Introduction to Computer Science

2.

Data Representation and Number Systems

2.1.

Fundamentals of Digital Representation

2.1.1.

Digital vs Analog Information

2.1.2.

The Bit as Basic Unit

2.1.2.1.

2.1.2.2.

Electrical Implementation

2.1.3.

Bytes and Word Sizes

2.1.3.1.

Byte Definition

2.1.3.2.

Common Word Sizes

2.1.3.3.

Memory Addressing

2.2.

2.2.1.

Positional Number Systems

2.2.1.1.

Place Value Concept

2.2.1.2.

2.2.2.

Binary System (Base-2)

2.2.2.1.

2.2.2.2.

Place Values in Binary

2.2.2.3.

Binary Arithmetic

2.2.3.

Decimal System (Base-10)

2.2.3.1.

2.2.3.2.

Place Values in Decimal

2.2.4.

Octal System (Base-8)

2.2.4.1.

2.2.4.2.

Historical Use in Computing

2.2.5.

Hexadecimal System (Base-16)

2.2.5.1.

Hexadecimal Digits

2.2.5.2.

Compact Binary Representation

2.2.5.3.

Use in Memory Addresses

2.2.5.4.

Color Codes in Computing

2.3.

Number System Conversions

2.3.1.

Binary to Decimal Conversion

2.3.2.

Decimal to Binary Conversion

2.3.3.

Binary to Hexadecimal Conversion

2.3.4.

Hexadecimal to Binary Conversion

2.3.5.

Decimal to Hexadecimal Conversion

2.3.6.

Hexadecimal to Decimal Conversion

2.3.7.

Octal Conversions

2.3.8.

Conversion Shortcuts and Patterns

2.4.

Integer Representation

2.4.1.

Unsigned Integers

2.4.1.1.

Range and Limitations

2.4.1.2.

Overflow Conditions

2.4.2.

Signed Integer Representation

2.4.2.1.

Sign and Magnitude Method

2.4.2.2.

One's Complement

2.4.2.3.

Two's Complement

2.4.2.3.1.

Conversion Process

2.4.2.3.2.

Arithmetic Advantages

2.4.2.3.3.

Range Calculations

2.4.3.

Binary Arithmetic Operations

2.4.3.1.

2.4.3.2.

2.4.3.3.

Multiplication Basics

2.5.

Real Number Representation

2.5.1.

Fixed-Point Representation

2.5.1.1.

Format Structure

2.5.1.2.

Precision Limitations

2.5.1.3.

Scaling Factors

2.5.2.

Floating-Point Representation

2.5.2.1.

IEEE 754 Standard

2.5.2.2.

Single Precision Format

2.5.2.3.

Double Precision Format

2.5.2.4.

2.5.2.4.1.

2.5.2.4.2.

2.5.2.4.3.

Mantissa (Significand)

2.5.2.5.

2.5.2.6.

2.5.2.6.1.

2.5.2.6.2.

NaN (Not a Number)

2.5.2.7.

Precision and Rounding Errors

2.5.2.8.

Floating-Point Arithmetic Issues

2.6.

Character and Text Representation

2.6.1.

2.6.1.1.

Standard ASCII Table

2.6.1.2.

2.6.1.3.

Limitations for International Text

2.6.2.

Unicode Standard

2.6.2.1.

Unicode Code Points

2.6.2.2.

2.6.2.3.

UTF Encoding Schemes

2.6.2.3.1.

2.6.2.3.2.

2.6.2.3.3.

2.6.2.4.

Multilingual Support

2.6.2.5.

Emoji and Special Characters

2.7.

Multimedia Data Representation

2.7.1.

Image Representation

2.7.1.1.

Bitmap vs Vector Graphics

2.7.1.2.

Pixels and Resolution

2.7.1.3.

2.7.1.3.1.

RGB Color Model

2.7.1.3.2.

CMYK Color Model

2.7.1.3.3.

HSV Color Model

2.7.1.4.

Color Depth and Bit Depth

2.7.1.5.

Image Compression Concepts

2.7.2.

Audio Representation

2.7.2.1.

Analog to Digital Conversion

2.7.2.2.

2.7.2.3.

2.7.2.4.

Bit Depth for Audio

2.7.2.5.

Audio Compression Concepts

2.7.3.

Video Representation

2.7.3.1.

2.7.3.2.

Resolution Standards

2.7.3.3.

Compression Techniques

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