Class 11 CS - code. caffeine. chaos.

📒✨ CHAPTER 2 - NUMBER SYSTEM: QnAs and HOTs ✨📒

Example:
1010 = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10

💡 Q10. Convert (1101)₂ to decimal.

A:
= (1×2³) + (1×2²) + (0×2¹) + (1×2⁰)
= 8 + 4 + 0 + 1 = 13

✅ Answer: 13

💡 Q11. What is the octal equivalent of binary 110101?

A:
Group in 3s from right: 110 101
→ 110 = 6, 101 = 5
✅ Octal = 65₈

💡 Q12. Convert (B2)₁₆ to binary.

A:
B = 1011, 2 = 0010
→ Binary = 10110010

💡 Q13. Convert (256)₁₀ to hexadecimal.

A:
256 ÷ 16 = 16 R0
16 ÷ 16 = 1 R0
1 ÷ 16 = 0 R1

→ Read bottom to top = 100₁₆

💡 Q14. How many different numbers can be represented using 4 bits?

A:
Using 4 bits: 2⁴ = 16 different numbers
(From 0000 to 1111)

💡 Q15. What's the binary for hexadecimal 'F'?

A:
F = 1111

💡 Q16. What is ASCII?

A:
ASCII (American Standard Code for Information Interchange) is a 7-bit code used to represent characters and symbols in binary format.

Example:

A = 65 → Binary = 1000001

B = 66 → Binary = 1000010

HOTs:-

🌟 Q1. If a computer receives binary input 10011011, what would be its hexadecimal and decimal equivalent?

Answer:
Binary = 10011011
Group into 4-bits → 1001 1011

1001 = 9

1011 = B

✅ Hex: 9B₁₆
Decimal = (1×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 1×2⁰)
= 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155

✅ Decimal: 155

🌟 Q2. Can you write a binary number that will be same when reversed? Give an example and prove it.

Answer:
Such numbers are called palindromic binaries 🪞
Example: 1001 → reversed = 1001 (same)

Check:
Binary 1001 = (1×2³) + (0×2²) + (0×2¹) + (1×2⁰) = 8 + 0 + 0 + 1 = 9
Decimal 9 → Binary = 1001 ✅

🌟 Q3. A number is given in hexadecimal as 3C. Can you find the binary, octal, and decimal values?

Answer:
Hex = 3C

3 = 0011, C = 1100
→ Binary = 00111100

Now Decimal:
(3×16 + 12) = 48 + 12 = 60

Now Octal:
Binary 00111100 → group in 3s → 000 111 100
→ 000 = 0, 111 = 7, 100 = 4
✅ Octal = 074

🌟 Q4. Why is hexadecimal often preferred over binary in programming?

Answer:
Hex is:

Shorter & more compact (4 binary bits = 1 hex digit)

Easier to read & debug

Still maps directly to binary

Example:
Binary: 110100101111 = sooo long
Hex: D2F → same value but cleaner 👩‍💻💅

🌟 Q5. Suppose a 16-bit memory can store binary numbers. What is the maximum decimal number that can be stored?

Answer:
Max number with 16 bits = all 1s → 1111111111111111
= 2¹⁶ – 1 = 65535

✅ Answer: 65535

🌟 Q6. Can a decimal number be directly converted to hexadecimal? How?

Answer:
YES 💡 Using repeated division by 16 method.

Example: Convert 250 to Hex:

250 ÷ 16 = 15 R10 → A 15 ÷ 16 = 0 R15 → F Answer = FA₁₆ ✍️📄 WORKSHEET: 

🔘 A. Fill in the blanks

Binary number system uses ____ digits.

1 byte = ____ bits.

100110₍₂₎ = _____₁₀

The base of hexadecimal system is ____.

A group of 4 bits is called a _____.

🔢 B. Conversion Questions

Convert (47)₁₀ to Binary

Convert (101011)₂ to Decimal

Convert (7D)₁₆ to Decimal

Convert (88)₁₀ to Hexadecimal

Convert (10001000)₂ to Hexadecimal

❓ C. HOTS Think & Solve

If a number in binary is a palindrome, what's special about it?

If you have a 6-bit system, what's the highest number you can store?

Why is octal used in place of binary sometimes?

Decode: 1100001 → ASCII character?

Which is more space-efficient: binary or hexadecimal?

🎯 Bonus Challenge

🧠 Write a short Python code that converts any decimal to binary.

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