Practical No. 1
Title: To Perform Number System Conversions

Aim
To enable students to accurately convert numerical values between various number systems, including Decimal, Binary, Octal, and Hexadecimal, thereby reinforcing their understanding of place value and base conversion principles.

Introduction
In the realm of computer architecture, understanding different number systems is fundamental. While humans commonly use the decimal system (base-10), digital computers operate primarily on the binary system (base-2), using only two digits: 0 and 1. To bridge this gap and make binary data more manageable for humans, other number systems like Octal (base-8) and Hexadecimal (base-16) are frequently employed as shorthand notations for binary. These systems offer a more compact representation of binary data and facilitate easier conversion. This practical serves as a hands-on exercise to master the conversion techniques among these critical number systems.

Procedure / Example
Example: Converting Decimal to Binary
To convert the decimal number 13₁₀ to binary, perform successive division by 2 and collect the remainders:

1.     13 ÷ 2 = 6 remainder 1

2.     6 ÷ 2 = 3 remainder 0

3.     3 ÷ 2 = 1 remainder 1

4.     1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top, the binary equivalent of 13₁₀ is 1101₂.

Result / Conclusion
This practical successfully demonstrated the fundamental principles and methods for converting numerical data between decimal, binary, octal, and hexadecimal number systems. Mastery of these conversions is essential for understanding how computers represent and process information, forming a foundational skill in computer architecture.