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Class 11 Computer Science Chapter 2

NCERT Solutions for Class 11 Computer Science Chapter 2: Encoding Schemes and Number System

Class

Subject

Book

Chapter

Session

Questions covered

XI

Computer Science

Computer Science (NCERT)

2 – Encoding Schemes and Number System

2026-27

17 of 17

Chapter at a glance

Idea

Key point

Encoding

Converting characters into a standard code (binary) the computer can store

ASCII

American Standard Code for Information Interchange; 7-bit, 128 characters (A = 65, a = 97)

ISCII

Indian Script Code for Information Interchange; 8-bit, Indian scripts

UNICODE

Universal code for characters of all languages (UTF-8, UTF-16, UTF-32)

Number systems

Binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16, 0–9, A–F)

To decimal

Multiply each digit by base^position and add (negative powers after the point)

From decimal

Integer part: repeated division by the base (remainders read bottom-up); fraction: repeated multiplication

Binary groups

3 bits = 1 octal digit; 4 bits = 1 hex digit

Exercise Questions

Q1

Write base values of binary, octal and hexadecimal number system.

Answer

Answer

The base (radix) is the number of distinct symbols used by the system.

Number system

Symbols

Base

Binary

0, 1

2

Octal

0–7

8

Hexadecimal

0–9, A–F

16

Binary: 2; Octal: 8; Hexadecimal: 16.

Q2

Give full form of ASCII and ISCII.

Answer

Answer

  • ASCII: American Standard Code for Information Interchange.
  • ISCII: Indian Script Code for Information Interchange.

ASCII = American Standard Code for Information Interchange; ISCII = Indian Script Code for Information Interchange.

Q3

Try the following conversions.
(i) (514)8 = (?)10 (ii) (220)8 = (?)2 (iii) (76F)16 = (?)10 (iv) (4D9)16 = (?)10 (v) (11001010)2 = (?)10 (vi) (1010111)2 = (?)10

Answer

Answer

Method: multiply each digit by the base raised to its position (rightmost position = 0) and add.

  1. 5 × 8² + 1 × 8¹ + 4 × 8⁰ = 320 + 8 + 4 = 332
  2. Replace each octal digit by its 3-bit binary: 2 → 010, 2 → 010, 0 → 000 ⇒ 010 010 000 = 10010000
  3. 7 × 16² + 6 × 16¹ + F(15) × 16⁰ = 1792 + 96 + 15 = 1903
  4. 4 × 16² + D(13) × 16 + 9 = 1024 + 208 + 9 = 1241
  5. 1×2⁷ + 1×2⁶ + 0 + 0 + 1×2³ + 0 + 1×2¹ + 0 = 128 + 64 + 8 + 2 = 202
  6. 1×2⁶ + 0 + 1×2⁴ + 0 + 1×2² + 1×2¹ + 1×2⁰ = 64 + 16 + 4 + 2 + 1 = 87
  1. 332 (ii) 10010000 (iii) 1903 (iv) 1241 (v) 202 (vi) 87
Q4

Do the following conversions from decimal number to other number systems.
(i) (54)10 = (?)2 (ii) (120)10 = (?)2 (iii) (76)10 = (?)8 (iv) (889)10 = (?)8 (v) (789)10 = (?)16 (vi) (108)10 = (?)16

Answer

Answer

Method: divide repeatedly by the new base; read the remainders from the last to the first.

  1. 54 ÷ 2: 27 r0, 13 r1, 6 r1, 3 r0, 1 r1, 0 r1 ⇒ 110110
  2. 120 ÷ 2: 60 r0, 30 r0, 15 r0, 7 r1, 3 r1, 1 r1, 0 r1 ⇒ 1111000
  3. 76 ÷ 8: 9 r4, 1 r1, 0 r1 ⇒ 114
  4. 889 ÷ 8: 111 r1, 13 r7, 1 r5, 0 r1 ⇒ 1571
  5. 789 ÷ 16: 49 r5, 3 r1, 0 r3 ⇒ 315
  6. 108 ÷ 16: 6 r12 (C), 0 r6 ⇒ 6C
  1. 110110 (ii) 1111000 (iii) 114 (iv) 1571 (v) 315 (vi) 6C
Q5

Express the following octal numbers into their equivalent decimal numbers.
(i) 145 (ii) 6760 (iii) 455 (iv) 10.75

Answer

Answer

  1. 1×64 + 4×8 + 5 = 64 + 32 + 5 = 101
  2. 6×512 + 7×64 + 6×8 + 0 = 3072 + 448 + 48 = 3568
  3. 4×64 + 5×8 + 5 = 256 + 40 + 5 = 301
  4. 1×8 + 0 + 7×8⁻¹ + 5×8⁻² = 8 + 0.875 + 0.078125 = 8.953125
  1. 101 (ii) 3568 (iii) 301 (iv) 8.953125
Q6

Express the following decimal numbers into hexadecimal numbers.
(i) 548 (ii) 4052 (iii) 58 (iv) 100.25

Answer

Answer

  1. 548 ÷ 16: 34 r4, 2 r2, 0 r2 ⇒ 224
  2. 4052 ÷ 16: 253 r4, 15 r13 (D), 0 r15 (F) ⇒ FD4
  3. 58 ÷ 16: 3 r10 (A), 0 r3 ⇒ 3A
  4. Integer part 100 ÷ 16: 6 r4, 0 r6 ⇒ 64. Fraction 0.25 × 16 = 4.00 ⇒ digit 4. So 64.4
  1. 224 (ii) FD4 (iii) 3A (iv) 64.4
Q7

Express the following hexadecimal numbers into equivalent decimal numbers.
(i) 4A2 (ii) 9E1A (iii) 6BD (iv) 6C.34

Answer

Answer

  1. 4×256 + 10×16 + 2 = 1024 + 160 + 2 = 1186
  2. 9×4096 + 14×256 + 1×16 + 10 = 36864 + 3584 + 16 + 10 = 40474
  3. 6×256 + 11×16 + 13 = 1536 + 176 + 13 = 1725
  4. 6×16 + 12 + 3×16⁻¹ + 4×16⁻² = 108 + 0.1875 + 0.015625 = 108.203125
  1. 1186 (ii) 40474 (iii) 1725 (iv) 108.203125
Q8

Convert the following binary numbers into octal and hexadecimal numbers.
(i) 1110001000 (ii) 110110101 (iii) 1010100 (iv) 1010.1001

Answer

Answer

Method: for octal, group 3 bits; for hexadecimal, group 4 bits — from the point outwards (left for the integer part, right for the fraction), padding with zeros.

  1. Octal: 001 110 001 000 = 1610; Hex: 0011 1000 1000 = 388
  2. Octal: 110 110 101 = 665; Hex: 0001 1011 0101 = 1B5
  3. Octal: 001 010 100 = 124; Hex: 0101 0100 = 54
  4. Octal: 001 010 . 100 100 = 12.44; Hex: 1010 . 1001 = A.9
  1. (1610)8, (388)16 (ii) (665)8, (1B5)16 (iii) (124)8, (54)16 (iv) (12.44)8, (A.9)16
Q9

Write binary equivalent of the following octal numbers.
(i) 2306 (ii) 5610 (iii) 742 (iv) 65.203

Answer

Answer

Replace each octal digit by its 3-bit binary equivalent.

  1. 2 3 0 6 → 010 011 000 110 = 10011000110
  2. 5 6 1 0 → 101 110 001 000 = 101110001000
  3. 7 4 2 → 111 100 010 = 111100010
  4. 6 5 . 2 0 3 → 110 101 . 010 000 011 = 110101.010000011
  1. 10011000110 (ii) 101110001000 (iii) 111100010 (iv) 110101.010000011
Q10

Write binary representation of the following hexadecimal numbers.
(i) 4026 (ii) BCA1 (iii) 98E (iv) 132.45

Answer

Answer

Replace each hex digit by its 4-bit binary equivalent.

  1. 4 0 2 6 → 0100 0000 0010 0110 = 100000000100110
  2. B C A 1 → 1011 1100 1010 0001 = 1011110010100001
  3. 9 8 E → 1001 1000 1110 = 100110001110
  4. 1 3 2 . 4 5 → 0001 0011 0010 . 0100 0101 = 100110010.01000101
  1. 100000000100110 (ii) 1011110010100001 (iii) 100110001110 (iv) 100110010.01000101
Q11

How does computer understand the following text? (hint: 7 bit ASCII code).
(i) HOTS (ii) Main (iii) CaSe

Answer

Answer

Each character is stored as its ASCII code in binary.

Text

Character → ASCII (decimal) → 7-bit binary

HOTS

H 72 1001000, O 79 1001111, T 84 1010100, S 83 1010011

Main

M 77 1001101, a 97 1100001, i 105 1101001, n 110 1101110

CaSe

C 67 1000011, a 97 1100001, S 83 1010011, e 101 1100101

HOTS = 1001000 1001111 1010100 1010011; Main = 1001101 1100001 1101001 1101110; CaSe = 1000011 1100001 1010011 1100101

Q12

The hexadecimal number system uses 16 literals (0 – 9, A– F). Write down its base value.

Answer

Answer

The base of a number system equals the number of distinct symbols it uses. Hexadecimal uses 16 symbols.

Base value = 16

Q13

Let X be a number system having B symbols only. Write down the base value of this number system.

Answer

Answer

The base (radix) of a number system is the number of unique symbols it has. X has B symbols, so its base is B (digits run from 0 to B − 1).

Base value = B

Q14

Write the equivalent hexadecimal and binary values for each character of the phrase given below.
“हम सब एक”

Answer

Answer

Using UNICODE (Devanagari block U+0900–U+097F); the space is U+0020.

Character

Hexadecimal (Unicode)

Binary (16-bit)

ह

0939

0000 1001 0011 1001

म

092E

0000 1001 0010 1110

space

0020

0000 0000 0010 0000

स

0938

0000 1001 0011 1000

ब

092C

0000 1001 0010 1100

space

0020

0000 0000 0010 0000

ए

090F

0000 1001 0000 1111

क

0915

0000 1001 0001 0101

ह 0939, म 092E, स 0938, ब 092C, ए 090F, क 0915 (space 0020), with binary values as in the table.

Q15

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

Answer

Answer

  1. Universal: Unicode gives a unique code to every character of every script, so the content displays correctly on any computer, phone, OS or browser without installing special fonts.
  2. Portability and sharing: files can be exchanged and emailed without the text turning into junk characters.
  3. Searchable: text can be searched, sorted and indexed by search engines.
  4. Multilingual: several languages (Hindi, Tamil, English, etc.) can be used in the same document.
  5. Standard input: it works with standard keyboards, transliteration tools and software.

Unicode content is platform-independent, displays correctly everywhere, can be shared, searched and mixed with other languages without special fonts.

Q16

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

Answer

Answer

(For Windows; similar options exist on Linux, macOS, Android.)

  1. Open Settings → Time & Language → Language & region.
  2. Click Add a language and choose the Indian language (e.g. Hindi).
  3. Select a keyboard layout — e.g. Hindi Traditional / INSCRIPT or Hindi Phonetic.
  4. Use Windows + Space (or the language icon on the taskbar) to switch the input language.
  5. Open any application (Word, Notepad, browser) and type; the text is entered in a Unicode font such as Mangal or Nirmala UI.
  6. Alternatively, use transliteration tools such as Google Input Tools, which convert typed English phonetics into the Indian script.

Add the Indian language and a keyboard (INSCRIPT/phonetic) in language settings, switch input with Windows + Space, and type in any app using a Unicode font like Mangal or Nirmala UI (or use a transliteration tool).

Q17

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

Answer

Answer

Character

C

O

M

P

U

T

E

R

ASCII

67

79

77

80

85

84

69

82

Binary

1000011

1001111

1001101

1010000

1010101

1010100

1000101

1010010

COMPUTER = 67 79 77 80 85 84 69 82 = 1000011 1001111 1001101 1010000 1010101 1010100 1000101 1010010

Topic checklist

  • ☒ Base values (Q1, 12, 13)
  • ☒ ASCII, ISCII, UNICODE (Q2, 11, 14–17)
  • ☒ Conversions between number systems (Q3–10)

Total questions answered: 17 of 17

Frequently Asked Questions

What do these NCERT solutions for Class 11 Computer Science Chapter 2 (Encoding Schemes and Number System) cover?

All 17 questions from the latest NCERT textbook for this chapter are answered step by step, organised as Exercise Questions.

Are these solutions based on the new NCERT syllabus?

Yes. The answers follow the current NCERT textbook for Class 11 Computer Science and the latest CBSE syllabus, so the question numbers and wording match the book you use in class.

How should I use these solutions to prepare for exams?

Attempt each question on your own first, then compare your working with the answer here. Note the steps or keywords you missed, and revise the chapter notes before taking a chapter-wise MCQ test to check your understanding.

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