Understanding Binary, Decimal, Octal, and Hexadecimal Number Systems and Conversions, Exercises of Network Design

Download Understanding Binary, Decimal, Octal, and Hexadecimal Number Systems and Conversions and more Exercises Network Design in PDF only on Docsity!

Number System

Number

Systems

Number

Conversion

Introduction to

Subnetting

Objectives

Introduction: What is a Number System?

• You probably already know what a number system is - ever hear of binary numbers or hexadecimal

numbers?

• Simply put, a number system is a way to represent numbers.
• We are used to using the base-10 number system, which is also called decimal.
• Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary).

Decimal number system

• Decimal number system, also called Hindu-Arabic, or Arabic,

number system, in mathematics, positional numeral

system employing 10 as the base and requiring 10 different

numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

• 100 = 10 x 10 OR 10

2

• 1000= 10 x 10 x 10 OR 10

3

• Minimum Value is 0, Maximum value is 255

Counting in Binary

Hexadecimal System

• In mathematics and computing, hexadecimal (also base 16 , or hex) is a positional numeral system with

a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0 – 9 to represent values

zero to nine, and A, B, C, D, E, F (or alternatively a, b, c, d, e, f) to represent values ten to fifteen.

Octal System

• The octal numeral system, or oct for short, is the base- 8 number system, and uses the digits 0 to 7
• It is represented in series of 8 digits
• 0 - 7, 10 - 17, 20-27, 30-37…….. 70-77,100-177,200-277……..

NUMBER CONVERSION

2 200 0

2 100 0

2 50. 0

2 25. 1

2 12 0

2 6. 0

2 3. 1

1

2 200

2 100

2 50.

2 25.

2 12

2 6.

2 3.

1

Decimal to Binary

= FC

1 1 0 0 1 0 0 0 C

= C

EF

Binary to hexadecimal

Summary

• Different numbering systems
• Counting according to number systems
• IPv4 & IPv6 number systems
• Number conversion