🔢 Implementing extract_end_bits (LSB Extraction) — Complete Q&A Guide

[Rajeev Bagra]

 

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🔰 Initial Context (Read This First)

In image processing and steganography, hidden data is stored in the Least Significant Bits (LSBs) of pixel values.

A pixel value is just a number (for example, 13, 200, 255).
You are not required to convert this number into binary to extract its LSBs.

Instead, Python’s modulo (%) operator can do this efficiently.

Your task is to implement a helper function:

extract_end_bits(num_end_bits, pixel)

This function extracts the last num_end_bits bits of a pixel value and returns them as a base-10 integer.

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📌 Problem Statement (Simplified)

• Input:
  • num_end_bits: how many LSBs you want
  • pixel: a pixel value (0–255)
• Output:
  • The integer represented by the last num_end_bits bits

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🧪 Given Examples

extract_end_bits(1, 13)  # returns 1
extract_end_bits(2, 13)  # returns 1
extract_end_bits(3, 13)  # returns 5

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🧠 Key Insight (Very Important)

What does modulo do?

The modulo operator returns the remainder after division.

pixel % (2 ** num_end_bits)

This remainder is exactly the value represented by the last num_end_bits bits.

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❓ Q&A Explanation

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Q1. What does “extracting LSBs” mean?

Answer:
It means taking the rightmost bits of a number’s binary representation and interpreting them as a new number.

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Q2. Why are we told not to convert to binary?

Answer:
Because:

• Binary conversion is unnecessary
• Modulo math already isolates the lower bits
• The solution should be short, efficient, and clean

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Q3. How does modulo extract bits?

Answer:

Dividing by 2ⁿ splits the number into:

• Higher bits (quotient)
• Lower n bits (remainder)

The remainder is exactly what we want.

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Q4. Why do we use 2 ** num_end_bits?

Answer:
Because:

• Each bit doubles the number of possibilities
• n bits → 2ⁿ combinations
• Modulo 2ⁿ keeps only the last n bits

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Q5. Can you show this with pixel = 13?

Answer:

Binary of 13:

1101

Bits extracted	Operation	Result
1 LSB	13 % 2	1
2 LSBs	13 % 4	1
3 LSBs	13 % 8	5

No binary conversion needed.

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Q6. Why does extract_end_bits(3, 13) return 5?

Answer:

• Last 3 bits of 1101 → 101
• 101 in binary = 5 in decimal
• Modulo automatically gives this value

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Q7. What is the shortest correct implementation?

Answer:

def extract_end_bits(num_end_bits, pixel):
    return pixel % (2 ** num_end_bits)

That’s it.

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Q8. Why does this work for images?

Answer:
Because:

• Pixel values are integers
• Hidden image data is stored in LSBs
• Modulo isolates exactly those bits

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Q9. How is this used later?

Answer:
This function is used in:

• Grayscale image recovery
• RGB image recovery
• Bit-plane extraction
• Steganography decoding

Example usage:

lsb = extract_end_bits(1, pixel)

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Q10. What would happen if we didn’t use modulo?

Answer:
We would need:

• Binary conversion
• String slicing
• Re-conversion to decimal

All unnecessary and inefficient.

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✅ Final Takeaways

• LSBs contain hidden data
• Modulo isolates lower bits cleanly
• pixel % (2 ** n) extracts n LSBs
• No binary conversion needed
• One-line solution is intentional

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🧠 One-Line Intuition

Modulo by 2ⁿ throws away higher bits and keeps exactly the last n bits.

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