number system

1. DATA REPRESENTATION
CONVERSION

2. NUMBER SYSTEM
Decimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System

3. Decimal Number System
 The decimal system is composed of 1- numerals or
symbols (Deca means 10, that is why this is called decimal
system). These 10 symbols are 0,1,2,3,4,5,6,7,8,9 ; using
these symbols as digit as number, we can express any
quantity. The decimal system, also called the base-10
system

4. Binary Number System
 Binary System, there are only two symbols or possible
digit values, 0 and 1. This base-2 system can be used to
represent any quantity that can be represented in
decimal or other number systems.
 The Binary system is also a positional-value system,
wherein each binary digit has its own value expressed as
a power of 2.

5. Octal Number System
 The Octal number system is very important in digital
computer work. The octal number system has a base of
eight, meaning that it has eight unique symbols :
0,1,2,3,4,5,6,7 . Thus each digit of an octal number can
have any value from 0 to 7.
 The octal system is a positional value system, wherein
each octal digit has its own value expressed as a power of
8.

6. Hexadecimal Number System
 The Hexadecimal System uses base 16. Thus, it has 16
possible digit symbols. It uses the digits 0 – 9 and the
letter A, B, C, D, E & F as the 16 digit symbols.
 Hexadecimal is a positional value System has its own
value expressed as a power of 16.

7. NUMBER CONVERSIONS
CONVERSIONS WITH BINARY
Decimal To Binary
Decimal Fraction To Binary
Binary To Decimal
Binary Fraction To Decimal

8. Decimal To Binary
 To converting decimal to Binary we use Repeated division
method. In this the no. is successively divide by 2 and its
remainder recorded.
 For Example convert decimal to Binary 4310
2 43
2 21 1
2 10 1
2 5 0
2 2 1
2 1 0
1 1
CONVERSIONS WITH BINARY
WRITE IN
THIS ORDER
From Down to Up
Your Answer 4310
= 1010112

9. Decimal Fraction To Binary
 To Convert a decimal fraction into binary, multiply the
decimal fraction by the base that’s 2. Do untill you will
get zero at fractional part.
 For Example Convert 0.37510 to Binary Integer Part
Multiply(fractional part)0.375 * 2 = 0.750 0
0.75 * 2 = 1.50 1
0.50 * 2 = 1.00 1
Your Answer is 0.37510 = 0.0112
Write
From
Up to
Down
CONVERSIONS WITH BINARY

10. Binary To Decimal
 To convert Binary to Decimal, Add positional weights or
values with power of 2 start from right side.
 For Example Convert 11011 to Decimal.
24 23 22 21 20
1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20
= 16 + 8 + 0 + 2 + 1
= 2710 (decimal)
1 1 0 1 1
CONVERSIONS WITH BINARY

11. Binary Fraction To Decimal
 To find binary fraction, take the sum of products of each
digit value (0 – 1) and its positional value. Starts from left
side.
 For Example convert 0.0101 to Decimal.
2-1 2-2 2-3 2-4
0 * 2-1 + 1 * 2-2 + 0 * 2-3 + 1 * 2-4
= 0 + 0.25 + 0 + 0.0625
0.01012 = 0.312510 (decimal)
CONVERSIONS WITH BINARY
. 0 1 0 1

12. NUMBER CONVERSIONS
CONVERSIONS WITH OCTAL
Decimal To Octal
Decimal Fraction To Octal
Octal To Decimal
Octal To Binary
Binary To Octal

13. Decimal To Octal
 A decimal integer can be converted to octal by
repeated-division method with division factor of 8.
 Example Convert 26610 to Octal
remainder
8 266 2
8 33 1
8 4 4
0
26610 = 4128
WRITE IN
THIS ORDER
From Down to Up
CONVERSIONS WITH OCTAL

14. Decimal Fraction To Octal
 To convert Decimal fraction into Octal, multiply
fractional part with 8 till you get fractional part 0.
 Example : convert 0.37510 to Octal
Integer Part
0.375 * 8 = 3.0 3
 0.37510 = 0.38
CONVERSIONS WITH OCTAL
Write
From
Up to
Down

15. Octal To Decimal
 It can easily converted into decimal by multiplying
each octal digit by its positional weight.
 For Example 3728 to Decimal
82 81 80
3 * 82 + 7 * 81 + 2 * 80
= 3 * 64 + 7 * 8 + 2 * 1
= 25010
CONVERSIONS WITH OCTAL
3 7 2

16. Octal To Binary
 To convert Octal To Binary is easy. This converting is
performed by converting each octal digit to its 3 bit
binary. Possible digits converted as indicated in Table
 Example : 4728 to binary
From table , 4 = 100 , 7 = 111 & 2 = 010
We get 4728 = 1001110102
CONVERSIONS WITH OCTAL
Octal
Digit
0 1 2 3 4 5 6 7
Binary 000 001 010 011 100 101 110 111

17. Binary To Octal
 Its simply the reverse of octal to binary. Make the three
bits group starting from LSB. Then convert it with
using Table
 For Example: 110101102 to Octal
Make group of three 011 , 010 & 110
011 = 3 , 010 = 2 & 110 = 6
110101102 = 3268
CONVERSIONS WITH OCTAL
Octal
Digit
0 1 2 3 4 5 6 7
Binary 000 001 010 011 100 101 110 111
Add Zero
To Make it
group of
3 bit.

18. NUMBER CONVERSIONS
CONVERSIONS WITH HEX
Decimal To HEX
Decimal Fraction To HEX
HEX To Decimal
HEX To Binary
Binary To HEX

19. Decimal To HEX
 A decimal integer can be converted to hex by repeated-
division method with division factor of 16.
 Example Convert 26610 to Hex
remainder
16 423 7
16 26 A
16 1 1
0
42310 = 1A716
1010 = A16
WRITE IN
THIS ORDER
From Down to Up
CONVERSIONS WITH HEX

20. Decimal Fraction To Hex
 To convert Decimal fraction into Hex, multiply
fractional part with 16 till you get fractional part 0.
 Example : convert 0.0312510 to Hex
Integer Part
0. 03125 * 16 =0.5 0
0. 5 * 16 = 8.0 8
 0.0312510 = 0.0816
CONVERSIONS WITH HEX
Write
From
Up to
Down

21. HEX To Decimal
 It can easily converted into decimal by multiplying
each Hex digit by its positional weight has power of 16.
 For Example 2AF16 to Decimal
162 161 160
2 * 162 + A * 161 + F * 160
= 2 * 256 + 10 * 8 + 15 * 1
= 60710
CONVERSIONS WITH HEX
2 A F
Decimal Hex
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
Decimal Hex
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F

22. HEX To Binary
 To convert Hex To Binary is easy. This converting is
performed by converting each hex digit to its 4 bit
binary. Possible digits converted as indicated in Table
Example : 3A616 to binary
From table, 3 = 0011 ,
A = 1010 & 6 = 0110
We get 3A616 = 0011101001102
CONVERSIONS WITH HEX
Binary Hex
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
Binary Hex
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

23. Binary To HEX
 Its simply the reverse of Hex to binary. Make the four
bits group starting from LSB. Then convert it with
using Table
 For Example: 10101110102 to Hex
Make group of four 0010
, 1011 & 1010
0010 = 2 , 1011 = B & 1010 = A
10101110102 = 2BA16
CONVERSIONS WITH HEX
Add Zero to Make it
group of 4 bit.
Binary Hex
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
Binary Hex
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F