Formula & Theorem Quick Reference for Year 7 SQA Computing | SQA Year 7 计算机公式定理速查手册

📚 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。

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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。

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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。

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3. Binary to Denary Conversion | 二进制转十进制

Decimal = d_n-1 × 2^n-1 + d_n-2 × 2^n-2 + ... + d₁ × 2¹ + d₀ × 2⁰

Here d_i nificant bit. Simply add up the place values of the positions where the binary digit is 1.

其中 d_i 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。

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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

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。

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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。

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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。

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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

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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）

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）。

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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）

: 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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