Encoding Scheme and Number System Notes – Class 11 CS (083) | NCERT Chapter-2
I am sure you have come here after completing Chapter 1: Computer System Organization. If not, I highly recommend studying that chapter first, as it provides the foundation for understanding the concepts covered here. You can find the link to those notes below.
Now, Encoding Scheme and Number System is the next part of Unit 1 – Computer System Organization in the CBSE Class 11 Computer Science (Code 083) curriculum. This chapter covers important topics such as different number systems, conversions between number systems, and various encoding schemes used in computers.
These Encoding Scheme and Number System Notes have been prepared strictly according to the latest CBSE syllabus for Class 11 Computer Science (083) and present every topic in a clear, pointwise, and well-organized sequence. This makes learning faster, easier, and more effective for both classroom study and exam preparation.
Chapter-1 Computer System Notes
Chapter-2 Encoding Scheme and Number System Notes
Number System
- A number system is a method used to represent numbers using a set of symbols, and each system has a base (radix) that defines the number of unique symbols it uses.
- It is a positional system where the value of each digit depends on its position in the number, and computers convert characters (like ASCII codes) into binary form for processing.
Decimal Number System
- The decimal number system is used in our day-to-day life and is also called the base-10 system because it uses 10 digits (0 to 9).
- In this system, each number has a symbol value (digit from 0 to 9) and a positional value based on powers of 10.
- The value of a decimal number is obtained by multiplying each digit with its positional weight and then adding all the results.
Binary Number System
- The binary number system is used in computers and is based on two digits, 0 and 1, hence it is also called the base-2 system.
- It represents the ON (1) and OFF (0) states of electronic circuits (transistors) in a computer.
- Any binary number can be converted into an equivalent decimal number for human understanding.
Octal Number System
- The octal number system is used to represent binary numbers in a compact form because binary numbers can become very large and difficult to handle.
- It is a base-8 system that uses digits from 0 to 7, and its positional value is based on powers of 8.
- Each octal digit can be represented using 3 binary digits (since 8 = 2³), making conversion between binary and octal easier.
Hexadecimal Number System
- The hexadecimal number system is used for compact representation of binary numbers and is a base-16 system.
- It uses 16 symbols: 0–9 and A–F (where A–F represent decimal values 10–15).
- Each hexadecimal digit is represented using 4 binary bits, since 4 bits can represent 16 values (2⁴ = 16).
- Examples of hexadecimal numbers include (23A.05)₁₆, (1C3)₁₆, and (619B.A)₁₆.
Conversion from Decimal to Other Number Systems
- Step 1: Divide the given number by the base of the target number system (2 for binary, 8 for octal, 16 for hexadecimal).
- Step 2: Write down the remainder.
- Step 3: Repeat the division using the quotient until it becomes 0, noting each remainder.
- Step 4: Write all remainders in reverse order (bottom to top) to get the final result.
Decimal to Binary Conversion
Decimal to Octal Conversion
Decimal to Hexadecimal Conversion
Conversion from Other Number Systems to Decimal Number System
- Step 1: Write the position number for each digit in the given number.
- Step 2: Find the positional value by raising the base (b = 2, 8, or 16) to the power of the position.
- Step 3: Multiply each digit by its positional value.
- Step 4: Add all the values to get the equivalent decimal number.
Binary Number to Decimal Number
Octal Number to Decimal Number
Hexadecimal Number to Decimal Number
Conversion from Binary Number to Octal
Octal Number to Binary Number
Binary Number to Hexadecimal Number
Hexadecimal Number to Binary Number
Conversion of a Number with Fractional Part
Decimal Number with Fractional Part to another Number System
Non-decimal Number with Fractional Part to Decimal Number System
Fractional Binary Number to Octal or Hexadecimal Number
Encoding Scheme
What is Encoding?
Encoding is the process of converting data into a coded format using a specific set of rules or codes so that a computer can store and understand it.
Each character, number, and symbol is assigned a unique code value. These code values are then converted into binary form for computer processing.
For example:
- A → 65
- B → 66
Standard Encoding Schemes
Standard encoding schemes are used to assign fixed unique codes to characters and symbols.
Some popular encoding schemes are:
- ASCII
- ISCII
- Unicode
These schemes help computers interpret text correctly across different systems and languages.
American Standard Code for Information Interchange (ASCII)
- ASCII stands for American Standard Code for Information Interchange and is one of the most commonly used encoding schemes.
- Initially, ASCII used 7 bits to represent characters. Therefore, the total number of characters that can be represented is: 27 = 128
- ASCII can encode 128 different characters, including letters, digits, and symbols. However, it can represent only the English character set.
ASCII code for some printable characters
| Character | Decimal Value | Character | Decimal Value | Character | Decimal Value |
| Space | 32 | @ | 64 | ` | 96 |
| ! | 33 | A | 65 | a | 97 |
| “ | 34 | B | 66 | b | 98 |
| # | 35 | C | 67 | c | 99 |
| $ | 36 | D | 68 | d | 100 |
| % | 37 | E | 69 | e | 101 |
| & | 38 | F | 70 | f | 102 |
| ‘ | 39 | G | 71 | g | 103 |
| ( | 40 | H | 72 | h | 104 |
| ) | 41 | I | 73 | i | 105 |
Example: Encode the word CODE and convert the encoded values into binary values which can be understood by a computer.
Each alphabet in the word CODE is replaced with its ASCII code value and corresponding 7-bit binary code.
| Character | ASCII Code | Binary Code |
| C | 67 | 1000011 |
| O | 79 | 1001111 |
| D | 68 | 1000100 |
| E | 69 | 1000101 |
Indian Script Code for Information Interchange (ISCII)
- ISCII stands for Indian Script Code for Information Interchange. It is an 8-bit encoding scheme used for Indian languages.
- Since ISCII uses 8 bits, the total number of characters it can represent is: 28 = 256
- ISCII retains all 128 ASCII codes and uses the remaining 128 codes for Indian language characters.
- The additional codes in the range 160–255 are used for representing Indian language “aksharas”.
UNICODE
- Unicode was developed to provide a common encoding standard for almost all languages of the world so that text can be correctly recognised and shared across different systems.
- UNICODE assigns a unique number to every character, irrespective of the device, operating system, or software application being used.
- Common Unicode encoding formats are UTF-8, UTF-16, and UTF-32.
Chapter-1 Computer System Notes
Chapter-2 Encoding Scheme and Number System Notes
