Lecture Notes: Information Representation

Introduction

• Presenter: James, a computer science graduate turned teacher
• Series focus: A-level computer science

Chapter 1: Information Representation

Learning Objectives

• How computers use binary to represent numbers, text, images, and sound
• Compression techniques for different file formats to reduce file size

Subtopic: Number Systems

Decimal System (Denary)

• Base 10 system: 10 unique values (0-9)
• Place value: Importance of digit position (e.g., 365: 5 is units, 6 is tens, 3 is hundreds)

Binary System

• Base 2 system: Only two unique values (0 and 1)
• Used due to electrical components representing two states (ON/OFF)
• Transistors use binary switches to represent various data

Binary to Denary Conversion

• Multiply digit value by place value and sum (e.g., binary 10101 = 1x16 + 0x8 + 1x4 + 0x2 + 1x1)

Byte and Nibble

• 1 Byte: 8 bits
• 1 Nibble: 4 bits (half-byte)

Hexadecimal System

• Base 16 system: 16 unique values (0-9 and A-F)
• Simplifies binary representation (e.g., 4 binary bits = 1 hexadecimal character)
• Usage: Error codes, IP addresses, MAC addresses, HTML color codes

Converting Between Systems

Binary to Hexadecimal Conversion

• Split binary into chunks of four, then convert chunks to hexadecimal

Denary to Binary Conversion

• Divide the number by 2, record the remainder, and read remainders bottom-up

Hexadecimal to Denary

• Multiply each digit by its place value (16^position) and sum

Representing Large Numbers

Decimal Prefixes

• Kilo: 10^3 = 1,000

Binary Prefixes

• Kibibyte (KiB): 2^10 = 1,024 bytes
• Mebibyte (MiB): 1,024 KiB

Terminology and Conversions

• Formula for conversions between bits, bytes, KiB, MiB, etc.
• Examples of converting between these units

Two's Complement

• Representing negative numbers in binary
• Sign bit: Leftmost bit used for the sign (0 for positive, 1 for negative)
• Examples: Converting positive/negative numbers using two's complement

Arithmetic in Binary

Addition

• Follow borrowing rules but in binary (e.g., 1+1 = 10 in binary, carry the 1)

Subtraction

• Borrowing in binary (e.g., 0-1, borrow from next column)

Overflow Problem

• Extra bit generated that a register cannot handle, causing errors
• Importance of detecting overflow and handling it

Representing Text

ASCII

• American Standard Code for Information Interchange (ASCII): 7-bit code for characters

Unicode

• UTF encoding systems: 1-byte, 2-byte, 3-byte, 4-byte codes
• Variable length: Allows more characters to be represented

Representing Images

Vector Graphics

• Defined by mathematical equations
• Scalable without loss of quality

Bitmap Graphics

• Made up of pixels, each pixel represented by bits
• Color depth: Number of bits per pixel determines the number of colors
• Resolution: Number of pixels in an image grid

File Size Calculations

• Image size: Multiply resolution by color depth (in bits), then convert to bytes
• Sound file size: Multiply sampling rate by sampling resolution and time, convert as needed

Compression Techniques

Lossless Compression

• Run-length Encoding: Encodes repeated values by specifying the count
• Huffman Encoding: Assigns shorter codes to more frequent characters

Lossy Compression

• Some information lost to achieve higher compression
• Techniques include reducing sample rate or color depth for images

Conclusion

• Recap of key points: Number systems, conversions, text representation, images, sound, compression
• Next steps: Transition to Chapter 2