Chapter 2 Encoding Scheme And Number System Class 11 NCERT Easy Solutions

In this article, I will provide Chapter 2 Encoding Scheme and Number System Class 11 NCERT Solutions. So let’s start1

Chapter 2 Encoding Scheme and Number System Class 11

Let’s start the solution of the encoding scheme and number system class 11 with basic questions.

Write base values of binary, octal and hexadecimal number system.
- Binary – 2
- Octal – 8
- Hexadecimal – 16
Give the full form of ASCII and ISCII.
- ASCII – Americal Standard Code for Information Interchange
- ISCII – Indian Script Code for Information Interchange
Try the following conversions:

Chapter 2 Encoding Schemes and Number System Q2 1

Chapter 2 Encoding Scheme and Number System Class 11 NCERT Easy solutions

(IV) (49D)₁₆=(?)₁₀

4	9	D
2	1	0
4 x 16²	9 x 16¹	13 x 16⁰
4 x 256	9 x 16	13 x 1
1024	144	13
		1181

(VI) (1010111)₂ = (?)₁₀

1	0	1	0	1	1	1
6	5	4	3	2	1	0
1 x 2⁶	0 x 2⁵	1 x 2⁴	0 x 2³	1 x 2²	1 x 2¹	1 x 2⁰
1 x 64	0 x 32	1 x 16	0 x 8	1 x 4	1 x 2	1 x 1
64	0	16	0	4	2	1
						87

Do the following conversions from decimal numbers to other number systems.

(ii)

encoding schmes and number system decimal to binary

(iv) (889)₁₀ = (?)₈

8	889	1
8	111	7
8	13	5
	1	1
Ans.:	889	1571

(vi) (108)₁₀=(?)₁₆

16	108	12-C
	6	6
Ans.:	108	6C

Watch this video for more understanding:

5. Express the following octal numbers into their equivalent decimal numbers.
(i) 145

Encoding Scheme and Number System Octal to decimal

(ii) 6760

6	7	6	0
3	2	1	0
6 x 8³	7 x 8²	6 x 8¹	0 x 8⁰
6 x 512	7 x 64	6 x 8	0 x 0
3072	448	48	0
			3568

(iii) 455

Watch this video for more understanding:

6. Express the following decimal numbers into hexadecimal numbers.
(i) 548

16	548	4
16	34	2
	2
Ans.:	548	224

(ii) 4052

16	4052	4
16	253	13-D
	15	15-F
Ans.:	548	FD4

(iii) 58

16	58	10-A
	3
Ans.:	58	3A

Watch this video for more understanding:

Express the following hexadecimal numbers into equivalent decimal numbers.

(II) 9E1A

9	E	1	A
3	2	1	0
9 x 16³	14 x 16²	1 x 16¹	10 X 16⁰
9 x 4096	14 x 256	1 X 16	10 X 1
36864	3584	16	10
		Ans.:	40474

(iii) 6DB

6	B	D
2	1	0
6 x 16²	11 x 16¹	13 x 16⁰
6 X 256	11 x 16	13 X 1
1536	176	13
		1725

Convert the following binary numbers into octal and hexadecimal numbers.
Whenever you are going to convert binary to hexadecimal follow the shortcut method.

(i) 1110001000

Octal Number

0	0	1	1	1	0	0	0	1	0	0	0
Z			Y			X			W
1			6			1			0

0	0	0	0	W
1	0	0	1	X & Z
2	0	1	0
3	0	1	1
4	1	0	0
5	1	0	1
6	1	1	0	Y
7	1	1	1

Hexadecimal Number

0	0	1	1	1	0	0	0	1	0	0	0
Z				Y				X

0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1	Z
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0	X & Y
9	1	0	0	1
10	1	0	1	0
11	1	0	1	1
12	1	1	0	0
13	1	1	0	1
14	1	1	1	0
15	1	1	1	1

(ii) 110110101

Octal Number

1	1	0	1	1	0	1	0	1
Z			Y			X

0	0	0	0
1	0	0	1
2	0	1	0
3	0	1	1
4	1	0	0
5	1	0	1	X
6	1	1	0	Y & Z
7	1	1	1

Ans. : (110110101)₂ = (665)₈

Hexadecimal Number

1	1	0	1	1	0	1	0	1
Z	Y				X

0	0	0	0	0
1	0	0	0	1	Z
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1	X
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0
9	1	0	0	1
10	1	0	1	0
11	1	0	1	1	Y
12	1	1	0	0
13	1	1	0	1
14	1	1	1	0
15	1	1	1	1

Ans. (110110101)₂=(1B5)₁₆

(iii) 1010100

Octal Number

1	0	1	0	1	0	0
Z	Y			X

0	0	0	0
1	0	0	1	Z
2	0	1	0	Y
3	0	1	1
4	1	0	0	X
5	1	0	1
6	1	1	0
7	1	1	1

Ans. : (1010100)₂=(124)₈

Hexadecimal Number

1	0	1	0	1	0	0
Y			X

0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0	X
5	0	1	0	1	Y
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0
9	1	0	0	1
10	1	0	1	0
11	1	0	1	1
12	1	1	0	0
13	1	1	0	1
14	1	1	1	0
15	1	1	1	1

Ans.: (1010100)₂=(54)₁₆

(iv) 1010.1001

Octal Number

Integer Part
1	0	1	0
Y	X
Fractional Part
1	0	0	1	0	0
X			Y

0	0	0	0	Integer	Fractional
1	0	0	1	Y
2	0	1	0	X
3	0	1	1
4	1	0	0		X & Y
5	1	0	1
6	1	1	0
7	1	1	1

(1010.1001)₂=(12.44)₈

Hexadecimal Number

1	0	1	0
X
Fractional Part
1	0	0	1
X

0	0	0	0	0	Integer	Fractional
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0
9	1	0	0	1		X
10	1	0	1	0	X
11	1	0	1	1
12	1	1	0	0
13	1	1	0	1
14	1	1	1	0
15	1	1	1	1

Ans.: (1010.1001)₂=(A.9)₁₆

Write the binary equivalent of the following octal numbers.

(ii) 5610

0	0	0	0	Z
1	0	0	1	Y
2	0	1	0
3	0	1	1
4	1	0	0
5	1	0	1	W
6	1	1	0	X
7	1	1	1

(5610)₈=(101 110 001 000)₂

(iii) 742

0	0	0	0
1	0	0	1
2	0	1	0	Z
3	0	1	1
4	1	0	0	Y
5	1	0	1
6	1	1	0
7	1	1	1	X

(742)₈=(111 100 010)₂

(iv) 65.203

0	0	0	0	Integer	Fractional
1	0	0	1
2	0	1	0		X
3	0	1	1		Z
4	1	0	0		Y
5	1	0	1	Y
6	1	1	0	X
7	1	1	1

(65.243)₈=(110 101. 010 100 011)₂

If you are looking for a calculator to check the conversion follow this link: Rapid tables

Write a binary representation of the following hexadecimal numbers: (i) 4026 (ii) BCA1 (iii) 98E (iv) 132.45 – Do yourself.
How does computer understand the following text? (hint: 7 bit ASCII code)

(i) HOTS

ASCII value of H is 72 and its equivalent 7-bit binary code = 1001000
ASCII value of O is 79 and its equivalent 7-bit binary code = 1001111
ASCII value of S is 83 and its equivalent 7-bit binary code = 1010011
ASCII value of T is 84 and its equivalent 7-bit binary code = 1010100

	H	O	S	T
ASCII Code	72	79	83	84
Binary Value	1001000	1001111	1010011	1010100

(ii) Main

ASCII value of M is 77 and its equivalent 7-bit binary code = 1001101
ASCII value of a is 97 and its equivalent 7-bit binary code = 1100001
ASCII value of i is 105 and its equivalent 7-bit binary code = 1101001
ASCII value of n is 110 and its equivalent 7-bit binary code = 1101110

	M	a	i	n
ASCII Code	77	97	105	110
Binary Value	1001101	1100001	1101001	1101110

(iii) CaSe

ASCII value of C is 67 and its equivalent 7-bit binary code = 1000011
ASCII value of a is 97 and its equivalent 7-bit binary code = 1100001
ASCII value of S is 83 and its equivalent 7-bit binary code = 1010011
ASCII value of e is 101 and its equivalent 7-bit binary code = 1100101

	C	a	S	e
ASCII Code	67	97	83	101
Binary Value	1000011	1100001	1010011	1100101

The hexadecimal number system uses 16 literals (0 – 9, A– F). Write down its base value.
- The base value of Binary number is 16.
Let X be a number system having B symbols only. Write down the base value of this number system.
- A base of the number system is the symbols or digits used in the number system. Hence the base of the X number system is B.
Write the equivalent hexadecimal and binary values for each character of the phrase given below. – ‘‘ हम सब एक”

ह – 0939 – 100100111001
म – 092E – 100100101110
स – 0938 – 100100111000
ब – 092C – 100100101100
ए – 090F – 100100001111
क – 0915 – 100100010101

What is the advantage of preparing a digital content in Indian language using UNICODE font?

It allows to incorporate all the characters of every written language.
It provides a unique number for every character
Every character represented thorugh unicode is compatible for various devices like mobile, tables, computer and os like Linux, Windows, Android etc.

Explore and list the steps required to type in an Indian language using UNICODE.

Step 1: Type the instruction in the Indian language
Step 2: Each character has its own hexadecimal code that the machine will read that code.
Step 3: The machine will then convert that UNICODE to binary code and do the task according to the instruction given

Encode the word ‘COMPUTER’ using ASCII and convert the encoded value into binary values.

Ans.:

C	67	1000011
O	79	1001111
M	77	1001101
P	80	1010000
U	85	1010101
T	84	1010100
E	69	1000101
R	82	1010010

Follow this link to read NCERT Solution for Chapter 1 Computer System.

Chapter The Computer System

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Computer Science Class 11

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Chapter 2 Encoding Scheme and Number System Class 11 NCERT Easy solutions