Home › Free notes › Class 11 Computer Science › Encoding Schemes and Number System

Encoding Schemes and Number System – Class 11 Computer Science notes, important questions and MCQs

NCERT Class 11 Computer Science, chapter 2. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Computers store all data as binary digits (0 and 1), so characters and numbers must be encoded. Encoding schemes such as ASCII, ISCII and Unicode assign codes to characters. Number systems used in computing include decimal (base 10), binary (base 2), octal (base 8) and hexadecimal (base 16). Numbers can be converted between these systems using standard methods.

Encoding schemes

ASCII (American Standard Code for Information Interchange) uses 7 bits to represent 128 characters; for example 'A' is 65 and 'a' is 97.
ISCII (Indian Script Code for Information Interchange) is an 8-bit code for Indian scripts.
Unicode provides a unique code for every character of all the world's languages; encodings such as UTF-8, UTF-16 and UTF-32 store Unicode characters, and UTF-8 is widely used on the web.

Number systems and conversion

Decimal uses digits 0–9; binary uses 0 and 1; octal uses 0–7; hexadecimal uses 0–9 and A–F (A = 10, F = 15). Each position has a place value that is a power of the base.
Decimal to another base: divide repeatedly by the base and read the remainders from bottom to top; for fractions, multiply the fractional part by the base and read the integer parts from top to bottom.
Another base to decimal: multiply each digit by its place value and add. Binary to octal groups bits in threes and binary to hexadecimal groups bits in fours, starting from the binary point.

Key terms

Encoding: representing characters as binary codes
ASCII: a 7-bit code representing 128 characters
Unicode: a universal character encoding for all languages
Base (radix): the number of digits used in a number system
Hexadecimal: base-16 number system using 0–9 and A–F

Important questions with answers

What is Unicode and why is it needed?2 marks

Unicode is a universal encoding standard that gives a unique number to every character in all languages and scripts. It is needed because ASCII and ISCII cover only limited characters, while Unicode allows text in many languages, including Hindi and Odia, to be stored and exchanged consistently.

Convert (45)10 into binary, octal and hexadecimal.3 marks

Dividing 45 by 2 repeatedly gives remainders 1, 0, 1, 1, 0, 1, so (45)10 = (101101)2. Grouping in threes: 101 101 = (55)8. Grouping in fours: 0010 1101 = (2D)16.

Explain the methods of converting numbers between decimal and binary, including fractions, with examples.5 marks

To convert a decimal integer to binary, divide the number by 2 repeatedly, noting the remainder each time, until the quotient becomes 0; the binary number is the remainders read from bottom to top. For example, 22 ÷ 2 = 11 remainder 0, 11 ÷ 2 = 5 remainder 1, 5 ÷ 2 = 2 remainder 1, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1, so (22)10 = (10110)2. To convert a decimal fraction to binary, multiply the fractional part by 2 repeatedly and note the integer part each time, reading the integer parts from top to bottom. For example, 0.625 × 2 = 1.25 (1), 0.25 × 2 = 0.5 (0), 0.5 × 2 = 1.0 (1), so (0.625)10 = (0.101)2. To convert binary to decimal, multiply each digit by its place value, which is a power of 2, and add. For the integer part, place values are 2^0, 2^1, 2^2 and so on from right to left; for the fractional part, they are 2^-1, 2^-2 and so on after the binary point. For example, (1011.01)2 = 1×8 + 0×4 + 1×2 + 1×1 + 0×0.5 + 1×0.25 = 11.25. The same methods work for octal and hexadecimal by using base 8 or 16 instead of 2.

Quick revision

ASCII, ISCII, Unicode, UTF-8.
Decimal, binary, octal, hexadecimal.
Decimal to other bases by repeated division.
Other bases to decimal by place values; binary grouping.

Exam tips

Practise: (25)10 = (11001)2 = (31)8 = (19)16.
Group 3 bits for octal and 4 bits for hexadecimal.

Practice MCQs

The base of the binary number system is
1. 2
2. 10
3. 8
4. 16
Show answer
Answer: (a) 2. It uses only 0 and 1.
How many characters can 7-bit ASCII represent
1. 64
2. 128
3. 256
4. 65536
Show answer
Answer: (b) 128. 2 to the power 7 is 128.
In hexadecimal, the digit F represents
1. 14
2. 16
3. 15
4. 10
Show answer
Answer: (c) 15. A to F stand for 10 to 15.
The binary equivalent of decimal 13 is
1. 1011
2. 1110
3. 1101
4. 1001
Show answer
Answer: (c) 1101. 8 + 4 + 1 = 13.
The decimal value of binary 101010 is
1. 40
2. 42
3. 44
4. 52
Show answer
Answer: (b) 42. 32 + 8 + 2 = 42.
The encoding scheme that can represent characters of all world languages is
1. ASCII
2. BCD
3. ISCII
4. Unicode
Show answer
Answer: (d) Unicode. It has codes for many scripts.
The hexadecimal equivalent of binary 11010110 is
1. C6
2. D6
3. E6
4. D5
Show answer
Answer: (b) D6. 1101 = D and 0110 = 6.
The octal equivalent of decimal 100 is
1. 124
2. 144
3. 154
4. 164
Show answer
Answer: (b) 144. 100 = 1×64 + 4×8 + 4.

All chapters of Class 11 Computer Science

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.