Reverse Bits of a Number in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of reversing bits of 13 in 8-bit representation?

Given the 8-bit binary representation of the number 13, what is the decimal value after reversing its bits?

DSA Python

def reverse_bits(n, bits=8):
    result = 0
    for _ in range(bits):
        result = (result << 1) | (n & 1)
        n >>= 1
    return result

print(reverse_bits(13))

A 176

B 212

C 134

D 104

💡 Hint

Think about the binary form of 13: 00001101. Reverse the bits and convert back to decimal.

13 in 8 bits is 00001101. Reversing bits gives 10110000 which is 176 in decimal.

❓ Predict Output

intermediate

What is the output of reversing bits of 1 in 4-bit representation?

What decimal number results from reversing the bits of 1 using 4 bits?

DSA Python

def reverse_bits(n, bits=4):
    result = 0
    for _ in range(bits):
        result = (result << 1) | (n & 1)
        n >>= 1
    return result

print(reverse_bits(1, 4))

A 2

B 4

C 1

D 8

💡 Hint

1 in 4 bits is 0001. Reverse bits and convert to decimal.

0001 reversed is 1000 which equals 8 in decimal.

🔧 Debug

advanced

What error does this code raise when reversing bits?

Identify the error raised by this code snippet when reversing bits of 5 in 3 bits:

DSA Python

def reverse_bits(n, bits=3):
    result = 0
    for i in range(bits):
        result = (result << 1) | (n & 1)
        n = n >> 1
    return result

print(reverse_bits(5))

A No error, output is 5

B IndexError

C SyntaxError

D TypeError

💡 Hint

Check if the code runs without exceptions and what output it produces.

The code correctly reverses bits of 5 (101) in 3 bits to 101 which is 5 decimal. No error occurs.

❓ Predict Output

advanced

What is the output of reversing bits of 19 in 5-bit representation?

Calculate the decimal value after reversing the 5-bit binary representation of 19.

DSA Python

def reverse_bits(n, bits=5):
    result = 0
    for _ in range(bits):
        result = (result << 1) | (n & 1)
        n >>= 1
    return result

print(reverse_bits(19, 5))

A 13

B 25

C 22

D 17

💡 Hint

19 in 5 bits is 10011. Reverse bits and convert to decimal.

10011 reversed is 11001 which equals 25 decimal.

🧠 Conceptual

expert

How many bits are needed to reverse bits of the number 1023 correctly?

To reverse the bits of the number 1023 correctly, how many bits should be used in the reversal process?

A 16 bits

B 8 bits

C 10 bits

D 12 bits

💡 Hint

Think about the binary length of 1023.

1023 in binary is 1111111111 which is 10 bits long, so 10 bits are needed to reverse it correctly.

Practice

1. What does reversing the bits of a number mean in simple terms?

easy

A. Multiplying the number by 2

B. Changing all 0 bits to 1 bits

C. Flipping the order of all bits from left to right

D. Adding 1 to the number

Solution

1. Step 1: Understand bits as binary digits

   Bits are the 0s and 1s that make up a number in binary form.

2. Step 2: Define reversing bits

   Reversing bits means reading the bits from right to left instead of left to right, flipping their order.

3. Final Answer:

   Flipping the order of all bits from left to right -> Option C

4. Quick Check:

   Reverse bits = flip order [OK]

Hint: Think of bits as beads on a string flipped end to end [OK]

Common Mistakes:

• Confusing reversing bits with flipping bits (0 to 1)
• Thinking reversing bits means adding or multiplying
• Assuming reversing bits changes the number's value directly

2. Which of the following Python code snippets correctly reverses the bits of an 8-bit number n?

easy

A. reversed_num = 0
for i in range(8):
reversed_num |= ((n >> i) & 1) << (7 - i)

B. reversed_num = 0
for i in range(8):
reversed_num |= ((n << i) & 1) << i

C. reversed_num = n << 8

D. reversed_num = n >> 8

Solution

1. Step 1: Analyze bit extraction and placement

   reversed_num = 0 for i in range(8): reversed_num |= ((n >> i) & 1) << (7 - i) extracts each bit from right to left and places it reversed from left to right.

2. Step 2: Check other options for correctness

   reversed_num = 0 for i in range(8): reversed_num |= ((n << i) & 1) << i shifts bits incorrectly; C and D just shift without reversing bits.

3. Final Answer:

   Option A code correctly reverses bits -> Option A

4. Quick Check:

   Shift right, mask, shift left reversed position [OK]

Hint: Use bit shifts and masks to pick and place bits reversed [OK]

Common Mistakes:

• Using left shift instead of right shift to extract bits
• Not shifting bits to reversed positions
• Confusing bitwise OR with addition

3. What is the output of the following Python code?

def reverse_bits(n):
    result = 0
    for i in range(4):
        result |= ((n >> i) & 1) << (3 - i)
    return result

print(reverse_bits(13))  # 13 in binary is 1101

medium

A. 13

B. 7

C. 14

D. 11

Solution

1. Step 1: Convert 13 to 4-bit binary and reverse bits

   13 in 4 bits is 1101. Reversing bits: 1011.

2. Step 2: Convert reversed bits back to decimal

   1011 in binary is 8+0+2+1 = 11.

3. Final Answer:

   11 -> Option D

4. Quick Check:

   1101 reversed = 1011 = 11 [OK]

Hint: Reverse bits visually, then convert back to decimal [OK]

Common Mistakes:

• Not reversing bits correctly (reading left to right)
• Confusing binary to decimal conversion
• Using wrong bit length for reversal

4. Find the error in this code that attempts to reverse bits of a 3-bit number n:

def reverse_bits(n):
    result = 0
    for i in range(3):
        bit = (n >> i) & 1
        result |= bit << i
    return result

medium

A. It uses wrong bitwise AND operator

B. It shifts bits to the same position instead of reversed position

C. It does not initialize result to zero

D. It uses range(3) instead of range(4)

Solution

1. Step 1: Check bit shifting logic

   The code shifts extracted bits back to the same position i, not reversed (2 - i).

2. Step 2: Identify correct reversed position

   For 3 bits, reversed position should be (2 - i) to flip bits order.

3. Final Answer:

   It shifts bits to the same position instead of reversed position -> Option B

4. Quick Check:

   Shift bits to reversed index, not original [OK]

Hint: Shift bits to (bit_length - 1 - i) for reversal [OK]

Common Mistakes:

• Shifting bits back to original position
• Forgetting to reverse bit positions
• Incorrect loop range for bit length

5. You want to reverse the bits of a 5-bit number n and then add it to the original number. Which Python code correctly does this?

hard

A. def reverse_bits(n):
result = 0
for i in range(5):
result |= ((n >> i) & 1) << (4 - i)
return result

print(n + reverse_bits(n))

B. def reverse_bits(n):
result = 0
for i in range(5):
result |= ((n << i) & 1) << i
return result

print(n - reverse_bits(n))

C. def reverse_bits(n):
return n << 5

print(n + reverse_bits(n))

D. def reverse_bits(n):
return n >> 5

print(n + reverse_bits(n))

Solution

1. Step 1: Verify bit reversal logic for 5 bits

   def reverse_bits(n): result = 0 for i in range(5): result |= ((n >> i) & 1) << (4 - i) return result print(n + reverse_bits(n)) correctly reverses bits by shifting each bit from position i to (4 - i).

2. Step 2: Check addition of reversed bits to original

   def reverse_bits(n): result = 0 for i in range(5): result |= ((n >> i) & 1) << (4 - i) return result print(n + reverse_bits(n)) prints sum of n and reversed bits, matching the problem requirement.

3. Final Answer:

   Option A code correctly reverses bits and adds to original -> Option A

4. Quick Check:

   Reverse bits with correct shifts, then add [OK]

Hint: Reverse bits by shifting to (bit_length - 1 - i), then add [OK]

Common Mistakes:

• Using left shift instead of right shift for extraction
• Subtracting instead of adding reversed bits
• Incorrect bit length or shift positions