The document provides a guide on converting numbers between binary, decimal, octal, and hexadecimal systems. It details methods for converting fractional binary to decimal and mixed binary numbers to octal and hexadecimal, including step-by-step examples. It emphasizes the significance of grouping digits and using appropriate base values for conversion.

1. DATA REPRESENTATION
CLASS : XI
COMPUTER SCIENCE(083) - PYTHON
https://computerassignmentsforu.blogspot.com
PART-5

2. Number System Conversion
TO CONVERT FRACTIONAL BINARY TO FRACTIONAL DECIMAL NUMBER
TO CONVERT MIXED BINARY NUMBER TO MIXED OCTAL NUMBER
TO CONVERT MIXED BINARY NUMBER TO MIXED HEXADECIMAL NUMBER

3. CONVERT FRACTIONAL BINARY NUMBER TO FRACTIONAL DECIMAL NUMBER:
(.1011)2 ( ? )10
=
In this case of converting fractional
binary number to fractional decimal
number multiply each binary digit from
Left To Right (starting from .[Period or
Dot] ) by base value of binary 2 and
power value starts from -1 to….. N
numbers[Negative]

4. Convert fractional binary NUMBER to fractional decimal Number
Example:
(.1011)2
0 1 1
From Left To Right
1 =
=
=
1 x 0.0625 =0.0625
1 x 0.125 = 0.125
Total: 0.68751
1
1
0
1
x
x
x
x
2
2
2
2
-4
-3
-2
0 x 0.25 = 0
1 x 0.5 = 0.5
0.06251
0.125
0
0.5
Add
=
-1
0.06251 0.125 0 0.5
=

5. CONVERT MIXED BINARY NUMBER TO MIXED DECIMAL NUMBER:
Let us take one decimal number first and then convert it to DECIMAL number:
(1101.111)2 ( ? )2
=
In this case of SPLIT THE BINARY NUMBER INTO TWO PART
FROM DOT(.) SIGN.
1101 1111101.111

6. (1101.101)2=
1101 101
1 1 10 1 10
1
1
0
1
1
1
0
x
x
x
x
x
x
x
2 =
2 =
2 =
2 =
2 =1x0.125=
2 =0x0.25=
2 =1x0.5=
0
1
2
3
-3
-2
-1
1
0
4
8
0.125
0
0.5
Total: 13
Total: 0.625
( )10
13
625

7. CONVERT MIXED BINARY NUMBER TO MIXED OCTAL NUMBER:
(1111011.1101)10 ( ? )8
=
In this case make the group of 3 binary numbers and read
numbers from RIGHT TO LEFT before (.)DOT and read numbers
from LEFT TO RIGHT after (.)DOT.
1111011.1101

8. 11 111011
CONVERT MIXED BINARY NUMBER TO MIXED OCTAL NUMBER:
(1111011.1101)10 ( )8=
1111011.1101
00
110
00
1 7 3 6 4

9. CONVERT MIXED BINARY NUMBER TO MIXED HEXADECIMAL NUMBER:
(1011011101.10101101)10 ( ? )16
=
In this case make the group of 4 binary numbers and read
numbers from RIGHT TO LEFT before (.)DOT and read numbers
from LEFT TO RIGHT after (.)DOT.
1011011101.10101101

10. CONVERT MIXED BINARY NUMBER TO MIXED HEXADECIMAL NUMBER:
(1011011101.101011011)10 ( )16=
1011011101.1010110111101110110
00
1010
1101
1
000
2 13=D 10=A 8
2 D D DA 82 D D A D 8