Introduction to Number System,
Number Conversion
NUMBER SYSTEM
AND DATA REPRESENTATION
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Introduction to Number Systems and Data Representation, Study notes of Civil Engineering
A comprehensive overview of different number systems, including the decimal, binary, octal, and hexadecimal systems. It explains the characteristics and applications of each system, as well as the methods for converting between them. Topics such as the concept of number systems, the representation of numbers in different bases, and the conversion techniques like the radix divide method and the radix multiply method. It also discusses the relationship between the various number systems and their practical implications in computer science and digital systems. The document serves as a valuable resource for understanding the fundamental principles of number representation and data encoding, which are essential for students and professionals working in fields like computer programming, digital electronics, and information technology.
Typology: Study notes
2022/2023
1 / 31
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Introduction to Number Systems and Data Representation and more Study notes Civil Engineering in PDF only on Docsity!
Introduction to Number System, Number Conversion
NUMBER SYSTEM
AND DATA REPRESENTATION
-is the system of naming or representing numbers
WHAT IS NUMBER
SYSTEM?
Decimal Number system has a base of 10 we use this number system in our day to day life 0 1 2 3 4 5 6 7 8 9 DECIMAL NUMBER SYSTEM represented by INTRODUCTION TO NUMBER SYSTEM
Example: 378 1234 404 DECIMAL NUMBER SYSTEM 10 10 10 Take note: If radix or base is not given in a certain number, then it is a decimal number. Example: 378 1234 404 INTRODUCTION TO NUMBER SYSTEM
BINARY NUMBER SYSTEM INTRODUCTION TO NUMBER SYSTEM 1 byte (B) = 8 bits 1 Kilobytes (KB) = 1024 bytes 1 Megabyte (MB) = 1024 KB 1 Gigabyte (GB) = 1024 MB 1 Terabyte (TB) = 1024 GB
Example: 101111010 10011010010 110010100 BINARY NUMBER SYSTEM 2 2 2 11111010 2 Most Significant bit (MSB) Least Significant bit (LSB) INTRODUCTION TO NUMBER SYSTEM
Example: 572 2322 624 OCTAL NUMBER SYSTEM 8 8 8 INTRODUCTION TO NUMBER SYSTEM
Example: 16 HEXADECIMAL NUMBER SYSTEM 17A 4D 194 16 16 INTRODUCTION TO NUMBER SYSTEM
NUMBER SYSTEM
CONVERSION
NUMBER SYSTEM CONVERSION Radix Divide Method –can be used in converting from decimal integer (base
- to equivalent base integer. Radix Multiple Method -can be used in converting from base integer to decimal integer.
10
17A
2 8 16
2 8 16 10 10 10
DECIMAL TO BINARY CONVERSION 378 10 Example: 2 Radix Divide Method using: 378 ÷ 2 = 189 0 189 ÷ 2 = 94 1 94 ÷ 2 = 47 0 47 ÷ 2 = 23 1 23 ÷ 2 = 11 1 11 ÷ 2 = 5 1 5 ÷ 2 = 2 1 2 ÷ 2 = 1 0 1 ÷ 2 = 0 1 Quotient Ramainder
Answer: 101111010
2
DECIMAL TO OCTAL CONVERSION 378 10 Example: 8 Radix Divide Method using: 378 ÷ 8 = 47 2 47 ÷ 8 = 5 7 5 ÷ 8 = 0 5 Quotient Ramainder
Answer: 572
8
101111010 2 Example: 10 Radix Multiply Method using: 101111010 2 8 7 6 5 4 3 2 1 0 0 X 2 = 0 1 X 2 = 2 0 X 2 = 0 1 X 2 = 8 1 X 2 = 16 1 X 2 = 32 1 X 2 = 64 0 X 2 = 0 1 X 2 = 256 0 1 2 3 4 5 6 7 8
ADD = 378 10 BINARY TO DECIMAL CONVERSION
2 2 2 2 2 2 2 2 2 2 ... 256 128 64 32 16 8 4 2 1 BINARY TO DECIMAL CONVERSION 101111010 2 Example: 10 using: Table Method N 8 7 6 5 4 3 2 1 0 1 0 1 1 1 1 0 1 0 = 256 + 64 + 32 + 16 + 8 + 2 = 10 BINARY TO DECIMAL CONVERSION