Year 9 WJEC Computer Science: Formula & Theorem Quick Reference Guide | 九年级 WJEC 计算机科学公式定理速查手册

📚 Year 9 WJEC Computer Science: Formula & Theorem Quick Reference Guide | 九年级 WJEC 计算机科学公式定理速查手册

This quick reference guide gathers every formula, theorem, and conversion rule you require for the Year 9 WJEC Computer Science course. Covering binary arithmetic, data storage, sound and image calculations, logic gates, and algorithm efficiency, the content is presented in paired English–Chinese explanations to support quick revision. Use the handbook to check key equations, practise worked examples, and build confidence for class tests and end-of-year assessments.

本速查手册汇集了九年级 WJEC 计算机科学课程所需的全部公式、定理和转换规则。内容涵盖二进制算术、数据存储、声音与图像计算、逻辑门以及算法效率，所有解释均采用中英双语配对呈现，方便快速复习。请利用本手册查阅关键方程式、练习典型例题，并为课堂测验和年终评估做好充分准备。

1. Binary to Decimal Conversion | 二进制转十进制

To convert a binary number into denary (decimal), multiply each bit by 2 raised to the power of its position. Position numbering begins at 0 from the rightmost bit (the least significant bit). Add up all the contributions to obtain the denary value.

要将二进制数转换为十进制数，将每一位上的数字乘以 2 的该位位置次方。位置编号从最右边的位（最低有效位）开始，计为 0。将所有乘积相加即得到十进制数值。

(1101)₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13

A common example is 1011₂, which equates to (1×8) + (0×4) + (1×2) + (1×1) = 11 in denary. An 8-bit binary number can represent denary values from 0 up to 255 (2⁸ – 1), which is why 8-bit colour and ASCII codes often use that range.

常见的例子是 1011₂，它等于 (1×8) + (0×4) + (1×2) + (1×1) = 11（十进制）。一个 8 位二进制数可以表示 0 至 255 的十进制值（2⁸ – 1），这也是 8 位彩色和 ASCII 码常用该范围的原因。

2. Decimal to Binary Conversion | 十进制转二进制

To change a decimal number to binary, repeatedly divide the number by 2, noting the remainder each time. Continue until the quotient is 0. The binary equivalent is read backwards from the last remainder to the first remainder obtained.

要将十进制数转换为二进制，反复将该数除以 2，并记下每次的余数。一直除到商为 0。从最后的余数开始，反向读取得到的所有余数，即为对应的二进制数。

Example: 29 to binary → 29 ÷ 2 = 14 rem 1; 14 ÷ 2 = 7 rem 0; 7 ÷ 2 = 3 rem 1; 3 ÷ 2 = 1 rem 1; 1 ÷ 2 = 0 rem 1 → 11101₂

Always check your result by converting back to decimal: 11101₂ = 16+8+4+1 = 29. This method works for any positive integer, no matter how large.

务必通过回转为十进制来验证结果：11101₂ = 16+8+4+1 = 29。无论整数多大，该方法均适用。

3. Binary Addition Rules | 二进制加法法则

When performing binary addition, follow these fundamental rules for each column:

进行二进制加法时，须逐列遵守以下基本法则：

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0, with a carry of 1 to the next column
• 1 + 1 + 1 (after carry-in) = 1, with a carry of 1

Example: 101₂ (5) + 011₂ (3). Steps: rightmost column 1+1 = 0 carry 1; next column 0+1+carry = 0 carry 1; leftmost column 1+0+carry = 0 carry 1. Result is 1000₂ (8).

示例：101₂ (5) + 011₂ (3)。步骤：最右列 1+1 = 0 进 1；下一列 0+1+进位 = 0 进 1；最左列 1+0+进位 = 0 进 1。结果为 1000₂ (8)。

101₂ + 011₂ = 1000₂

4. Hexadecimal to Binary and Denary | 十六进制与二进制、十进制转换

Hexadecimal (base 16) uses digits 0–9 and letters A–F to represent the values 0–15. Every hex digit can be exactly represented by a 4-bit binary nibble.

十六进制（基数为 16）使用数字 0–9 和字母 A–F 表示 0–15 的值。每个十六进制位都可精确地由一个 4 位二进制半字节表示。