IGCSE计算机 核心笔记

学科重点

IG CS是一门比较难的学科，因为它的内容非常抽象，只能通过想象进行理解。生活中的例子都没法完美类比CS中的许多概念。而当这些概念需要用英文进行应答时，就会变得更加困难。

学习时建议先确保自己对于概念充分理解，一定要多花时间进行基本框架的构建，然后再使用标准的英语进行解释和定义，记背是必不可少的。这样才能在答题时得到高分。

Study Strategy

Take your time building the conceptual framework first. Once you truly understand the “why” behind each concept, the English definitions become much easier to memorize and recall during exams.

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• Data Representation

  Number systems, text, sound, images, compression
• Data Transmission

  Packets, error detection, encryption
• Hardware & Architecture

  CPU, FDE cycle, embedded systems

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1. Data Representation

1.1 Number Systems

Think of computers as really simple machines that only understand two things: electricity on or off. That’s why binary (just 0s and 1s) is perfect for them. But here’s the thing - humans aren’t great at reading long strings of 0s and 1s. That’s where hexadecimal comes in as our “translator.”

Why Binary?

Number System Basics

Here’s how these three number systems relate:

System	Base	Digits	Common Use
Denary	10	0-9	What humans naturally use
Binary	2	0-1	What computers naturally use
Hexadecimal	16	0-9, A-F	Human-friendly representation of binary

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Converting Between Number Systems

Denary to Binary - Think about place values!

Convert Denary to Binary

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Binary to Denary - Just add up the place values where you see a 1!

Convert Binary to Denary

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Binary ↔ Hexadecimal - The easy one!

Hexadecimal is just a shorthand for binary. Group binary digits into chunks of 4 (nibbles), since .

Binary to Hex Conversion

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Denary to Hexadecimal - Use division!

Denary to Hex

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Binary Arithmetic

Binary Addition follows the same rules as denary, but simpler!

Binary Addition Rules

Binary Addition

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Watch Out for Overflow!

Overflow happens when your result is too big for the number of bits available.

In 8-bit binary, the maximum value is .

Example:

That 9th bit doesn’t fit - that’s an overflow error!

Logical Binary Shifts - A clever shortcut for multiplication and division by powers of 2.

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Left Shift Practice

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Two’s Complement - Representing Negative Numbers

Computers need to store negative numbers too. Two’s complement is the clever system they use.

Understanding Two's Complement

Converting Negative Denary to Two’s Complement:

Two's Complement Conversion

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1.2 Text, Sound and Images

Everything in a computer - words, music, photos - is ultimately just numbers in binary. Here’s how that magic happens:

Text Representation

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Character Set	Bits per Character	Total Characters	What It Includes
ASCII	7 bits	128	Basic English letters, numbers, symbols
Unicode	16-32 bits	100,000+	All languages, emojis, special symbols

Note

ASCII was created first and is very compact, but it only works for English. Unicode was designed to include every language and symbol in the world - Chinese, Arabic, emojis, mathematical symbols, you name it. The trade-off? Unicode files are larger.

Sound Representation

Sound waves are continuous (analog), but computers are digital. To convert sound to digital:

Sound Digitization

The Quality Trade-off:

Factor	Higher Value	Result
Sample Rate	More samples/second	Better accuracy, larger file
Sample Resolution	More bits/sample	More precise amplitude, larger file

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Image Representation

Images are made of pixels (picture elements) arranged in a grid.

Image Properties

Calculate Image File Size

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1.3 Data Storage and Compression

Storage Units - The Computer’s Measuring System

IGCSE Uses 1024, Not 1000!

In IGCSE, we use the binary standard (1024) not the decimal standard (1000). So 1 KiB = 1024 bytes, NOT 1000 bytes.

Unit	Size	Remember This
Bit	1 binary digit	Smallest unit
Nibble	4 bits	One hex digit
Byte	8 bits	One ASCII character
Kibibyte (KiB)	1024 bytes
Mebibyte (MiB)	1024 KiB	bytes
Gibibyte (GiB)	1024 MiB	bytes
Tebibyte (TiB)	1024 GiB	bytes

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File Size Calculations

Image File Size:

Sound File Size:

Sound File Calculation

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Data Compression

Files can be huge. Compression makes them smaller so they’re faster to send and take up less space.

Two Types of Compression

Lossless Compression: Run Length Encoding (RLE)

Instead of storing repeated values, store: value + count.

RLE Practice

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Lossy Compression

Method	What It Does	Used For
MP3 Audio	Removes frequencies humans can’t hear well	Music streaming
JPEG Images	Reduces colour depth and resolution slightly	Photos on websites

When to Use Which?

Use lossless when you need the exact original (documents, programs, medical images).

Use lossy when a small quality loss is acceptable in exchange for much smaller files (streaming, social media, email attachments).

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2. Data Transmission

2.1 Types and Methods of Data Transmission

When you send data over the internet, it doesn’t go as one big chunk. Think of it like sending a long letter - you break it into pages, mail them separately, and reassemble them at the destination.

Packet Structure

What's in a Packet?

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Packet Switching

Routers direct packets along the network, and each packet might take a different route. They arrive potentially out of order, then get reassembled at the destination. Brilliant!

Note

This is why the packet number in the header is so important - it tells the receiving computer how to put all the pieces back in the correct order.

Serial vs Parallel Transmission

Type	How It Works	Advantages	Disadvantages	Used For
Serial	Bits sent one after another over one wire	Reliable over long distances	Slower	USB, Ethernet, long distances
Parallel	Multiple bits sent simultaneously over multiple wires	Faster over short distances	Data can desynchronise (skew) over distance	Inside CPU, old printer cables

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Simplex, Half-Duplex, and Full-Duplex

Think about conversations:

Mode	Data Flow	Real-Life Example	Technical Use
Simplex	One direction only	Radio broadcast (you only listen)	Sensor → Monitor
Half-Duplex	Both directions, but one at a time	Walkie-talkie (take turns speaking)	-
Full-Duplex	Both directions simultaneously	Phone call (can interrupt each other)	Broadband internet

USB Interface

Why USB is Everywhere

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2.2 Methods of Error Detection

Things can go wrong during transmission - electrical interference, loose cables, cosmic rays (seriously!). We need ways to detect errors.

Parity Check - The Simple Approach

Add an extra bit to make the total number of 1s either always even or always odd.

Even Parity

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Caution

Parity can only detect an odd number of bit errors. If two bits flip, the parity still looks correct! That’s why more sophisticated methods exist.

More Robust Methods

Method	How It Works	Strength
Checksum	Calculate a value from all the data (e.g., sum of bytes), send it along	Detects multiple errors better than parity
Echo Check	Receiver sends data back, sender compares	Very reliable but doubles transmission time
Check Digit	Special digit calculated from others using an algorithm	Used in barcodes, ISBNs

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Automatic Repeat Query (ARQ) - Error Correction

This is the full protocol for guaranteeing error-free transmission:

ARQ Protocol Steps

Real World Example

When you download a large file, ARQ is working behind the scenes. If some packets get corrupted, they’re automatically resent without you even knowing!

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2.3 Encryption

Imagine sending a postcard versus sending a sealed letter. Encryption is like that sealed envelope - it scrambles data so only the intended recipient can read it.

Symmetric Encryption

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Pros: Fast, efficient

Cons: How do you securely share the key in the first place? That’s the key distribution problem!

Asymmetric Encryption

The clever solution: use two different keys!

Public & Private Keys

Understanding Asymmetric Encryption

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Real-World Usage

HTTPS websites use asymmetric encryption to establish a secure connection, then switch to symmetric encryption for the actual data transfer (because it’s faster). Best of both worlds!

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3. Hardware

3.1 Computer Architecture

The Central Processing Unit (CPU)

The CPU is the “brain” of the computer - it processes all instructions and data. Every calculation, every decision, every operation goes through here.

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Von Neumann Architecture Components

These components work together in a beautiful choreographed dance to execute programs:

Registers (tiny, super-fast storage inside the CPU):

Register	Full Name	What It Stores
PC	Program Counter	Address of the next instruction
MAR	Memory Address Register	Address in RAM being accessed right now
MDR	Memory Data Register	Data being transferred to/from RAM
CIR	Current Instruction Register	Instruction currently being decoded/executed
ACC	Accumulator	Results of calculations from ALU

Processing Units:

CPU Core Components

Buses (highways for data inside the computer):

Bus	Carries	Direction
Address Bus	Memory addresses	CPU → RAM (one-way)
Data Bus	Actual data/instructions	Both ways (two-way)
Control Bus	Control signals (read, write, clock)	Both ways (two-way)

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The Fetch-Decode-Execute (FDE) Cycle

This happens billions of times per second in your computer. Every single instruction goes through these three stages:

FDE Cycle Steps

Detailed FDE Steps:

FETCH:

1. PC holds the address of next instruction
2. Copy address from PC to MAR (via Address Bus)
3. Instruction at that address copied into MDR (via Data Bus)
4. Instruction from MDR copied to CIR
5. PC incremented (points to next instruction)

DECODE: 6. CU decodes the instruction in CIR (Is it ADD? LOAD? JUMP?)

EXECUTE: 7. CU sends control signals to execute the instruction 8. ALU performs operation if needed, stores result in ACC

Trace the FDE Cycle

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What Makes a CPU Faster?

Performance Factors

Note

A 2.5 GHz quad-core processor can theoretically execute 2.5 billion FDE cycles per second, across 4 cores simultaneously. That’s 10 billion operations per second!

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Instruction Set

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Different CPUs can have different instruction sets (like different languages). That’s why a program compiled for an Intel CPU might not work on an ARM CPU.

Embedded Systems

Not all computers are PCs! Many devices have specialized computers inside them.

Embedded Systems Characteristics

Examples:

• Washing machines (control cycles and timing)
• Cars (Engine Management System, ABS, airbags)
• Digital cameras (image processing)
• Smart home devices (thermostats, security cameras)
• Microwave ovens (timing and power control)

Identify Embedded vs General-Purpose

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Course Summary

Key Takeaways

Exam Prep Checklist

Progress 0%

Congratulations! You've completed all items!

• Can convert between binary, denary, and hex

  Practice all conversion types
• Understand two's complement for negative numbers

  Know the 3-step process
• Can calculate image and sound file sizes

  Memorize the formulas
• Explain lossless vs lossy compression

  Know when to use each
• Understand packet switching and transmission types

  Serial, parallel, simplex, duplex
• Know error detection methods and their trade-offs

  Parity, checksum, ARQ
• Explain symmetric vs asymmetric encryption

  Key distribution problem
• Trace through the FDE cycle step-by-step

  Know all register functions
• Identify CPU performance factors

  Clock speed, cores, cache
• Define and give examples of embedded systems

  Characteristics and real-world uses

Reset Progress

Final Study Advice

Remember the advice at the beginning: build the conceptual framework first. Understand why computers use binary, why packets are useful, why the FDE cycle works the way it does. Once the concepts click, memorizing the English definitions becomes much easier.

Practice explaining concepts out loud. If you can teach it to someone else, you truly understand it. Good luck! 加油！