Chapter 2 - Encoding Schemes and Number System
Exercise Solutions ( continued .. )
9. Write binary equivalent of the following octal numbers.
(i) 2306
Convert to Decimal: 1222
Now convert 1222 to Binary:
1222 ÷ 2 = 611 with a remainder of 0
611 ÷ 2 = 305 with a remainder of 1
305 ÷ 2 = 152 with a remainder of 1
152 ÷ 2 = 76 with a remainder of 0
76 ÷ 2 = 38 with a remainder of 0
38 ÷ 2 = 19 with a remainder of 0
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Binary value: 1 0 0 1 1 0 0 0 1 1 0
(ii) 5610
Convert to Decimal: 2952
Now convert 2952 to Binary:
2952 ÷ 2 = 1476 with a remainder of 0
1476 ÷ 2 = 738 with a remainder of 0
738 ÷ 2 = 369 with a remainder of 0
369 ÷ 2 = 184 with a remainder of 1
184 ÷ 2 = 92 with a remainder of 0
92 ÷ 2 = 46 with a remainder of 0
46 ÷ 2 = 23 with a remainder of 0
23 ÷ 2 = 11 with a remainder of 1
11 ÷ 2 = 5 with a remainder of 1
5 ÷ 2 = 2 with a remainder of 1
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Binary value: 101110001000
(iii) 742
Convert to Decimal: 482
Now convert 482 to Binary:
482 ÷ 2 = 241 with a remainder of 0
241 ÷ 2 = 120 with a remainder of 1
120 ÷ 2 = 60 with a remainder of 0
60 ÷ 2 = 30 with a remainder of 0
30 ÷ 2 = 15 with a remainder of 0
15 ÷ 2 = 7 with a remainder of 1
7 ÷ 2 = 3 with a remainder of 1
3 ÷ 2 = 1 with a remainder of 1
1 ÷ 2 = 0 with a remainder of 1
Binary value: 111100010
(iv) 65.203
Convert to Decimal: 53.255859375
Now convert 53.255859375 to Binary:
Integer Part:
53 ÷ 2 = 26 with a remainder of 1
26 ÷ 2 = 13 with a remainder of 0
13 ÷ 2 = 6 with a remainder of 1
6 ÷ 2 = 3 with a remainder of 0
3 ÷ 2 = 1 with a remainder of 1
1 ÷ 2 = 0 with a remainder of 1
Fractional Part:
0.255859375 × 2 = 0.51171875 (integer part = 0)
0.51171875 × 2 = 1.0234375 (integer part = 1)
0.0234375 × 2 = 0.046875 (integer part = 0)
0.046875 × 2 = 0.09375 (integer part = 0)
0.09375 × 2 = 0.1875 (integer part = 0)
0.1875 × 2 = 0.375 (integer part = 0)
0.375 × 2 = 0.75 (integer part = 0)
0.75 × 2 = 1.5 (integer part = 1)
0.5 × 2 = 1.0 (integer part = 1, and we stop here as we reach zero)
Thus 65.203 in Binary is: 110101 . 010000011
10. Write binary representation of the following hexadecimal numbers:
(i) 4026
Convert to Decimal: 16422
Now convert 16422 to Binary:
16422 ÷ 2 = 8211 with a remainder of 0
8211 ÷ 2 = 4105 with a remainder of 1
4105 ÷ 2 = 2052 with a remainder of 1
2052 ÷ 2 = 1026 with a remainder of 0
1026 ÷ 2 = 513 with a remainder of 0
513 ÷ 2 = 256 with a remainder of 1
256 ÷ 2 = 128 with a remainder of 0
128 ÷ 2 = 64 with a remainder of 0
64 ÷ 2 = 32 with a remainder of 0
32 ÷ 2 = 16 with a remainder of 0
16 ÷ 2 = 8 with a remainder of 0
8 ÷ 2 = 4 with a remainder of 0
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Binary value: 100000000100110
(ii) BCA1
Convert to Decimal: 48289
Now convert 48289 to Binary:
48289 ÷ 2 = 24144 with a remainder of 1
24144 ÷ 2 = 12072 with a remainder of 0
12072 ÷ 2 = 6036 with a remainder of 0
6036 ÷ 2 = 3018 with a remainder of 0
3018 ÷ 2 = 1509 with a remainder of 0
1509 ÷ 2 = 754 with a remainder of 1
754 ÷ 2 = 377 with a remainder of 0
377 ÷ 2 = 188 with a remainder of 1
188 ÷ 2 = 94 with a remainder of 0
94 ÷ 2 = 47 with a remainder of 0
47 ÷ 2 = 23 with a remainder of 1
23 ÷ 2 = 11 with a remainder of 1
11 ÷ 2 = 5 with a remainder of 1
5 ÷ 2 = 2 with a remainder of 1
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Binary value: 1011110010100001
(iii) 98E
Convert to Decimal: 2446
Now convert 2446 to Binary:
2446 ÷ 2 = 1223 with a remainder of 0
1223 ÷ 2 = 611 with a remainder of 1
611 ÷ 2 = 305 with a remainder of 1
305 ÷ 2 = 152 with a remainder of 1
152 ÷ 2 = 76 with a remainder of 0
76 ÷ 2 = 38 with a remainder of 0
38 ÷ 2 = 19 with a remainder of 0
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Binary value: 100110001110
(iv) 132.45
Convert to Decimal: 306.26953125
Now convert the integer part to Binary:
306 ÷ 2 = 153 with a remainder of 0
153 ÷ 2 = 76 with a remainder of 1
76 ÷ 2 = 38 with a remainder of 0
38 ÷ 2 = 19 with a remainder of 0
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1
Now convert the fraction part to Binary:
0.26953125 × 2 = 0.5390625 (integer part = 0)
0.5390625 × 2 = 1.078125 (integer part = 1)
0.078125 × 2 = 0.15625 (integer part = 0)
0.15625 × 2 = 0.3125 (integer part = 0)
0.3125 × 2 = 0.625 (integer part = 0)
0.625 × 2 = 1.25 (integer part = 1)
0.25 × 2 = 0.5 (integer part = 0)
0.5 × 2 = 1.0 (integer part = 1, and we stop here as we reach zero)
Combine to get final Binary value: 100110010 . 01000101
11. How does computer understand the following text? (hint: 7 bit ASCII code).
(i) HOTS
Each character in "HOTS" has a specific ASCII value:
H:
ASCII = 72, Binary = 1001000
O:
ASCII = 79, Binary = 1001111
T:
ASCII = 84, Binary = 1010100
S:
ASCII = 83, Binary = 1010011
(ii) Main
M: ASCII = 77,
Binary = 1001101
a: ASCII = 97,
Binary = 1100001
i: ASCII = 105, Binary
= 1101001
n: ASCII = 110, Binary
= 1101110
(iii) CaSe
C: ASCII = 67 Binary
= 1000011
a: ASCII = 97 Binary
= 1100001
S: ASCII
= 83 Binary
= 1010011
e: ASCII = 101 Binary
= 1100101
12. The hexadecimal number system uses 16 literals (0 – 9, A– F). Write down
its base value.
The base value in Hexadecimal system is: 16
13. Let X be a number system having B symbols only. Write down the base
value of this number system.
In a number system where XX has BB symbols, the base value of that number
system is B.
Example:
In the Decimal system (base-10), there are 10 symbols (0-9), so B=10
In the Binary system (base-2), there are 2 symbols (0 and 1), so B=2
In the Hexadecimal system (base-16), there are 16 symbols (0-9 and A-F),
so B=16.
14. Write the equivalent hexadecimal and binary values for each character of
the phrase given below. हम
सब एक.
Representation:
ह: Hex = 0939,
Binary = 0000100100111001
म: Hex = 092E,
Binary = 0000100100101110
स: Hex = 0938,
Binary = 0000100100111000
ब: Hex = 092C,
Binary = 0000100100101100
ए: Hex = 090F,
Binary = 0000100100001111
क: Hex = 0915,
Binary = 0000100100010101
15. What is the advantage of preparing a digital content in Indian language
using UNICODE font?
- Universal Compatibility: Ensures consistent
display across various devices and operating systems without needing
specific font installations.
- Multilingual Support: Allows seamless
integration of multiple Indian languages on a single platform.
- Consistent Representation: Maintains
uniformity in text appearance, reducing misinterpretation when sharing
content.
- Ease of Use: Simplifies typing and
displaying text without requiring special software or encoding schemes.
17. Encode the word 'COMPUTER' using ASCII and convert the encode value into Binary value.
|
Character
|
ASCII Value
|
Binary
|
|
C
|
67
|
1000011
|
|
O
|
79
|
1001111
|
|
M
|
77
|
1001101
|
|
P
|
80
|
1010000
|
|
U
|
85
|
1010101
|
|
T
|
84
|
1010100
|
|
E
|
69
|
1000101
|
|
R
|
82
|
1010010
|
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