Encoding Schemes and Number System – NCERT Class 11 Computer Science Chapter 2 – ASCII, ISCII, UNICODE, Binary, Octal, Decimal, Hexadecimal

Explains how character encoding allows computers to interpret human-readable input using schemes like ASCII, ISCII, and UNICODE. Covers the fundamentals of binary, octal, decimal, and hexadecimal number systems, including positional values, conversion methods, and real-world applications such as text processing and color representation.

Updated: just now

Categories: NCERT, Class XI, Computer Science, Encoding Schemes, Number System, ASCII, UNICODE, Chapter 2

Tags: Encoding Schemes, ASCII, ISCII, UNICODE, Number System, Binary, Octal, Decimal, Hexadecimal, Data Conversion, Computer Science, NCERT Class 11, Chapter 2

Encoding Schemes and Number System: NCERT Class 11 Chapter 2 - Enhanced Study Guide, Precise Notes, Diagrams & Quiz 2025

Enhanced Full Chapter Summary & Precise Notes from NCERT PDF

Overview & Key Concepts

Exact Definition: "The mechanism of converting data into an equivalent cipher using specific code is called encoding."

Introduction: Keys mapped to codes (e.g., 'A' → 65 decimal → 01000001 binary); Hindi 'अ' → 0905 hex → 0000100100000101 binary. Einstein quote on Indian numerals.
Chapter Structure: Encoding (ASCII/ISCII/Unicode), Number Systems (Decimal/Binary/Octal/Hex), Conversions (Integer/Fractional).
2025 Relevance: Unicode for multilingual AI; Hex in web colors/RGB for digital design.

2.1 Introduction to Encoding

Precise: Computers understand binary; Keys → Unique code → Binary. Encoding standardizes for interoperability.

Precise Fig 2.1: Encoding of Data Entered Using Keyboard (SVG)

2.1.1 ASCII

Exact: "Developed in 1960s for standardising character representation... 7-bit (128 chars, English only)." Table 2.1: Space=32, A=65, a=97. Example: DATA → ASCII 68,65,84,65 → Binary 1000100 1000001 1010100 1000001 (Table 2.2).

Character	Decimal	Character	Decimal
Space	32	A	65
!	33	B	66
@	64	a	97

2.1.2 ISCII

Precise: "8-bit (256 chars) for Indian scripts... Retains 128 ASCII, 128 for aksharas (160-255)." Developed mid-1980s.

2.1.3 Unicode

Exact: "Unique number for every character... Independent of device/OS/software. Encodings: UTF-8/16/32 (superset of ASCII)." Table 2.3: Devanagari अ=0905 hex, etc. Activity 2.1: Fonts like Mangal for Hindi Unicode.

Think & Reflect: UTF-32 uses 32 bits/char (fixed, more space) vs UTF-16 (16/32 variable) or UTF-8 (8-32 variable).

Character	Hex	Character	Hex
अ	0905	क	0915
आ	0906	ख	0916
॥	0965	०	0966

2.2 Number System

Precise: Method to represent numbers; Base=radix (# unique literals). Positional: Value= symbol × base^position. Fig 2.2: Binary(2:0-1), Octal(8:0-7), Decimal(10:0-9), Hex(16:0-9,A-F).

Precise Fig 2.2: Four Different Number Systems (SVG)

Precise Fig 2.3: Computation of Decimal 123.45 (SVG)

2.2.1 Decimal: Base-10; Positional powers (Fig 2.4: 237.25=2×10² + ...).

Precise Fig 2.4: Positional Value for Decimal 237.25 (SVG)

2.2.2 Binary: Base-2 (0/1); Transistor ON/OFF. E.g., 0-9 decimal binaries.

Decimal	Binary
0	0
5	101
9	1001

2.2.3 Octal: Base-8 (0-7); Groups of 3 bits (2^3=8).

2.2.4 Hex: Base-16 (0-9,A-F); Groups of 4 bits (2^4=16).

Hex	Decimal	Binary
A	10	1010
F	15	1111

2.2.5 Hex Applications: Memory addresses (16-bit binary → C0F1 hex); Colors (RGB 24-bit → #FF0000 red).

Color Decimal Binary Hex
Black (0,0,0) (00...) (00,00,00)
Red (255,0,0) (1111...) (FF,00,00)

Color	Decimal	Binary	Hex
Black	(0,0,0)	(00...)	(00,00,00)
Red	(255,0,0)	(1111...)	(FF,00,00)

2.3 Conversions

Precise: Detailed in dedicated section.

Enhanced Features

Precise PDF quotes, derivations (positional b^n), SVGs (Figs 2.1-2.7), Unicode table subset, 30 Q&A (mark-based), 10-Q quiz. 2025: Focus on Unicode for global apps.

Exam Tips

Practice conversions with steps; Draw positional diagrams; Explain why 3/4 bits for Oct/Hex (2^3=8, 2^4=16).

Conversions - Precise Steps & Examples

Decimal to Binary (Integer Example: 65 to Binary)

Step 1: Divide number by 2, note remainder (LSB first).
Step 2: Continue dividing quotient until quotient=0.
Step 3: Read remainders from bottom to top.

65 ÷ 2 = 32 R 1
32 ÷ 2 = 16 R 0
16 ÷ 2 = 8 R 0
8 ÷ 2 = 4 R 0
4 ÷ 2 = 2 R 0
2 ÷ 2 = 1 R 0
1 ÷ 2 = 0 R 1
Binary: 1000001 (Read bottom-up)

Fig 2.5: Decimal 65 to Binary (SVG)

Decimal to Octal (Integer Example: 122 to Octal)

Step 1: Divide by 8, note remainders.
Step 2: Continue until quotient=0.
Step 3: Read remainders bottom-up.

122 ÷ 8 = 15 R 2
15 ÷ 8 = 1 R 7
1 ÷ 8 = 0 R 1
Octal: 172

Decimal to Hex (Integer Example: 122 to Hex)

Step 1: Divide by 16, remainders (10=A,11=B,...).
Step 2: Continue until 0.
Step 3: Bottom-up.

122 ÷ 16 = 7 R 10 (A)
7 ÷ 16 = 0 R 7
Hex: 7A

Binary to Decimal (Example: 1101_2 to Decimal)

Step 1: Multiply each bit by 2^position (right=0).
Step 2: Sum products.

1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 8 + 4 + 0 + 1 = 13

Binary to Octal/Hex (Example: 10101100_2 to Octal)

Step 1: Group 3 bits from right (pad left if needed).
Step 2: Convert each group to decimal (0-7).

10101100 → 010 101 100 (pad 0) → 2 5 4 → 254_8

To Hex: Group 4: 1010 1100 → A C → AC_16

Fractional Conversions (Example: 0.625_10 to Binary)

Step 1: Multiply fraction by base (2), take integer part (MSB first).
Step 2: Repeat with new fraction until 1 or precision.

0.625 × 2 = 1.25 → 1 (frac 0.25)
0.25 × 2 = 0.5 → 0 (frac 0.5)
0.5 × 2 = 1.0 → 1
Binary: 0.101

Binary Fractional to Octal (Example: 0.1101_2 to Octal)

Step 1: Group 3 bits left from point (pad right).
Step 2: Convert groups.

0.1101 → 110 . 100 (pad) → 6 . 4 → 0.64_8

Precise Tip: For repeating fractions, stop after 10 digits or detect cycle.

30 Questions & Answers - NCERT Precise (Attractive Q&A Cards)

Engaging cards for practice: 10 Short (1 Mark - Quick Facts), 10 Medium (4 Marks - Explain/Short Steps), 10 Long (8 Marks - Detailed Steps/Examples/Comparisons). All in clean black text for focus.

Short Questions (1 Mark Each - Quick Recall)

Q1: What is encoding?

Ans: The mechanism of converting data into an equivalent cipher using a specific code.

Q2: How many bits in ASCII?

Ans: 7 bits for 128 characters.

Q3: ASCII value of 'A'?

Ans: 65 decimal.

Q4: ISCII base?

Ans: 8 bits for 256 characters.

Q5: Unicode key feature?

Ans: Unique number for every character across languages.

Q6: Number system radix?

Ans: Count of unique literals.

Q7: Binary digits?

Ans: 0 and 1.

Q8: Octal base and range?

Ans: Base 8, digits 0-7.

Q9: Hex for 10?

Ans: A.

Q10: Hex red color?

Ans: #FF0000.

Medium Questions (4 Marks Each - Explain with Steps)

Q11: Explain ASCII with DATA example.

Ans: ASCII: 7-bit English code. For DATA: D=68 (1000100_2), A=65 (1000001_2), T=84 (1010100_2), A=65. Steps: Map char to decimal, convert to 7-bit binary by division by 2.

Q12: Compare ISCII and ASCII.

Ans: ASCII: 7-bit English only. ISCII: 8-bit, includes ASCII + 128 Indian aksharas (160-255). Steps: Extend ASCII for scripts like Devanagari.

Q13: Why UTF-32 more space?

Ans: Fixed 32 bits per char vs UTF-16 (16/32 variable) or UTF-8 (8-32). Steps: UTF-32 always 4 bytes, inefficient for ASCII but simple.

Q14: Define positional value with decimal example.

Ans: Value = digit × base^position. For 123.45: 1×10^2 + 2×10^1 + 3×10^0 + 4×10^{-1} + 5×10^{-2} = 123.45. Steps: Assign positions, multiply, sum.

Q15: Steps for decimal to binary (65).

Ans: Divide by 2: 65/2=32 R1, 32/2=16 R0, ..., 1/2=0 R1. Binary: 1000001 (reverse remainders).

Q16: Binary to decimal (1101_2).

Ans: 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 8+4+0+1=13. Steps: Positions from right, power of 2, sum.

Q17: Why group 3 bits for octal?

Ans: 2^3=8 matches octal digits 0-7. Steps: Binary 10101100 → 010101100 → 2 5 4 = 254_8.

Q18: Hex symbols explanation.

Ans: 0-9 numeric, A=10 to F=15. Steps: Binary 1010=10=A, 1111=15=F.

Q19: Fractional decimal to binary (0.625_10).

Ans: 0.625×2=1.25 (1), 0.25×2=0.5 (0), 0.5×2=1.0 (1). Binary: 0.101.

Q20: Binary frac to octal (0.1101_2).

Ans: 110.100 (pad) → 6.4_8. Steps: Group 3 left from point.

Long Questions (8 Marks Each - Detailed with Examples/Comparisons)

Q21: Explain encoding process with 'A' and 'अ' examples.

Ans: Encoding: Human input → Code → Binary. For 'A': Key press → 65 decimal → Divide by 2: remainders 1000001_2. For 'अ': → 0905 hex → Binary 0000100100000101_2. Comparison: ASCII decimal, Unicode hex for multilingual. Detailed steps: Mapping ensures universality.

Q22: Detail ASCII, encode DATA fully.

Ans: ASCII: 1960s standard, 7-bit 128 chars English. DATA: D=68 (68/2=34 R0, ... →1000100_2), A=65→1000001_2, T=84→1010100_2, A=65. Table: Full binaries. Importance: Standardized communication.

Q23: Describe ISCII development and structure.

Ans: Mid-1980s India for scripts. 8-bit: 0-127 ASCII, 128-255 aksharas. Example: Devanagari in upper region. Comparison: Vs ASCII (English limited), enables Indian lang software. Steps: Assign codes, retain compatibility.

Q24: Unicode advantages with Devanagari table examples.

Ans: Solves incompatibility, UTF-8/16/32. Examples: अ=0905, क=0915, १=0967. Superset ASCII. Detailed: Independent of OS/device, full table covers 097F. Why better: Global text exchange.

Q25: Explain all number systems with Fig 2.2.

Ans: Positional bases: Binary(2:0-1 transistor), Octal(8:0-7 3bits), Decimal(10:0-9 human), Hex(16:0-F 4bits compact). Fig 2.2 visuals. Examples: 5_10=101_2. Comparisons: Binary core, others shorthand.

Q26: Positional computation for 237.25_10 and binary equivalent.

Ans: 2×10^2 + 3×10^1 + 7×10^0 + 2×10^{-1} + 5×10^{-2}=200+30+7+0.2+0.05=237.25. To binary: Integer 237→11101101_2, Frac 0.25→0.01_2. Full: 11101101.01_2. Steps detailed.

Q27: Binary system details with 0-9 table.

Ans: Base-2 for logic gates. Table: 0=0,1=1,2=10,...,9=1001. Conversion example: 13_10=1101_2. Importance: Computer language. Comparisons: Vs decimal (powers 10 vs 2).

Q28: Octal/Hex as binary shortcuts with conversions.

Ans: Octal: 3bits/group (254_8=10101100_2). Hex: 4bits (AC_16=10101100_2). Steps: Group, convert. Example full: 10101100_2 → Octal 254, Hex AC. Why: Reduces binary length.

Q29: Hex applications: Addresses and colors with examples.

Ans: Addresses: 1100000011110001_2=C0F1_16 (compact). Colors: RGB 255,0,0=#FF0000 (8bits/hex digit). Examples: Black=#000000, Yellow=#FFFF00. Steps: Binary to hex groups, apply to 24-bit RGB.

Q30: Full fractional conversion: 0.8125_10 to binary/octal, explain repeating.

Ans: Binary: 0.8125×2=1.625(1),0.625×2=1.25(1),...→0.1101_2 (exact). Octal: To binary first, group. Repeating ex: 0.1_10=0.000110011..._2 (cycle 0011). Steps: Multiply till cycle/precision, detect repeat.

Tip: Short: 1 sentence. Medium: Steps + calc. Long: Examples + compare + importance.

Concept	Precise Description	Example	Process/Derivation
Encoding	Key→Code→Binary	'A'=65=1000001_2	Map→Convert binary
ASCII	7-bit English	DATA binaries	Table lookup
Unicode	Universal UTF	अ=0905	Hex unique ID
Positional	Symbol×base^pos	123.45 calc	Sum products
Conversions	Divide/Multiply base	65→1000001_2	Rem/Int parts
Hex Apps	Addresses/Colors	#FF0000 Red	24-bit→6 hex digits

This article has been published in CBSE Class 11 Annual Assessment. Explore everything related to it here.

Group Discussions

No forum posts available.

Easily Share with Your Tribe