📚 Year 7 Edexcel Computer Science: Formula & Theorem Quick Reference Handbook | Year 7 Edexcel 计算机：公式定理速查手册
This handbook collects the essential formulas, conversion rules, and logical principles you need for Year 7 Edexcel Computing. Keep it handy for quick checks when tackling binary arithmetic, file size estimation, logic gates, and data representation tasks.
本手册汇集了 Year 7 Edexcel 计算机课程所需的核心公式、转换规则和逻辑原理。在应对二进制运算、文件大小估算、逻辑门和数据表示时，它可以为你提供快速参考。
1. Binary Weighted Value Formula | 二进制加权值公式
In binary, each digit (bit) holds a place value that is a power of 2. The rightmost bit has weight 2⁰, the next 2¹, then 2², and so on. A binary number is converted to decimal by summing each bit multiplied by its place value.
在二进制中，每位数字（比特）都有一个基于 2 的幂次的位置权值。最右边的位权为 2⁰，下一位为 2¹，然后是 2²，依此类推。二进制数可通过每位乘以位权再求总和转换为十进制。
Decimal = dₙ₋₁ × 2ⁿ⁻¹ + dₙ₋₂ × 2ⁿ⁻² + … + d₀ × 2⁰
Example: binary 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀.
示例：二进制 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀。
2. Decimal to Binary by Repeated Division | 重复除法十进制转二进制
To convert a decimal integer to binary, repeatedly divide the number by 2. Record the remainder (0 or 1) at each step. Stop when the quotient becomes 0. The binary result is the sequence of remainders read from bottom to top.
将十进制整数转换为二进制时，重复将数字除以 2。每一步记录余数（0 或 1）。当商变为 0 时停止。从下往上读取余数序列即得到二进制结果。
While N > 0: remainder = N mod 2; N = N div 2; prepend remainder
Example: Convert 13 to binary: 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1 → 1101₂.
示例：将 13 转二进制：13 ÷ 2 = 6 余 1, 6 ÷ 2 = 3 余 0, 3 ÷ 2 = 1 余 1, 1 ÷ 2 = 0 余 1 → 1101₂。
3. Binary Addition Rules | 二进制加法规则
Binary addition follows simple bitwise rules: 0+0=0, 0+1=1, 1+0=1, 1+1=0 with a carry of 1 to the next higher bit. The carry propagates leftwards until no further carry is produced.
二进制加法按位遵循以下简单规则：0+0=0，0+1=1，1+0=1，1+1=0 并向高位进 1。进位向左传播，直到不再产生进位为止。
Sum = A XOR B XOR Carry_in; Carry_out = (A AND B) OR (Carry_in AND (A XOR B))
Example: 1010₂ + 0111₂ = 10001₂. Notice the carry travels through several columns.
示例：1010₂ + 0111₂ = 10001₂。注意进位穿过了几列。
4. Storage Unit Conversion Factors | 存储单位转换因数
In computing, storage units are based on powers of 2. The basic unit is the byte. Larger units follow these exact conversions: 1 KB = 2¹⁰ bytes = 1024 bytes; 1 MB = 2²⁰ bytes; 1 GB = 2³⁰ bytes; 1 TB = 2⁴⁰ bytes. To convert to a smaller unit, multiply by 1024; to convert to a larger unit, divide by 1024.
在计算机中，存储单位基于 2 的幂次。基本单位是字节。更大单位遵循以下精确转换：1 KB = 2¹⁰ 字节 = 1024 字节；1 MB = 2²⁰ 字节；1 GB = 2³⁰ 字节；1 TB = 2⁴⁰ 字节。转换为更小单位乘以 1024；转换为更大单位除以 1024。
Always use 1024, not 1000, for data storage conversions in this course.
在本课程中，始终使用 1024 而非 1000 进行存储单位转换。
5. Image File Size Formula | 图像文件大小公式
An uncompressed bitmap image’s file size depends on its resolution (width × height in pixels) and colour depth (bits per pixel). The total number of bits is width × height × colour depth. Convert to bytes by dividing by 8.
未压缩位图图像的文件大小取决于其分辨率（宽×高像素）和色深（每像素位数）。总位数 = 宽度 × 高度 × 色深。除以 8 转换为字节。
File size (bytes) = (Width × Height × Bit depth) / 8
Example: A 200×200 pixel photo with 24-bit colour uses 200×200×24 = 960 000 bits = 120 000 bytes ≈ 117 KB.
示例：一张 200×200 像素、24 位色的照片使用 200×200×24 = 960 000 位 = 120 000 字节 ≈ 117 KB。
6. Sound File Size Formula | 声音文件大小公式
Uncompressed digital audio size is calculated by multiplying sample rate (Hz), bit depth (bits per sample), duration (seconds), and number of channels. The result is in bits; divide by 8 to get bytes, then further by 1024 for KB or MB.
未压缩数字音频的大小由采样率（Hz）、位深（每样本位数）、时长（秒）和声道数相乘计算。结果为比特；除以 8 得到字节，再根据需要除以 1024 转换为 KB 或 MB。
Size (bits) = Sample rate × Bit depth × Time × Channels
Example: 44.1 kHz CD-quality stereo sound for 30 seconds: 44100 × 16 × 30 × 2 = 42 336 000 bits ≈ 5.04 MB.
示例：44.1 kHz CD 音质立体声 30 秒：44100 × 16 × 30 × 2 = 42 336 000 位 ≈ 5.04 MB。
7. AND Gate Truth Table | 与门真值表
An AND gate implements logical conjunction. The output Q is 1 only when all inputs are 1. Its Boolean expression is Q = A · B (or A AND B).
与门实现逻辑与运算。只有当所有输入均为 1 时，输出 Q 才为 1。其布尔表达式为 Q = A · B（或 A AND B）。
| A | B | Q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
In your work, 0 represents FALSE and 1 represents TRUE. Memorise this table for quick logic evaluations.
在做题时，0 表示假，1 表示真。记住此表可快速进行逻辑评估。
8. OR Gate Truth Table | 或门真值表
An OR gate outputs 1 if at least one input is 1. The Boolean expression is Q = A + B (or A OR B). It performs logical disjunction.
或门只要至少一个输入为 1 就输出 1。布尔表达式为 Q = A + B（或 A OR B）。它执行逻辑或运算。
| A | B | Q |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Note the difference from AND: only the (0,0) row gives 0; all other input combinations produce 1.
注意与 AND 的区别：仅当 (0,0) 时输出 0；其他所有输入组合均输出 1。
9. NOT Gate Truth Table | 非门真值表
A NOT gate (inverter) flips the input. If input A is 1, output Q is 0; if A is 0, Q is 1. Boolean notation: Q = ¬A or Q = A’.
非门（反相器）将输入取反。若输入 A 为 1，则输出 Q 为 0；若 A 为 0，则 Q 为 1。布尔记法：Q = ¬A 或 Q = A’。
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