### Class XI Data Representation PPT

```DATA REPRESENTATION
CONVERSION
NUMBER SYSTEM
Decimal Number System
Binary Number System
Octal 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.
 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
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
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
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
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
```