Activity - 1 Computer Number Systems

Introduction to Number Systems

In computer science and digital electronics, understanding different number systems is fundamental. While we commonly use the Decimal system in our daily lives, computers operate using Binary. Other systems like Octal and Hexadecimal are used as convenient shortcuts to represent long binary numbers.

This guide will help you understand these systems and how to convert numbers between them, using practical tables and examples.

The Basics of Number Systems

A number system is a way of representing numbers. The "base" or "radix" of a number system determines the number of unique digits (including zero) used to represent numbers.

1. Decimal Number System (Base-10)

Base: 10
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Usage: Our everyday number system. Each position represents a power of 10.
Example: $123_{10} = (1 \times 10^2) + (2 \times 10^1) + (3 \times 10^0)$

2. Binary Number System (Base-2)

Base: 2
Digits: 0, 1 (called bits)
Usage: The native language of computers. All data in a computer is stored and processed in binary.
Example: $1011_2 = (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 8 + 0 + 2 + 1 = 11_{10}$

3. Octal Number System (Base-8)

Base: 8
Digits: 0, 1, 2, 3, 4, 5, 6, 7
Usage: Used as a compact way to represent binary numbers. Each octal digit corresponds to exactly three binary digits (bits).
Example: $27_8 = (2 \times 8^1) + (7 \times 8^0) = 16 + 7 = 23_{10}$

4. Hexadecimal Number System (Base-16)

Base: 16
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F (where A=10, B=11, ..., F=15)
Usage: Widely used in computing for memory addresses, color codes, and representing large binary numbers concisely. Each hexadecimal digit corresponds to exactly four binary digits (bits).
Example: $2F_{16} = (2 \times 16^1) + (15 \times 16^0) = 32 + 15 = 47_{10}$

Where are Number Systems Used?

Understanding number systems is crucial for students pursuing careers or studies in:

Computer Science & Programming: Essential for understanding data storage, memory addressing, bitwise operations, and low-level programming.
Digital Electronics & Hardware Design: Used in designing and analyzing digital circuits, microprocessors, and embedded systems.
Networking: IP addresses and MAC addresses are often represented in decimal, binary, or hexadecimal formats.
Cybersecurity: Understanding data representation is vital for analyzing network traffic, reverse engineering, and cryptography.
Mathematics: Provides a deeper understanding of numerical representation and abstract algebra.

Search This Blog

Revision Worksheet