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:**

(IV) (49D)_{16}=(?)_{10}

4 | 9 | D |

2 | 1 | 0 |

4 x 16^{2} | 9 x 16^{1} | 13 x 16^{0} |

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 2^{6} | 0 x 2^{5} | 1 x 2^{4} | 0 x 2^{3} | 1 x 2^{2} | 1 x 2^{1} | 1 x 2^{0} |

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)

(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 |

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5. Express the following octal numbers into their equivalent decimal numbers.

(i) 145

(ii) 6760

6 | 7 | 6 | 0 |

3 | 2 | 1 | 0 |

6 x 8^{3} | 7 x 8^{2} | 6 x 8^{1} | 0 x 8^{0} |

6 x 512 | 7 x 64 | 6 x 8 | 0 x 0 |

3072 | 448 | 48 | 0 |

| | | 3568 |

(iii) 455

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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 |

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- Express the following hexadecimal numbers into equivalent decimal numbers.

(II) 9E1A

9 | E | 1 | A |

3 | 2 | 1 | 0 |

9 x 16^{3} | 14 x 16^{2} | 1 x 16^{1} | 10 X 16^{0} |

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 16^{2} | 11 x 16^{1} | 13 x 16^{0} |

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.

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