This document discusses four main number systems: binary, octal, decimal, and hexadecimal. It defines key terms like base, bits, bytes, and nibbles. For each number system, it provides the symbols used, the base, and examples of conversions between them. The binary system uses 0 and 1, with a base of 2. Octal uses 0-7 with a base of 8. Decimal uses 0-9 with a base of 10. Hexadecimal uses 0-9 and A-F, with a base of 16. A table compares and contrasts the number systems.

1. T H E O R Y

2. C H A P T E R N O : - 1
1.Binary Number System
2. Octal Number System
3. Decimal number System
4. Hexadecimal number system

3. NUMBER : -
• A number is a symbol which is used to express a quantity or amount
NUMBER SYSTEM : -
• Number system is an organized and systematic way of representing
numbers.
There are four types of number system : -
1. Binary Number System
2. Octal Number System
3. Decimal number System
4. Hexadecimal number system
BASE : -
It is the number of symbols which is available to a number system.
Or,
The number of symbols which is used to express the amount or quantity in
a number system is known as base.

4. BITS : -
• Binary numbers are made of binary digits (bits).
Example : - 0 and 1
BYTE : -
• Group of eight bits are called a byte.
Example : - (11001001)2
NIBBLE : -
• Group of four bits are called a nibble.
Example : - (1101)2

5. Binary Number System
Octal Number System
Decimal Number System
Hexadecimal Number
System
0 & 1
0 to 7
0 to 9
0 to 9 & A to F

6. S/no Number System Symbols Base Known as For calculation
1. Binary Number 0,1 2 5 4 3 2 1 0 Direct or x
2. Octal Number 0,1,2,3,4,5,6,7 8 4 2 1 +
3. Decimal Number 0,1,2,3,4,5,6,7,8,
9
10 5 4 3 2 1 0 X or /
4. Hexadecimal
Number
0,1,2,3,4,5,6,7,8,
9,A,B,C,D,E,F
16 8 4 2 1 +

7. C O N V E RT
( B I N A RY )
1. 1. Octal to Binary
2. 2. Decimal to Binary
3. 3. Hexadecimal to Binary
B I N A RY
N U M B E R S YS T E M
This number system have two symbols to
represent the
numbers. The symbols are 0 or 1.It has base 2.

8. C O N V E RT
( O C TA L )
1. 1. Binary to Octal
2. 2. Decimal to Octal
3. 3. Hexadecimal to Octal
O C TA L
N U M B E R S YS T E M
This number system have eight symbols to
represent the numbers.
The symbols are 0,1,2,3,4,5,6 & 7.It has base 8.

9. C O N V E RT
( D E C I M A L )
1. 1. Binary to Decimal
2. 2. Octal to Decimal
3. 3. Hexadecimal to Decimal
D E C I M A L
N U M B E R S YS T E M
In this number system ten symbols are used to
represent the
numbers .The ten symbols are 0,1,2,3,4,5,6,7,8 & 9.It
is also known as Arbaic
numerals. It has base 10.

10. C O N V E RT
( H E X A D E C I M A L )
1. 1. Binary to Hexadecimal
2. 2. Octal to Hexadecimal
3. 3. Decimal to Hexadecimal
H E X A D E C I M A L
N U M B E R S YS T E M
This number system have 16 symbols to represent
the numbers. The
symbols are 0,1,2,3,4,5,6,7,8 , 9,A,B,C,D,E & F. it
has base 16.

11. The following table represents the
comparisons
of all the number system.
Binary Octal Decimal Hexadecimal Number
0 0 (000) 0 0 (0000) A (1010)
1 1 (001) 1 1 (0001) B (1011)
2 (010) 2 2 (0010) C (1100)
3 (011) 3 3 (0011) D (1101)
4 (100) 4 4 (0100) E (1110)
5 (101) 5 5 (0101) F (1111)
6 (110) 6 6 (0110)
7 (111) 7 7 (0111)
8 8 (1000)
9 9 (1001)

12. THANK YOU
P R E S E N T E D B Y
DURGESH SAHU