DATA REPRESENTATION
CONVERSION
NUMBER SYSTEM
Decimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System
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
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.
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.
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.
NUMBER CONVERSIONS
CONVERSIONS WITH BINARY
Decimal To Binary
Decimal Fraction To Binary
Binary To Decimal
Binary Fraction To Decimal
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
2
2
2
2
2
2
43
21
10
5
2
1
1
1
1
0
1
0
1
WRITE IN
THIS ORDER
From Down to Up
Your Answer 4310 = 101011
2
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 0.37510 to Binary
Integer Part
Multiply(fractional part)0.375 * 2 = 0.750
0
Write
0.75 * 2 = 1.50
1
From
Up to
0.50 * 2 = 1.00
1
Down
Your Answer is 0.37510 = 0.0112
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 11011 to Decimal.
1
24
1
0
22
1
21
1
20
23
1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20
= 16 + 8 + 0 + 2 + 1
= 2710 (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 0.0101 to Decimal.
.
0
2-1
1
0
2-3
2-2
0 * 2-1 + 1 * 2-2 + 0 * 2-3 + 1 * 2-4
= 0 + 0.25 + 0 + 0.0625
0.01012 = 0.312510 (decimal)
1
2-4
NUMBER CONVERSIONS
CONVERSIONS WITH OCTAL
Decimal To Octal
Decimal Fraction To Octal
Octal To Decimal
Octal To Binary
Binary To Octal
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 26610 to Octal
remainder
8
8
8
266
33
4
0
2
1
4
WRITE IN
THIS ORDER
From Down to Up
26610 = 4128
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 0.37510 to Octal
Integer Part
Write
0.375 * 8 = 3.0
3
From
 0.37510 = 0.38
Up to
Down
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
82
7
81
3 * 82 + 7 * 81 + 2 * 80
= 3 * 64 + 7 * 8 + 2 * 1
= 25010
2
80
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
Octal
Digit
0
1
2
3
4
5
6
7
Binary
000
001
010
011
100
101
110
111
 Example : 4728 to binary
From table , 4 = 100 , 7 = 111 & 2 = 010
We get 4728 = 1001110102
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
Octal
Digit
0
1
2
3
4
5
6
7
Binary
000
001
010
011
100
101
110
111
 For Example: 110101102 to Octal
Make group of three 011 , 010 & 110
011 = 3 , 010 = 2 & 110 = 6
110101102 = 3268
Add Zero
To Make it
group of
3 bit.
NUMBER CONVERSIONS
CONVERSIONS WITH HEX
Decimal To HEX
Decimal Fraction To HEX
HEX To Decimal
HEX To Binary
Binary To HEX
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 26610 to Hex
remainder
16
16
16
423
26
1
0
7
A
1
1010 = A16
WRITE IN
THIS ORDER
From Down to Up
42310 = 1A716
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 0.0312510 to Hex
Integer Part
Write
0. 03125 * 16 =0.5
0
From
Up to
0. 5 * 16 = 8.0
8
Down
 0.0312510 = 0.0816
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
Decimal Hex
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
2
162
A
F
161
160
2 * 162 + A * 161 + F * 160
= 2 * 256 + 10 * 8 + 15 * 1
= 60710
Decimal Hex
8
8
9
9
10
A
11
B
12
C
13
D
14
E
15
F
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
Binary
Binary
Hex
Hex
1000
8
1001
9
1010
A
1011
B
1100
C
5
1101
D
0110
6
1110
E
0111
7
1111
F
0000
0
0001
1
0010
2
0011
3
0100
4
0101
Example : 3A616 to binary
From table, 3 = 0011 ,
A = 1010 & 6 = 0110
We get 3A616 = 0011101001102
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
Add Zero to Make it
Binary
Hex
group of 4 bit.
Binary
Hex
1000
8
1001
9
1010
A
1011
B
1100
C
1101
D
6
1110
E
7
1111
F
0000
0
0001
1
0010
2
0011
3
0100
4
0101
5
0110
0111
 For Example: 10101110102 to Hex
Make group of four 0010
, 1011 & 1010
0010 = 2 , 1011 = B & 1010 = A
10101110102 = 2BA16