Chapter 2: Encoding Schemes and Number System

CBSE Unit: Unit 1, Computer Systems and Organisation (10 marks) Marks Weightage: ~4-5 marks (shared with Ch 1) Priority: HIGH, numerical problems frequently asked

Key Concepts

2.1 Encoding Schemes

Encoding: Mechanism of converting data into equivalent code using a specific standard.

ASCII (American Standard Code for Information Interchange), Developed in early 1960s for standardising character representation, Originally 7-bit code: 2^7 = 128 characters

Encodes English language characters only, Key ASCII values: A=65, B=66, ... Z=90; a=97, b=98, ... z=122; 0=48, ... 9=57; Space=32

ISCII (Indian Script Code for Information Interchange), Developed in India during mid-1980s for Indian languages

8-bit code: 2^8 = 256 characters
Retains all 128 ASCII codes; additional 128 codes (160-255) for Indian language characters (aksharas)

UNICODE, Standard to incorporate characters of every written language of the world, Provides unique number for every character regardless of device, OS, or application

Superset of ASCII (values 0-128 are same), Common encodings: UTF-8, UTF-16, UTF-32
UTF-32 uses more space per character than UTF-16 or UTF-8

Encoding	Bits	Characters	Scope
ASCII (7-bit)	7	128	English only
ISCII	8	256	Indian languages (includes ASCII)
UNICODE	8/16/32	All languages	Universal

2.2 Number Systems

A number system is a method to represent numbers. It is positional, value depends on position.

Number System	Base	Digits/Symbols	Example
Binary	2	0, 1	(1010)2
Octal	8	0-7	(237)8
Decimal	10	0-9	(123)10
Hexadecimal	16	0-9, A-F	(3A5)16

Position values: Integer part reads right to left (0, 1, 2, ...); Fractional part reads left to right (-1, -2, -3, ...)

Binary Number System (Base 2), Used internally by computers (transistor ON=1, OFF=0), 3 binary digits = 1 octal digit (2^3 = 8), 4 binary digits = 1 hexadecimal digit (2^4 = 16)

Octal Number System (Base 8), Compact representation of binary (group of 3 bits), Digits: 0 through 7

Hexadecimal Number System (Base 16), Even more compact representation of binary (group of 4 bits), Symbols: 0-9 and A(10), B(11), C(12), D(13), E(14), F(15)

Applications: Memory addresses, colour codes (RGB), RGB colours: 24-bit = 8 bits each for Red, Green, Blue
RED = (FF,00,00), WHITE = (FF,FF,FF), BLACK = (00,00,00)

2.3 Number System Conversions

Decimal to Binary (Divide by 2)

Repeatedly divide by 2, note remainders, read bottom to top.

(65)10 = (1000001)2
(122)10 = (1111010)2

Decimal to Octal (Divide by 8)

Repeatedly divide by 8, note remainders, read bottom to top.

(65)10 = (101)8
(122)10 = (172)8

Decimal to Hexadecimal (Divide by 16)

Repeatedly divide by 16, note remainders (use A-F for 10-15), read bottom to top.

(65)10 = (41)16
(122)10 = (7A)16

Binary/Octal/Hex to Decimal (Multiply by positional value)

Multiply each digit by base^position, then add all.

(1101)2 = 1x2^3 + 1x2^2 + 0x2^1 + 1x2^0 = 8+4+0+1 = (13)10
(257)8 = 2x8^2 + 5x8^1 + 7x8^0 = 128+40+7 = (175)10
(3A5)16 = 3x16^2 + 10x16^1 + 5x16^0 = 768+160+5 = (933)10

Binary to Octal (Group 3 bits from right)

(10101100)2 --> 010 101 100 --> (254)8

Binary to Hexadecimal (Group 4 bits from right)

(0110101100)2 --> 0001 1010 1100 --> (1AC)16

Octal to Binary (Each digit = 3 bits)

(705)8 --> 111 000 101 --> (111000101)2

Hexadecimal to Binary (Each digit = 4 bits)

(23D)16 --> 0010 0011 1101 --> (001000111101)2

Fractional Decimal to Binary/Octal/Hex

Multiply fractional part by base repeatedly; collect integer parts top to bottom.

(0.25)10 to binary: 0.25x2=0.50(0), 0.50x2=1.00(1) --> (0.01)2
(0.675)10 to octal: 0.675x8=5.4(5), 0.4x8=3.2(3), ... --> (0.53146)8

Fractional Binary to Decimal

Use negative powers for fractional positions.

(100101.101)2 = 32+4+1 + 0.5+0.125 = (37.625)10

Fractional Binary to Octal/Hex, Integer part: group from right to left, Fractional part: group from left to right (add trailing 0s if needed)

(10101100.01011)2 --> 010 101 100 . 010 110 --> (254.26)8

Important Definitions

Encoding: Converting data into equivalent code using a specific standard
ASCII: 7-bit encoding for 128 English characters
ISCII: 8-bit encoding for Indian languages (256 characters)
UNICODE: Universal encoding for all world languages
Number System: Method to represent numbers using specific base
Base/Radix: Count of unique digits in a number system
Positional Value: Value of digit based on its position (base^position)
Bit: Binary digit (0 or 1)

Common Board Exam Question Patterns

Convert decimal to binary/octal/hex (2-3 marks): Show complete working
Convert binary/octal/hex to decimal (2-3 marks): Show positional value calculation
Convert binary to octal/hex (1-2 marks): Grouping method
Convert with fractional part (3 marks): Both integer and fractional conversion
ASCII encoding (1-2 marks): Find binary for a given word using ASCII
Expand abbreviations (1 mark): ASCII, ISCII, UNICODE
Differences (2 marks): ASCII vs UNICODE, ASCII vs ISCII
Hexadecimal colour codes (1-2 marks): RGB representation
Base value questions (1 mark): Identify base of given number system

Key Points Students Miss

3 bits for octal, 4 bits for hexadecimal, because 2^3=8 and 2^4=16
For binary to octal: group from RIGHT to LEFT (integer part); LEFT to RIGHT (fractional part)
Add leading 0s to leftmost group if needed (integer part); add trailing 0s to rightmost group (fractional part)
When converting fractional decimal to binary: multiply (don't divide); stop when fractional part = 0 or starts repeating
Read remainders bottom to top for decimal-to-other conversions
Read integer parts top to bottom for fractional conversions
A=10, B=11, C=12, D=13, E=14, F=15 in hexadecimal
UNICODE is a superset of ASCII (first 128 characters are identical)
ISCII retains all ASCII codes and adds Indian language characters in positions 160-255
In positional value: position 0 is rightmost digit in integer part