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. CONVERSIONS WITH BINARY
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
WRITE IN
THIS ORDER
From Down to Up
Your Answer =

9. Decimal Fraction To Binary
CONVERSIONS WITH BINARY
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 to Binary Integer Part
Multiply(fractional part)0.375 * 2 =
0.75 * 2 =
0.50 * 2 =
Your Answer is =
Write
From
Up to
Down

10. CONVERSIONS WITH BINARY
Binary To Decimal
To convert Binary to Decimal, Add positional weights or values with power of 2 start from right side.
For Example Convert to Decimal.
1 * * * * * 20 =
= 2710 (decimal) 1

11. Binary Fraction To Decimal
CONVERSIONS WITH BINARY
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 to Decimal.
0 * * * * 2-4 =
= (decimal) 1

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

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

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

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

16. CONVERSIONS WITH OCTAL
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 =
Octal Digit 1 2 3 4 5 6 7
Binary
000
001
010
011
100
101
110
111

17. CONVERSIONS WITH OCTAL
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: to Octal
Make group of three 011 , 010 & 110
011 = 3 , 010 = 2 & 110 = 6
= 3268
Octal Digit 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. CONVERSIONS WITH HEX
Decimal To HEX
A decimal integer can be converted to hex by repeated-division method with division factor of 16.
Example Convert to Hex
remainder A
42310 = 1A716
1010 = A16
WRITE IN
THIS ORDER
From Down to Up

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

21. CONVERSIONS WITH HEX
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
2 * A * F * 160
= 2 * * * 1
= 60710
Decimal
Hex 1 2 3 4 5 6 7
Decimal
Hex 8 9 10 A 11 B 12 C 13 D 14 E 15 F 2 A F

22. CONVERSIONS WITH HEX
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 = & 6 = 0110
We get 3A616 =
Binary
Hex
0000
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. CONVERSIONS WITH HEX
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: to Hex
Make group of four 0010
, & 1010
0010 = 2 , 1011 = B & 1010 = A
= 2BA16
Add Zero to Make it group of 4 bit.
Binary
Hex
0000
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

24. THANK YOU
Submitted by,
Anil
Yougnath
Rakesh and
Biswarup.