This document discusses different number systems used in digital computers and their conversions. It explains that computers understand numbers in binary format and all other data needs to be converted to binary. It then describes the commonly used number systems - decimal, binary, hexadecimal and octal. Decimal uses 10 digits, binary uses two digits 0 and 1, hexadecimal uses 16 digits with 0-9 and A-F, and octal uses 8 digits from 0-7. The document provides examples and methods to convert between these number systems.
3. WHAT IS NUMBER SYSTEM?
• Computers understand machine language. Every letter, symbol etc.
that we write in the instructions given to computer, it gets converted into machine
language.
• This machine language comprises of numbers. In order to
understand the language used by computers and other digital
system it is crucial to have a better understanding of number
system.
4. • Commonly Used Number system
• Consist of 10 Digits (0-9).Base-10
• Example: 107,78,98,2786
Types of Number System
Decimal
Number
System
Binary Number
System
Hexadecimal
Number System
Octal Number
System
• Use in Digital Computers
• Consist of 2 Digits (0 and 1).Base-2
• Example: 10001,10100
• Consist of 16 Digits (0-9) (A-F)
• Base-16
• Example: D1CE,2E6
• Consist of 8 Digits (0-7)
• Base-8
• Example: 6675,0453,655
5. The Decimal System (Base) 10
• The word decimal is derived from the Latin root
decem(ten)
• Base b = 10
• Ten symbols: S = {0,1,2,3,4,5,6,7,8,9}
Example:45,452,501,4521
• The symbols in this system are often referred to
as decimal digits or just digits.
6. THE BINARY SYSTEM (BASE) 2
• The word binary is derived from the Latin root
• bini (double).
• Base b = 2.
• Ten symbols: S = {0, 1}
Binary is a base 2 number system invented by Gottfried Leibniz that is made up of only
two numbers: 0 and 1. This number system is the basis for all binary code, which is used to
write data such as the instructions that computer processors use, or the digital text you
read every day.
24. THE HEXADECIMAL SYSTEM
(BASE 16)
• The word hexadecimal is derived from the Greek
root hex (six) and Latin root decem (ten).
• Base b = 16.
• Ten symbols: S = {0, 1,2,3,4,5,6,7, 8, 9, A, B, C, D,
E, F}
• Example: 2AF , 3DF4 , 5FAE3 , 8CF09
• The symbols in this system are often referred to
• as hexadecimal digits.
25. THE RELATIONSHIP BETWEEN
DECIMAL TO HEXADECIMAL
0
1
2
3
4
5
6
7
9
0
1
2
3
4
5
6
7
9
DECIMAL TO HEXADECIMAL
10
11
12
13
14
15
=
=
=
=
=
=
A
B
C
D
E
F
=
=
=
=
=
=
=
=
=
27. 2 3 E
HEXADECIMAL DECIMAL
=16
16
0
16
1
16
2
2 X 16
2
+ 3 X 16
1
+ 14 X 16
0
10
11
12
13
14
15
=
=
=
=
=
=
A
B
C
D
E
F
DH
2 X 256 + 3 X 16 + 14
512 + 48 + 14 574=
574 10
TO
29. THE OCTAL SYSTEM (BASE 8)
• The word octal is derived from the Latin root octo
• (eight).
• Base b = 8.
{0, 1, 2, 3, 4, 5, 6, 7}
Example: {1524 , 576 , 342}