Formula Summary Handbook for GCSE CCEA Computer Science | GCSE CCEA 计算机科学公式汇总手册

📚 Formula Summary Handbook for GCSE CCEA Computer Science | GCSE CCEA 计算机科学公式汇总手册

This comprehensive handbook brings together every essential formula, conversion, and calculation rule required for the GCSE CCEA Computer Science specification. Use it as a one‑stop revision resource to master file sizes, data transfer times, compression ratios, Boolean laws, and numeric conversions.

这本全面的手册汇集了 GCSE CCEA 计算机科学课程中所有必备的公式、换算和计算规则。把它作为一站式复习资源，掌握文件大小、数据传输时间、压缩比、布尔代数定律和数制转换。

1. Storage Units and Conversions | 存储单位与换算

All digital data is measured in bits and bytes. You must be able to convert between the common prefixes accurately.

所有数字数据都以比特和字节计量。你必须能准确地在常见前缀之间进行换算。

• 1 bit = smallest unit of data; 1 nibble = 4 bits; 1 byte = 8 bits
• 1 KB (kilobyte) = 1000 bytes; 1 KiB (kibibyte) = 1024 bytes
• 1 MB (megabyte) = 1000 KB; 1 MiB (mebibyte) = 1024 KiB
• 1 GB (gigabyte) = 1000 MB; 1 GiB (gibibyte) = 1024 MiB
• 1 TB (terabyte) = 1000 GB; 1 TiB (tebibyte) = 1024 GiB

• 1 bit = 数据的最小单位；1 nibble = 4 bits；1 byte = 8 bits
• 1 KB（千字节）= 1000 字节；1 KiB（kibibyte）= 1024 字节
• 1 MB（兆字节）= 1000 KB；1 MiB（mebibyte）= 1024 KiB
• 1 GB（吉字节）= 1000 MB；1 GiB（gibibyte）= 1024 MiB
• 1 TB（太字节）= 1000 GB；1 TiB（tebibyte）= 1024 GiB

The exam board accepts both decimal (1000) and binary (1024) meanings; always state which you are using.

考试局同时接受十进制（1000）和二进制（1024）的含义，务必说明你使用的是哪一种。

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2. Image File Size | 图像文件大小

ge depends on its resolution (width × height in pixels) and colour depth (bits per pixel).

位图图像的文件大小取决于它的分辨率（宽度×高度，以像素计）和颜色深度（每像素位数）。

File size (bits) = Width × Height × Colour Depth

文件大小（比特）= 宽度 × 高度 × 颜色深度

Convert this to bytes by dividing by 8, then to larger units as needed.

除以 8 转换为字节，再根据需要转换为更大的单位。

Example: a 1920 px × 1080 px image with 24‑bit colour depth.
File size = 1920 × 1080 × 24 = 49,766,400 bits ≈ 6,220,800 bytes ≈ 6.2 MB.

示例：一幅 1920 px × 1080 px、24 位颜色深度的图像。
文件大小 = 1920 × 1080 × 24 = 49,766,400 bits ≈ 6,220,800 字节 ≈ 6.2 MB。

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3. Sound File Size | 音频文件大小

The size of an uncompressed sound file is determined by the sample rate, bit depth, number of channels, and duration.

未压缩音频文件的大小由采样率、位深度、声道数和时长决定。

File size (bits) = Sample Rate × Bit Depth × Channels × Duration (seconds)

文件大小（比特）= 采样率 × 位深度 × 声道数 × 时长（秒）

Sample rate is measured in Hz (e.g. 44,100 Hz); bit depth is the number of bits per sample; channels are 1 (mono) or 2 (stereo).

采样率以赫兹（Hz，如 44,100 Hz）为单位；位深度是每个样本的位数；声道数为 1（单声道）或 2（立体声）。

Example: 60 seconds of stereo sound at 44.1 kHz, 16 bits.
File size = 44,100 × 16 × 2 × 60 = 84,672,000 bits ≈ 10.58 MB.

示例：44.1 kHz、16 位立体声 60 秒的音频。
文件大小 = 44,100 × 16 × 2 × 60 = 84,672,000 bits ≈ 10.58 MB。

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4. Text File Size | 文本文件大小

The size of a plain text file depends on the character encoding and the number of characters.

纯文本文件的大小取决于字符编码和字符数量。

File size (bits) = Number of characters × Bits per character

文件大小（比特）= 字符数量 × 每个字符的位数

• ASCII uses 7 or 8 bits per character (typically 8 bits = 1 byte).
• Unicode (UTF‑8) uses a variable number of bytes; UTF‑16 uses at least 16 bits per character.

• ASCII 每个字符使用 7 或 8 位（通常 8 位 = 1 字节）。
• Unicode（UTF‑8）使用可变字节数；UTF‑16 每个字符至少 16 位。

Example: a 500‑character ASCII file ≈ 500 bytes. A 500‑character UTF‑16 file ≈ 1000 bytes.

示例：一个 500 个字符的 ASCII 文件 ≈ 500 字节。一个 500 个字符的 UTF‑16 文件 ≈ 1000 字节。

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5. Data Transfer Time | 数据传输时间

To calculate how long it takes to transmit a file over a network, use the relationship between data size and transmission speed.

要计算通过网络传输文件所需的时间，使用数据大小和传输速度之间的关系。

Time (seconds) = Data size (bits) ÷ Transfer rate (bps)

时间（秒）= 数据大小（比特）÷ 传输速率（bps）

the file size is given in MB, convert to bits (×8×1000×1000) and the transfer rate to bps.

务必确保单位一致：如果文件大小以 MB 给出，则转换为比特（×8×1000×1000），传输速率也转换为 bps。

Example: a 25 MB file over a 10 Mbps connection.
25 MB = 25 × 8 × 1,000,000 = 200,000,000 bits.
Time = 200,000,000 ÷ 10,000,000 = 20 seconds.

示例：在 10 Mbps 的连线上传输一个 25 MB 的文件。
25 MB = 25 × 8 × 1,000,000 = 200,000,000 bits。
时间 = 200,000,000 ÷ 10,000,000 = 20 秒。

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6. Compression Ratio | 压缩比

Compression ratio expresses the relationship between the original file size and the compressed file size.

压缩比表示原始文件大小与压缩后文件大小之间的关系。

Compression Ratio = Original size : Compressed size

压缩比 = 原始大小 : 压缩后大小

It can also be stated as a percentage saving:

也可以用节省的百分比表示：

Space saved (%) = [(Original size – Compressed size) ÷ Original size] × 100

节省的空间 (%) = [(原始大小 – 压缩后大小) ÷ 原始大小] × 100

file compressed to 20 MB → ratio 50:20, simplified to 5:2. Space saved = (30÷50)×100 = 60%.

示例：一个 50 MB 的文件压缩到 20 MB → 比率 50:20，简化为 5:2。节省空间 = (30÷50)×100 = 60%。

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7. Audio Bit Rate and Streaming | 音频比特率与流式传输

processed per second. For uncompressed audio it equals sample rate × bit depth × channels.

比特率是每秒处理的数据量。对于未压缩音频，它等于采样率 × 位深度 × 声道数。

Bit rate (bps) = Sample Rate × Bit Depth × Channels

比特率 (bps) = 采样率 × 位深度 × 声道数

When streaming, a lower bit rate reduces quality but saves bandwidth. Compressed formats (MP3, AAC) use much lower bit rates.

流式传输时，较低的比特率会降低质量但节省带宽。压缩格式（MP3、AAC）使用低得多的比特率。

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8. Image Resolution and Printing | 图像分辨率与打印

Resolution determines the quality of an image on screen or in print. DPI (dots per inch) links pixel dimensions to physical size.

分辨率决定了图像在屏幕上或打印时的质量。DPI（每英寸点数）将像素尺寸与物理尺寸联系起来。

Physical size (inches) = Pixel width ÷ DPI

物理尺寸（英寸）= 像素宽度 ÷ DPI

Example: an 1800 px wide image at 300 DPI will print at 6 inches wide.

示例：一幅 1800 像素宽、300 DPI 的图像将打印出 6 英寸宽。

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9. Boolean Algebra Laws | 布尔代数定律

Logic circuits and expressions can be simplified using Boolean identities. Key laws are listed below.

可以使用布尔恒等式简化逻辑电路和表达式。关键定律如下所示。

Law / 定律	AND form / 与形式	OR form / 或形式
Identity / 恒等	A • 1 = A	A + 0 = A
Null / 归零	A • 0 = 0	A + 1 = 1
Idempotent / 幂等	A • A = A	A + A = A
Complement / 互补	A • ¬A = 0	A + ¬A = 1
De Morgan's / 德摩根	¬(A • B) = ¬A + ¬B	¬(A + B) = ¬A • ¬B

These identities are essential when simplifying circuits or writing efficient code.

在简化电路或编写高效代码时，这些恒等式至关重要。

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10. Binary and Hexadecimal Conversions | 二进制与十六进制转换

Understanding how to move between denary, binary, and hexadecimal is a core skill.

理解如何在十进制、二进制和十六进制之间转换是一项核心技能。

• Binary to Denary: sum of (digit × 2^position) starting from position 0 on the right.
• Denary to Binary: successive division by 2, recording remainders.
• Binary to Hex: group binary digits in nibbles (4 bits) from the right; convert each nibble to its hex equivalent (0‑9, A‑F).
• Hex to Denary: multiply each hex digit by 16^position.

• 二进制转十进制：从右侧位置 0 开始，每位数字 × 2^位置 再求和。
• 十进制转二进制：连续除以 2，记录余数。
• 二进制转十六进制：从右开始将二进制数字按 4 位一组分组；将每组转换为对应的十六进制符号（0‑9, A‑F）。
• 十六进制转十进制：每位十六进制数字乘以 16^位置 再求和。

Example: 1101 0111₂ → D7₁₆ (13 in decimal is D, 7 is 7).

示例：1101 0111₂ → D7₁₆（13 十进制为 D，7 为 7）。

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11. Error Detection: Parity and Checksums | 错误检测：奇偶校验与校验和

Parity checks and checksums help detect errors in transmitted data.

奇偶校验和校验和有助于检测传输数据中的错误。

Even parity: total number of 1s including parity bit is even. Odd parity: total number of 1s is odd.

偶校验：包括校验位在内的 1 的总数为偶数。奇校验：1 的总数为奇数。

Checksum: data is divided into equal‑sized blocks; sum of block values (often modulo 256) is transmitted. Receiver computes sum and compares.

校验和：将数据分成等长的块；传输块值的和（通常模 256）。接收方计算和并比较。

Checksum = (Sum of all bytes) mod 256

校验和 = （所有字节之和）mod 256

Note that a simple checksum cannot correct errors; it only detects some types of corruption.

请注意，简单的校验和无法纠正错误，只能检测某些类型的损坏。

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12. Network Speed and Bandwidth | 网络速度与带宽

Bandwidth is the maximum data transfer rate of a network, usually measured in bits per second (bps).

带宽是网络的最大数据传输速率，通常以每秒比特数（bps）计量。

Transfer Rate (bps) = Data transferred (bits) ÷ Time (seconds)

传输速率 (bps) = 传输的数据量（比特）÷ 时间（秒）

High‑frequency questions ask you to compare theoretical bandwidth with real‑world throughput, which is often lower due to protocol overhead and congestion.

高频考题要求比较理论带宽与实际吞吐量，后者因协议开销和拥塞通常较低。

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