Encoding Schemes and Number System โ€“ Chapter 2 Notes |1ST PU
1st pu notes

Encoding Schemes and Number System โ€“ Chapter 2 Notes |1ST PU

Venkatesh A August 12, 2026 13 min read
1st PUC / Class 11 Computer Science

Complete Short Notes & Exam Preparation Guide

1st PUC Computer Science Notes | Class 11 Computer Science Notes | Encoding Schemes and Number System

Based on the 1ST PU NCERT textbook

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๐Ÿ“˜ Chapter Overview

This chapter explains how text entered through a computer keyboard is encoded, how computers represent numbers, and how numbers can be converted between different number systems.

The chapter mainly covers:

  • Introduction to Encoding
  • ASCII
  • ISCII
  • UNICODE
  • Number System
  • Decimal Number System
  • Binary Number System
  • Octal Number System
  • Hexadecimal Number System
  • Applications of Hexadecimal Number System
  • Conversion Between Number Systems
  • Conversions involving fractional numbers

๐Ÿ“‘ Table of Contents

  1. Introduction to Encoding
  2. ASCII
  3. ISCII
  4. UNICODE
  5. Number System
  6. Decimal Number System
  7. Binary Number System
  8. Octal Number System
  9. Hexadecimal Number System
  10. Applications of Hexadecimal Number System
  11. Conversion Between Number Systems
  12. Decimal to Other Number Systems
  13. Other Number Systems to Decimal
  14. Binary, Octal and Hexadecimal Conversions
  15. Fractional Number Conversions
  16. Quick Revision
  17. Important Questions

2.1 Introduction to Encoding

Encoding: Encoding is the mechanism of converting data into an equivalent coded form using a specific code.

A computer understands binary language consisting of 0 and 1. Therefore, when a key on the keyboard is pressed, it is internally mapped to a unique code and then converted into binary.

๐Ÿ–ฅ๏ธ Encoding of Data Entered Using Keyboard

Q
W
A
S
D
Keyboard Key
A
โ†’
Decimal Code
65
โ†’
Binary Code
1000001

Figure: Encoding of data entered using keyboard

When the key A is pressed, it is internally mapped to decimal value 65, which is then converted into its equivalent binary value.

Example: The alphabet เค… on a Hindi keyboard is internally mapped to hexadecimal value 0905, whose binary equivalent is 0000100100000101.

Why are Standard Encoding Schemes Required?

  • Each letter, numeral and symbol can be assigned a unique code.
  • The same standard can be used on different keyboards.
  • Encoded information can be converted into binary for computer processing.

2.1.1 American Standard Code for Information Interchange (ASCII)

ASCII: American Standard Code for Information Interchange.

ASCII was developed to standardise character representation. It is one of the commonly used coding schemes.

  • Initially ASCII used 7 bits.
  • There are two binary digits: 0 and 1.
  • 7-bit ASCII can represent 27 = 128 different characters.
  • ASCII represents the character set of the English language.

ASCII Code for Some Printable Characters

Character Decimal Value Character Decimal Value Character Decimal Value
Space32@64`96
!33A65a97
“34B66b98
#35C67c99
$36D68d100
%37E69e101
&38F70f102
‘39G71g103
(40H72h104
)41I73i105

Example 2.2 โ€“ Encoding the Word DATA

ASCII values and their equivalent 7-bit binary codes are:

Character ASCII Code Binary Code
D681000100
A651000001
T841010100
A651000001
Exam Point: Remember that 7-bit ASCII can encode 128 different characters.

2.1.2 Indian Script Code for Information Interchange (ISCII)

ISCII: Indian Script Code for Information Interchange.

ISCII was developed in India during the mid-1980s to facilitate the use of Indian languages on computers.

  • ISCII uses 8-bit code representation.
  • 8 bits can represent 28 = 256 characters.
  • It retains all 128 ASCII codes.
  • The remaining codes are used for additional Indian language character sets.
  • Additional codes are assigned in the upper region 160โ€“255 for the aksharas of the language.

2.1.3 UNICODE

UNICODE: A standard developed to incorporate characters of written languages of the world and provide a unique number for every character.

Different encoding schemes for different languages could not always communicate with each other. Therefore, UNICODE was developed as a common standard.

  • UNICODE provides a unique number for every character.
  • It is independent of device, operating system and software application.
  • Commonly used UNICODE encodings are UTF-8, UTF-16 and UTF-32.
  • UNICODE is a superset of ASCII.
  • Values 0โ€“128 have the same character as ASCII.

Unicode โ€“ Devanagari Examples

Character Hexadecimal Value Character Hexadecimal Value
เค…0905เค†0906
เค‡0907เคˆ0908
เค‰0909เคŠ090A
เค•0915เค–0916
เค—0917เค˜0918
เคš091Aเคœ091C
เคค0924เคฆ0926
เคจ0928เคฎ092E
เคฐ0930เคฒ0932
เคต0935เคธ0938
เคน0939เฅ0950
เฅฆ0966เฅง0967
Exam Point: UNICODE makes it possible to represent characters of almost all languages of the world using a common encoding standard.

2.2 Number System

Number System: A number system is a method to represent or write numbers.

Every number system has a set of unique characters or literals. The count of these literals is called the radix or base of the number system.

Positional Number System

Number systems are also called positional number systems because the value of each symbol depends upon its position within the number.

  • The rightmost position in the integer part has position 0.
  • Position values increase from right to left.
  • The first symbol in the fractional part has position โˆ’1.
  • Fractional position values decrease from left to right.
  • Positional value is calculated using the position and base.

2.2.1 Decimal Number System

Decimal number system is used in our day-to-day life. It is called the base-10 system because it uses ten digits from 0 to 9.

Digit 1 2 3 . 4 5
Position Number 2 1 0 -1 -2
Positional Value 10ยฒ 10ยน 10โฐ 10โปยน 10โปยฒ
1 ร— 10ยฒ + 2 ร— 10ยน + 3 ร— 10โฐ + 4 ร— 10โปยน + 5 ร— 10โปยฒ = 100 + 20 + 3 + 0.4 + 0.05 = 123.45
The base value is written as a subscript to distinguish one number system from another. For example, (70)8 represents octal 70 and (70)10 represents decimal 70.

2.2.2 Binary Number System

The binary number system uses only two digits: 0 and 1.

It is called the base-2 system. The ON/high and OFF/low states of transistors are represented using 1 and 0 respectively.

Examples of Binary Numbers

  • 1001011
  • 1011.101
  • 111111.01

Binary Values for Decimal Digits

Decimal Binary Decimal Binary
005101
116110
2107111
31181000
410091001

2.2.3 Octal Number System

With an increase in decimal value, the number of bits in binary representation also increases. Octal number system provides a compact representation of binary numbers.

  • Octal is a base-8 system.
  • It uses digits 0 to 7.
  • Positional values are expressed in powers of 8.
  • Three binary digits are sufficient to represent any octal digit because 8 = 2ยณ.
Octal Digit Decimal Value 3-bit Binary
00000
11001
22010
33011
44100
55101
66110
77111

2.2.4 Hexadecimal Number System

Hexadecimal numbers are also used for compact representation of binary numbers.

  • Hexadecimal is a base-16 system.
  • It uses 16 symbols: 0โ€“9 and Aโ€“F.
  • A represents decimal 10.
  • B represents decimal 11.
  • C represents decimal 12.
  • D represents decimal 13.
  • E represents decimal 14.
  • F represents decimal 15.
  • Four binary bits represent one hexadecimal symbol because 16 = 2โด.
Hex Symbol Decimal 4-bit Binary
000000
110001
220010
330011
440100
550101
660110
770111
881000
991001
A101010
B111011
C121100
D131101
E141110
F151111

2.2.5 Applications of Hexadecimal Number System

1. Memory Address Representation

Main memory contains memory locations, and every location has a unique address. A 16-bit memory address can be difficult to handle in binary form, so hexadecimal notation provides a compact representation.

Example from the chapter
16-bit binary address: 1100000011110001 Hexadecimal: C0F1 Octal: 140361

2. Webpage Colour Representation

Colours are made from three primary components: Red, Green and Blue (RGB).

Each component uses 8 bits, making 24 bits for a colour. Hexadecimal notation is used as a compact representation.

Colour Decimal Binary Hexadecimal
Black (0,0,0) (00000000,00000000,00000000) (00,00,00)
White (255,255,255) (11111111,11111111,11111111) (FF,FF,FF)
Yellow (255,255,0) (11111111,11111111,00000000) (FF,FF,00)
Grey (128,128,128) (10000000,10000000,10000000) (80,80,80)

2.3 Conversion Between Number Systems

Decimal numbers are commonly used by humans, while digital systems understand binary numbers. Octal and hexadecimal systems help to simplify binary representation.

Important: Learn the base values first: Binary = 2, Octal = 8, Decimal = 10, Hexadecimal = 16.

2.3.1 Conversion from Decimal to Other Number Systems

General Steps

  1. Divide the given number by the base value of the required number system.
  2. Note the remainder.
  3. Continue dividing the quotient by the base until the quotient becomes zero.
  4. Write the remainders in reverse order, from bottom to top.
A. Decimal to Binary Conversion

Since the binary system has base 2, repeatedly divide the decimal number by 2.

65 รท 2 = 32 remainder 1 32 รท 2 = 16 remainder 0 16 รท 2 = 8 remainder 0 8 รท 2 = 4 remainder 0 4 รท 2 = 2 remainder 0 2 รท 2 = 1 remainder 0 1 รท 2 = 0 remainder 1 Read remainders from bottom to top: 1000001
Therefore, (65)10 = (1000001)2
Example 2.3 โ€“ Convert (122)10 to Binary
122 รท 2 = 61 remainder 0 61 รท 2 = 30 remainder 1 30 รท 2 = 15 remainder 0 15 รท 2 = 7 remainder 1 7 รท 2 = 3 remainder 1 3 รท 2 = 1 remainder 1 1 รท 2 = 0 remainder 1 Read bottom to top: 1111010
Therefore, (122)10 = (1111010)2
B. Decimal to Octal Conversion

Since the base value of octal is 8, repeatedly divide by 8.

65 รท 8 = 8 remainder 1 8 รท 8 = 1 remainder 0 1 รท 8 = 0 remainder 1 Read bottom to top: 101
Therefore, (65)10 = (101)8
Example 2.4 โ€“ Convert (122)10 to Octal
122 รท 8 = 15 remainder 2 15 รท 8 = 1 remainder 7 1 รท 8 = 0 remainder 1 Read bottom to top: 172
Therefore, (122)10 = (172)8
C. Decimal to Hexadecimal Conversion

Since hexadecimal has base 16, repeatedly divide the decimal number by 16.

65 รท 16 = 4 remainder 1 4 รท 16 = 0 remainder 4 Read bottom to top: 41
Therefore, (65)10 = (41)16
Example 2.5 โ€“ Convert (122)10 to Hexadecimal
122 รท 16 = 7 remainder 10 10 is represented by A. 7 รท 16 = 0 remainder 7 Read bottom to top: 7A
Therefore, (122)10 = (7A)16

2.3.2 Conversion from Other Number Systems to Decimal

General Steps

  1. Write the position number for each symbol.
  2. Calculate the positional value using the base.
  3. Multiply each digit by its positional value.
  4. Add all the values to obtain the decimal equivalent.
A. Binary to Decimal โ€“ Example 2.6
Digit 1 1 0 1
Position Number 3 2 1 0
Positional Value 2ยณ 2ยฒ 2ยน 2โฐ
1 ร— 2ยณ + 1 ร— 2ยฒ + 0 ร— 2ยน + 1 ร— 2โฐ = 8 + 4 + 0 + 1 = 13
Therefore, (1101)2 = (13)10
B. Octal to Decimal โ€“ Example 2.7
Digit 2 5 7
Position Number 2 1 0
Positional Value 8ยฒ 8ยน 8โฐ
2 ร— 8ยฒ + 5 ร— 8ยน + 7 ร— 8โฐ = 128 + 40 + 7 = 175
Therefore, (257)8 = (175)10
C. Hexadecimal to Decimal โ€“ Example 2.8
Hexadecimal digit A = decimal 10 3 ร— 16ยฒ + 10 ร— 16ยน + 5 ร— 16โฐ = 768 + 160 + 5 = 933
Therefore, (3A5)16 = (933)10

2.3.3 Conversion from Binary to Octal/Hexadecimal and Vice-Versa

A binary number is converted to octal or hexadecimal by grouping 3 or 4 bits respectively and replacing each group by its equivalent octal or hexadecimal digit.
A. Binary Number to Octal Number โ€“ Example 2.9
Given: 10101100 Group 3 bits from right to left: 010 | 101 | 100 Replace each group: 2 | 5 | 4
Therefore, (10101100)2 = (254)8

If the number of bits is not a multiple of 3, required zeroes are added at the most significant position.

B. Octal Number to Binary Number โ€“ Example 2.10
Octal digits: 7 0 5 3-bit binary: 111 000 101
Therefore, (705)8 = (111000101)2
C. Binary Number to Hexadecimal Number โ€“ Example 2.11
Given: 0110101100 Make groups of 4 bits from right to left: 0001 | 1010 | 1100 Hexadecimal symbols: 1 | A | C
Therefore, (0110101100)2 = (1AC)16
D. Hexadecimal Number to Binary Number โ€“ Example 2.12
Hexadecimal digits: 2 3 D 4-bit binary: 0010 0011 1101
Therefore, (23D)16 = (001000111101)2
Why 4 bits are grouped for hexadecimal?
Hexadecimal base is 16 and 16 = 2โด. Therefore four binary digits are sufficient to represent all 16 hexadecimal symbols.
Why 3 bits are grouped for octal?
Octal base is 8 and 8 = 2ยณ. Therefore three binary digits are sufficient to represent all 8 octal digits.

2.3.4 Conversion of a Number with Fractional Part

A. Decimal Number with Fractional Part to Another Number System

To convert the fractional part of a decimal number to another number system with base b, repeatedly multiply the fractional part by the base value.

  • Continue until the fractional part becomes 0.
  • Use the integer part obtained in each multiplication.
  • Write the integer parts from top to bottom.
  • If the fractional part does not become 0, calculation may be stopped after a suitable number of steps.
  • If a fractional part starts repeating, stop further calculation.
Example 2.13 โ€“ Convert (0.25)10 to Binary
0.25 ร— 2 = 0.50 โ†’ 0 0.50 ร— 2 = 1.00 โ†’ 1 Fractional part becomes 0. Read integer parts from top to bottom: 01
Therefore, (0.25)10 = (0.01)2
Example 2.14 โ€“ Convert (0.675)10 to Binary
0.675 ร— 2 = 1.350 โ†’ 1 0.350 ร— 2 = 0.700 โ†’ 0 0.700 ร— 2 = 1.400 โ†’ 1 0.400 ร— 2 = 0.800 โ†’ 0 0.800 ร— 2 = 1.600 โ†’ 1 0.600 ร— 2 = 1.200 โ†’ 1 0.200 ร— 2 = 0.400 โ†’ 0 The fractional part .400 repeats. Read integer parts from top to bottom: 1010110
Therefore, (0.675)10 = (0.1010110)2
Example 2.15 โ€“ Convert (0.675)10 to Octal
0.675 ร— 8 = 5.400 โ†’ 5 0.400 ร— 8 = 3.200 โ†’ 3 0.200 ร— 8 = 1.600 โ†’ 1 0.600 ร— 8 = 4.800 โ†’ 4 0.800 ร— 8 = 6.400 โ†’ 6 The fractional part .400 repeats. Read integer parts from top to bottom: 53146
Therefore, (0.675)10 = (0.53146)8
Example 2.16 โ€“ Convert (0.675)10 to Hexadecimal
0.675 ร— 16 = 10.800 โ†’ A 0.800 ร— 16 = 12.800 โ†’ C A represents decimal 10. C represents decimal 12. The fractional part .800 repeats.
Therefore, (0.675)10 = (0.AC)16

B. Non-decimal Number with Fractional Part to Decimal

Compute the positional value of every digit using its base. Multiply each digit by its positional value and add the values.

Example 2.17 โ€“ Convert (100101.101)2 to Decimal
Digit 1 0 0 1 0 1 . 1 0 1
Positional Value 2โต 2โด 2ยณ 2ยฒ 2ยน 2โฐ 2โปยน 2โปยฒ 2โปยณ
1ร—2โต + 0ร—2โด + 0ร—2ยณ + 1ร—2ยฒ + 0ร—2ยน + 1ร—2โฐ + 1ร—2โปยน + 0ร—2โปยฒ + 1ร—2โปยณ = 32 + 0 + 0 + 4 + 0 + 1 + 0.5 + 0 + 0.125 = 37.625
Therefore, (100101.101)2 = (37.625)10
Example 2.18 โ€“ Convert (605.12)8 to Decimal
6ร—8ยฒ + 0ร—8ยน + 5ร—8โฐ + 1ร—8โปยน + 2ร—8โปยฒ = 384 + 0 + 5 + 0.125 + 0.03125 = 389.15625
Therefore, (605.12)8 = (389.15625)10

C. Fractional Binary Number to Octal or Hexadecimal

For the integer part, make groups from right to left. For the fractional part, make groups from left to right. Add zeroes at the end of the fractional part to make complete groups of 3 or 4 bits.

Example 2.19 โ€“ Convert (10101100.01011)2 to Octal
Integer part: 10101100 โ†“ 010 | 101 | 100 2 | 5 | 4 Fractional part: 01011 โ†“ 010 | 110 2 | 6 Therefore: 254.26
Therefore, (10101100.01011)2 = (254.26)8
Note: Make 3-bit groups from right to left for the integer part and left to right for the fractional part.
Example 2.20 โ€“ Convert (10101100.010111)2 to Hexadecimal
Make groups of 4 bits: 1010 | 1100 . 0101 | 1100 Hexadecimal symbols: A | C . 5 | C Therefore: AC.5C
Therefore, (10101100.010111)2 = (AC.5C)16

โšก Quick Revision

Encoding: Converting data into an equivalent coded form using a specific code.
Topic Important Point
ASCII Initially 7-bit; 2โท = 128 characters
ISCII 8-bit code representation for Indian languages
UNICODE Common character encoding standard for written languages
Decimal Base 10; digits 0โ€“9
Binary Base 2; digits 0 and 1
Octal Base 8; digits 0โ€“7
Hexadecimal Base 16; digits 0โ€“9 and Aโ€“F
Binary โ†’ Octal Group 3 bits
Binary โ†’ Hexadecimal Group 4 bits
Decimal โ†’ Other Repeated division and read remainders bottom to top
Other โ†’ Decimal Use positional values and add the products
Fractional Decimal โ†’ Other Repeated multiplication by the required base

Important Base Values

Number System Base Symbols
Binary 2 0, 1
Octal 8 0โ€“7
Decimal 10 0โ€“9
Hexadecimal 16 0โ€“9, Aโ€“F

Important Conversion Rules

  • Decimal โ†’ Binary: divide repeatedly by 2.
  • Decimal โ†’ Octal: divide repeatedly by 8.
  • Decimal โ†’ Hexadecimal: divide repeatedly by 16.
  • Binary โ†’ Octal: group 3 bits.
  • Octal โ†’ Binary: replace each octal digit by 3-bit binary.
  • Binary โ†’ Hexadecimal: group 4 bits.
  • Hexadecimal โ†’ Binary: replace each hexadecimal symbol by 4-bit binary.
  • For fractional decimal conversion, multiply the fractional part by the base.
  • For fractional binary to octal/hexadecimal, group the integer part from right to left and fractional part from left to right.

๐Ÿ“ Important Questions & Answers

1. What is encoding?

Encoding is the mechanism of converting data into an equivalent coded form using a specific code.

2. Why is encoding required in computers?

It provides a standard way to represent characters using unique codes which can be converted into binary for computer processing.

3. What is ASCII?

ASCII stands for American Standard Code for Information Interchange.

4. How many characters can 7-bit ASCII represent?

2โท = 128 characters.

5. What is ISCII?

ISCII stands for Indian Script Code for Information Interchange.

6. How many characters can 8-bit ISCII represent?

2โธ = 256 characters.

7. What is UNICODE?

UNICODE is a character encoding standard that provides a unique number for characters of written languages.

8. Name three commonly used UNICODE encodings.

UTF-8, UTF-16 and UTF-32.

9. What is a number system?

A number system is a method to represent or write numbers.

10. What is radix or base?

The count of unique characters or literals in a number system is called its radix or base.

11. What is the base of binary number system?

2.

12. What is the base of octal number system?

8.

13. What is the base of decimal number system?

10.

14. What is the base of hexadecimal number system?

16.

15. Why are three binary bits grouped to obtain an octal number?

Because 8 = 2ยณ, so three binary bits are sufficient to represent all eight octal digits.

16. Why are four binary bits grouped to obtain a hexadecimal number?

Because 16 = 2โด, so four binary bits are sufficient to represent all sixteen hexadecimal symbols.

17. Convert (65)10 to binary.

(65)10 = (1000001)2

18. Convert (122)10 to octal.

(122)10 = (172)8

19. Convert (122)10 to hexadecimal.

(122)10 = (7A)16

20. Convert (1101)2 to decimal.

(1101)2 = (13)10

21. Convert (257)8 to decimal.

(257)8 = (175)10

22. Convert (3A5)16 to decimal.

(3A5)16 = (933)10

23. Convert (10101100)2 to octal.

(10101100)2 = (254)8

24. Convert (705)8 to binary.

(705)8 = (111000101)2

25. Convert (0110101100)2 to hexadecimal.

(0110101100)2 = (1AC)16

26. Convert (23D)16 to binary.

(23D)16 = (001000111101)2

27. Convert (0.25)10 to binary.

(0.25)10 = (0.01)2

28. What are the applications of hexadecimal numbers?

Hexadecimal numbers are used for compact representation of memory addresses and webpage colour codes.

๐Ÿ“ Important Conversion Practice Questions

  1. (514)8 = (?)10
  2. (220)8 = (?)2
  3. (76F)16 = (?)10
  4. (4D9)16 = (?)10
  5. (11001010)2 = (?)10
  6. (1010111)2 = (?)10
  7. (54)10 = (?)2
  8. (120)10 = (?)2
  9. (76)10 = (?)8
  10. (889)10 = (?)8
  11. (789)10 = (?)16
  12. (108)10 = (?)16
  13. Convert 145, 6760, 455 and 10.75 from octal to decimal.
  14. Convert 548, 4052, 58 and 100.25 from decimal to hexadecimal.
  15. Convert 4A2, 9E1A, 6BD and 6C.34 from hexadecimal to decimal.
  16. Convert 1110001000, 110110101, 1010100 and 1010.1001 into octal and hexadecimal.
  17. Write binary equivalents of 2306, 5610, 742 and 65.203.
  18. Write binary representations of 4026, BCA1, 98E and 132.45.
  19. How does a computer understand HOTS, Main and CaSe using 7-bit ASCII?
  20. Write the base value of a hexadecimal number system.
  21. Write the base value of a number system having B symbols.
  22. Write equivalent hexadecimal and binary values for the phrase โ€œเคนเคฎ เคธเคฌ เคเค•โ€.
  23. What is the advantage of preparing digital content in Indian language using UNICODE?
  24. Write the steps required to type in an Indian language using UNICODE.
  25. Encode the word COMPUTER using ASCII and convert the encoded values into binary.

๐ŸŽฏ Final Exam Revision

Must Remember:

  • ASCII โ†’ 7 bits โ†’ 128 characters.
  • ISCII โ†’ 8 bits โ†’ 256 characters.
  • UNICODE โ†’ common character encoding standard.
  • Binary โ†’ Base 2 โ†’ 0,1.
  • Octal โ†’ Base 8 โ†’ 0โ€“7.
  • Decimal โ†’ Base 10 โ†’ 0โ€“9.
  • Hexadecimal โ†’ Base 16 โ†’ 0โ€“9,Aโ€“F.
  • Binary โ†” Octal โ†’ 3-bit groups.
  • Binary โ†” Hexadecimal โ†’ 4-bit groups.
  • Decimal to another system โ†’ repeated division.
  • Fractional decimal to another system โ†’ repeated multiplication.
  • Other system to decimal โ†’ positional values and addition.

๐Ÿ“š Conclusion

Chapter 2 explains how computers represent text and numbers. Encoding schemes such as ASCII, ISCII and UNICODE provide methods for representing characters. Number systems such as binary, octal, decimal and hexadecimal are used to represent numbers, while conversion techniques help move between these systems.

For examination preparation, special attention should be given to encoding, ASCII, ISCII, UNICODE, base values, positional values and all number-system conversion methods.

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1st PUC / Class 11 Computer Science โ€“ Encoding Schemes and Number System
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