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1. Number System and Conversions
An Overview

2. What is a Number System?
• • A number system is a way to represent
numbers using symbols.
• • Defines a set of values and rules for
combination.

3. Types of Number Systems
• • Binary (Base 2)
• • Octal (Base 8)
• • Decimal (Base 10)
• • Hexadecimal (Base 16)

4. Binary Number System
• • Digits used: 0 and 1
• • Base: 2
• • Used in computers and digital electronics

5. Decimal Number System
• • Digits used: 0 to 9
• • Base: 10
• • Most commonly used in daily life

6. Hexadecimal Number System
• • Digits used: 0-9 and A-F
• • Base: 16
• • Widely used in computer memory
addressing

7. Conversions Between Number
Systems
• • Decimal ↔ Binary
• • Decimal ↔ Octal
• • Decimal ↔ Hexadecimal
• • Binary ↔ Octal/Hexadecimal

8. Example: Decimal to Binary
• Example: Convert 25 to Binary
• • 25 ÷ 2 = 12 R1
• • 12 ÷ 2 = 6 R0
• • 6 ÷ 2 = 3 R0
• • 3 ÷ 2 = 1 R1
• • 1 ÷ 2 = 0 R1
• Binary = 11001

9. Example: Binary to Decimal
• Example: Convert 1011 to Decimal
• • (1×2³) + (0×2²) + (1×2¹) + (1×2⁰)
• • 8 + 0 + 2 + 1 = 11