📚 Year 8 Edexcel Computer Science: Formula & Theorem Quick-Reference | Year 8 Edexcel 计算机：公式定理速查手册
This quick-reference handbook collates the essential formulas and theorems covered in the Year 8 Edexcel Computer Science curriculum. It is designed to help students revise key concepts in data representation, Boolean logic, storage calculations, network data transfer, binary arithmetic, and algorithmic thinking. Each section presents a concise explanation in English followed by its Chinese counterpart, ensuring a bilingual grasp of the material.
本速查手册汇集了Year 8 Edexcel 计算机科学课程中的核心公式与定理。旨在帮助学生复习数据表示、布尔逻辑、存储计算、网络数据传输、二进制运算以及算法思维等关键概念。每个部分先提供英文简明解释，再给出对应中文，确保双语掌握。
1. Binary to Denary Conversion | 二进制转十进制
To convert a binary number to its decimal equivalent, multiply each binary digit (bit) by 2 raised to the power of its place value, where the rightmost position is 2⁰. Sum all these products to obtain the decimal value. The general formula is:
要将二进制数转换为十进制，将每个二进制位乘以2的位权次方，最右侧位为2⁰。将所有乘积相加，即得十进制值。通用公式为：
Decimal value = Σ (bit × 2position)
Example: Convert 10112 to decimal. 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. Therefore, 10112 = 1110.
例：将10112转换为十进制。1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11。因此，10112 = 1110。
A quick check: an n-bit binary number can represent decimal values from 0 up to 2n – 1. For 4 bits, the maximum is 15 (11112).
快速检验：一个n位二进制数可以表示从0到2n – 1的十进制值。对于4位，最大值为15（11112）。
2. Denary to Binary Conversion | 十进制转二进制
To convert a decimal number to binary, repeatedly divide the number by 2, record the remainder (0 or 1) each time, and continue dividing the quotient until it becomes 0. The binary number is formed by reading the remainders in reverse order (from the last remainder to the first).
要将十进制数转换为二进制，反复除以2，每次记录余数（0或1），并继续除商直到商为0。将余数按逆序（从最后一个余数到第一个余数）排列，即得二进制数。
Example: Convert 2510 to binary.
25 ÷ 2 = 12 remainder 1; 12 ÷ 2 = 6 remainder 0; 6 ÷ 2 = 3 remainder 0; 3 ÷ 2 = 1 remainder 1; 1 ÷ 2 = 0 remainder 1.
Reading remainders backwards: 11001, so 2510 = 110012.
例：将2510转换为二进制。
25 ÷ 2 = 12 余 1；12 ÷ 2 = 6 余 0；6 ÷ 2 = 3 余 0；3 ÷ 2 = 1 余 1；1 ÷ 2 = 0 余 1。
逆向读取余数：11001，因此2510 = 110012。
3. Hexadecimal Number System | 十六进制系统
Hexadecimal (base-16) uses digits 0–9 and letters A–F, where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. To convert binary to hexadecimal, group binary digits into nibbles (4 bits) from right to left, then translate each group. The table below shows the equivalents:
十六进制（基数为16）使用数字0–9和字母A–F，其中A=10，B=11，C=12，D=13，E=14，F=15。将二进制转换为十六进制时，从右向左每4位（一个半字节）分组，然后转换每组。下表给出对应转换：
| Decimal | Binary (4 bits) | Hexadecimal |
|---|---|---|
| 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 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
Example: Binary 110110102 → group as 1101 1010 → D A → DA16.
例：二进制110110102 → 分组为1101 1010 → D A → DA16。
To convert hex to denary, expand using powers of 16: DA16 = (D×16¹) + (A×16⁰) = 13×16 + 10 = 21810.
将十六进制转换为十进制时，按16的幂展开：DA16 = (D×16¹) + (A×16⁰) = 13×16 + 10 = 21810。
4. Boolean Logic Gates and Truth Tables | 布尔逻辑门与真值表
The three fundamental logic gates are AND, OR, and NOT. Their symbols and truth tables define the output for all possible input combinations.
三种基本逻辑门为与门（AND）、或门（OR）和非门（NOT）。它们的符号与真值表定义了所有可能输入组合下的输出。
AND gate: output is true only when all inputs are true. Boolean expression: A ∧ B. Truth table:
与门：仅当所有输入为真时输出才为真。布尔表达式：A ∧ B。真值表：
| A | B | Q = A ∧ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR gate: output is true if at least one input is true. Expression: A ∨ B.
或门：只要至少一个输入为真，输出即为真。表达式：A ∨ B。
| A | B | Q = A ∨ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NOT gate: inverts the input. Expression: ¬A. Truth table:
非门：将输入取反。表达式：¬A。真值表：
| A | Q = ¬A |
|---|---|
| 0 | 1 |
| 1 | 0 |
5. Boolean Algebra Laws | 布尔代数定律
Boolean algebra provides a set of rules for simplifying logic expressions. The key laws are listed below.
布尔代数提供了一组简化逻辑表达式的规则。下面列出关键定律。
Identity Law: A + 0 = A, A · 1 = A
恒等律：A + 0 = A, A · 1 = A
Annulment Law: A + 1 = 1, A · 0 = 0
湮灭律：A + 1 = 1, A · 0 = 0
Idempotent Law: A + A = A, A · A = A
幂等律：A + A = A, A · A = A
Complement Law: A + ¬A = 1, A · ¬A = 0
互补律：A + ¬A = 1, A · ¬A = 0
Double Negation: ¬(¬A) = A
双重否定律：¬(¬A) = A
De Morgan’s Theorems: ¬(A ∧ B) = ¬A ∨ ¬B; ¬(A ∨ B) = ¬A ∧ ¬B
德摩根定律：¬(A ∧ B) = ¬A ∨ ¬B；¬(A ∨ B) = ¬A ∧ ¬B
These laws are essential for reducing logic circuit complexity and proving equivalence between expressions.
这些定律对于降低逻辑电路复杂度以及证明表达式等价性至关重要。
6. Units of Data Storage | 数据存储单位
Data storage capacity is measured using the following units in computer science. The base unit is a bit (binary digit). Conversions typically use powers of 2.
数据存储容量在计算机科学中使用以下单位衡量。基本单位是位（bit，二进制位）。转换通常使用2的幂。
| Unit | Abbreviation | Size in bits/bytes |
|---|---|---|
| Bit | b | 1 bit |
| Nibble | — | 4 bits |
| Byte | B | 8 bits |
| Kilobyte | KB | 2¹⁰ bytes = 1024 B |
| Megabyte | MB | 2²⁰ bytes = 1024 KB |
| Gigabyte | GB | 2³⁰ bytes = 1024 MB |
| Terabyte | TB | 2⁴⁰ bytes = 1024 GB |
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