WEEK 3 — Numbering System

Nera Sofiya Al-Fahmi (2410350) Section 6

UNDERSTANDING NUMBERING SYSTEM

1. Binary System & Computer Architecture

• Computer uses binary numbering system.
• crucial for comprehending how data is processed.

2. Data Representation

• used to represent different types of data (integers, characters, memory addresses.

3. Memory Addressing

• simple (more compact and readable).

4. Arithmetic Operations

• Mathematic problems are performed using binary system.
• understand how CPUs perform ALU operations & optimize performance.

5. Instruction Sets & Machine Language

• essential for interpreting machine language & assembly language.

Numbering System

1. Decimal System (base 10).
2. Binary System (base 2).
3. Octal System (Base 8).
4. Hexadecimal System (Base 16).

Conversion

Base 10 to Base 2

Base 10 to Base 2 (fraction)

Conversion for hexadecimal

Signed & Unsigned representation

1. Unsigned Representation

• Binary numbers that can only represent non-negative values.
• Used when you don’t need to work with negative numbers.

2. Signed Representation

• Represent both positive & negative values.
• Enabling mathematical operations.
• Solves issue of two zeros (arithmetic operations simpler and more efficient.