进制。
13 ÷ 2 = 6 余 1
6 ÷ 2 = 3 余 0
3 ÷ 2 = 1 余 1
1 ÷ 2 = 0 余 1
从下往上读取余数得到 11012。
3. Binary to Denary Conversion | 二进制转十进制
Decimal = dn-1 × 2n-1 + dn-2 × 2n-2 + … + d1 × 21 + d0 × 20
Here di is the binary digit (0 or 1) at position i, with i = 0 for the least significant bit. Simply add up the place values of the positions where the binary digit is 1.
其中 di 是第 i 位的二进制数字（0 或 1），i = 0 对应最低有效位。只需将二进制位为 1 的位值相加即可。
For 11012: d3 = 1, d2 = 1, d1 = 0, d0 = 1 → 1×8 + 1×4 + 0×2 + 1×1 = 13.
以 11012 为例：d3 = 1，d2 = 1，d1 = 0，d0 = 1 → 1×8 + 1×4 + 0×2 + 1×1 = 13。
4. Binary Addition Rules | 二进制加法规则
Binary addition follows four basic rules, similar to denary addition but carrying over when the sum reaches 2.
二进制加法遵循四条基本规则，与十进制加法类似，但当和达到 2 时产生进位。
| A | B | Sum | Carry |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
When adding 1 + 1, the result is 0 with a carry of 1 to the next higher bit, just as 1 + 1 = 102.
当计算 1 + 1 时，结果为 0，向高一位进位 1，正如 1 + 1 = 102。
5. Boolean Logic Identities | 布尔逻辑恒等式
Boolean algebra uses the operations AND, OR and NOT. The following identities always hold and help simplify logic circuits.
布尔代数使用 AND、OR 和 NOT 运算。以下恒等式始终成立，有助于简化逻辑电路。
| Identity name | Boolean expression |
|---|---|
| Identity for AND | A AND 1 = A |
| Identity for OR | A OR 0 = A |
| Annulment for AND | A AND 0 = 0 |
| Annulment for OR | A OR 1 = 1 |
| Idempotent for AND | A AND A = A |
| Idempotent for OR | A OR A = A |
| Complement for AND | A AND NOT A = 0 |
| Complement for OR | A OR NOT A = 1 |
These identities are the foundation for constructing and minimising digital circuits.
这些恒等式是构建和简化数字电路的基础。
6. Truth Tables for Basic Logic Gates | 基本逻辑门真值表
A truth table lists all possible input combinations and the corresponding output for a logic gate. The three fundamental gates are AND, OR and NOT.
真值表列出了逻辑门所有可能的输入组合及其对应的输出。三种基本门电路是 AND、OR 和 NOT。
AND gate: output is 1 only when all inputs are 1.
| A | B | A AND B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR gate: output is 1 if at least one input is 1.
| A | B | A OR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NOT gate: output is the inverse of the input.
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
AND 门：仅当所有输入都为 1 时，输出才为 1。
OR 门：只要至少一个输入为 1，输出即为 1。
NOT 门：输出是输入的反相。
7. Units of Digital Storage | 数字存储单位
Data size is measured using bits and bytes. Larger units are powers of 1024 (210).
数据大小用位和字节衡量。更大的单位是 1024（210）的幂。
| Unit | Abbreviation | Equal to |
|---|---|---|
| 1 bit | b | smallest unit |
| 1 byte | B | 8 bits |
| 1 kilobyte | KB | 1024 bytes |
| 1 megabyte | MB | 1024 KB |
| 1 gigabyte | GB | 1024 MB |
| 1 terabyte | TB | 1024 GB |
File size in bits = file size in bytes × 8
文件大小（位）= 文件大小（字节）× 8
8. Image Representation Formulas | 图像表示公式
A bitmap image is made of pixels. The resolution and colour depth determine the file size.
位图图像由像素构成。分辨率和颜色深度决定文件大小。
Total pixels = width (px) × height (px)
总像素数 = 宽（像素）× 高（像素）
File size (bits) = total pixels × colour depth (bits per pixel)
文件大小（位）= 总像素数 × 颜色深度（位/像素）
If an image is 800 × 600 pixels and uses 24-bit colour, the raw file size is 800 × 600 × 24 = 11,520,000 bits (about 1.44 MB).
若一幅图像为 800 × 600 像素、使用 24 位颜色，则原始文件大小为 800 × 600 × 24 = 11,520,000 位（约 1.44 MB）。
9. Sound Representation Formula | 声音表示公式
Digital sound is stored as a series of samples. The sample rate, bit depth and duration determine the file size.
数字音频以一系列样本的形式存储。采样率、位深度和时长决定文件大小。
File size (bits) = sample rate (Hz) × bit depth × duration (seconds)
文件大小（位）= 采样率（Hz）× 位深度 × 时长（秒）
For a mono sound track: 44,100 Hz × 16 bits × 10 s = 7,056,000 bits (approx. 882 KB). For stereo, multiply by 2.
以单声道音轨为例：44,100 Hz × 16 位
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