Reverse Bits of a Number in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to reverse the bits of a number?

Reversing the bits of a number means flipping the order of its binary digits from left to right. For example, if the binary is 1011, reversing it gives 1101.

beginner

How many bits are typically considered when reversing bits of a 32-bit integer?

Usually, all 32 bits of the integer are considered, including leading zeros, to keep the size consistent.

intermediate

What is the main operation used to reverse bits one by one?

The main operations are shifting bits right to read each bit and shifting bits left to build the reversed number, combined with bitwise AND and OR.

beginner

Why do we use bitwise AND with 1 when reversing bits?

Bitwise AND with 1 extracts the least significant bit (rightmost bit) of the number, which we then append to the reversed result.

intermediate

What is the time complexity of reversing bits of a fixed-size integer?

The time complexity is O(1) because the number of bits is fixed (e.g., 32 bits), so the operation takes constant time.

What does the expression (n & 1) do in bit manipulation?

A Sets the least significant bit of n to 1

B Extracts the most significant bit of n

C Extracts the least significant bit of n

D Shifts n to the right by 1 bit

Using bitwise AND with 1 extracts the rightmost bit of the number.

When reversing bits, why do we shift the result to the left before adding the next bit?

A To discard the leftmost bit

B To reset the result

C To double the number

D To make space for the new bit on the right

Shifting left moves bits to the left, making space on the right to add the next bit.

How many times do we repeat the bit extraction and shifting when reversing a 32-bit number?

A 32 times

B Depends on the number

C 64 times

D 16 times

We process all 32 bits to reverse the entire number.

What is the initial value of the reversed number before starting the bit reversal?

A 0

B 1

C The original number

D Depends on the input

We start with 0 and build the reversed number bit by bit.

If the input number is 0, what is the reversed bits output?

A 1

B 0

C All bits set to 1

D Undefined

Reversing bits of 0 results in 0 because all bits are zero.

Explain step-by-step how to reverse the bits of a 32-bit integer.

Think about reading bits from right to left and building the reversed number from left to right.

Why is bitwise shifting important in reversing bits of a number?

Consider how bits move when you shift left or right.

Practice

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

easy

A. Adding 1 to the binary number

B. Changing all 0s to 1s and 1s to 0s

C. Shifting bits to the left by one position

D. Flipping the order of bits from left to right

Solution

1. Step 1: Understand bit order

   Bits are arranged from left (most significant) to right (least significant).

2. Step 2: Reverse means flip order

   Reversing bits means the leftmost bit becomes rightmost and vice versa.

3. Final Answer:

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

4. Quick Check:

   Reverse bits = flip order [OK]

Hint: Reverse bits means flip their order, not invert values [OK]

Common Mistakes:

• Confusing reversing bits with bitwise NOT (inverting bits)
• Thinking reversing means shifting bits
• Assuming reversing adds or subtracts from the number

2. Which of the following C# code snippets correctly reverses the bits of a 4-bit number stored in an integer variable n?

easy

A. int reversed = 0; for(int i=0; i<4; i++) { reversed <<= 1; reversed |= (n & 1); n >>= 1; }

B. int reversed = 0; for(int i=0; i<4; i++) { reversed |= (n & 1) << i; n >>= 1; }

C. int reversed = n << 4;

D. int reversed = ~n;

Solution

1. Step 1: Analyze the loop logic in int reversed = 0; for(int i=0; i<4; i++) { reversed <<= 1; reversed |= (n & 1); n >>= 1; }

   It shifts reversed left by 1, adds least bit of n, then shifts n right by 1, effectively reversing bits.

2. Step 2: Check other options

   int reversed = 0; for(int i=0; i<4; i++) { reversed |= (n & 1) << i; n >>= 1; } does not reverse bits, it copies bits in same order. int reversed = n << 4; shifts bits left, not reverse. int reversed = ~n; inverts bits, not reverse.

3. Final Answer:

   Option A code correctly reverses bits -> Option A

4. Quick Check:

   Shift left + OR + shift right = reverse bits [OK]

Hint: Shift reversed left, OR with last bit, shift input right [OK]

Common Mistakes:

• Using bitwise NOT (~) instead of reversing bits
• Shifting bits without combining properly
• Not updating reversed variable inside loop

3. What is the output of the following C# code snippet?

int n = 13; // binary 1101
int reversed = 0;
for (int i = 0; i < 4; i++) {
  reversed <<= 1;
  reversed |= (n & 1);
  n >>= 1;
}
Console.WriteLine(reversed);

medium

A. 11

B. 7

C. 13

D. 14

Solution

1. Step 1: Convert 13 to 4-bit binary

   13 in binary (4 bits) is 1101.

2. Step 2: Reverse bits step-by-step

   Bits: 1 1 0 1 reversed: 1 0 1 1 which is binary 1011 = decimal 11.

3. Final Answer:

   11 -> Option A

4. Quick Check:

   1101 reversed = 1011 = 11 [OK]

Hint: Reverse bits manually and convert to decimal [OK]

Common Mistakes:

• Not limiting to 4 bits, causing wrong output
• Confusing bit order when reversing
• Assuming reversed number equals original

4. Identify the error in the following C# code that attempts to reverse bits of an 8-bit number:

int ReverseBits(int n) {
  int reversed = 0;
  for (int i = 0; i < 8; i++) {
    reversed |= (n & 1) << i;
    n >>= 1;
  }
  return reversed;
}

medium

A. The variable reversed should be initialized to 1

B. The loop should run 16 times for 8-bit numbers

C. The bits are not reversed; they are copied in the same order

D. The shift operator << is used incorrectly

Solution

1. Step 1: Analyze bit placement in loop

   The code places bits at increasing positions without reversing order.

2. Step 2: Understand reversing bits logic

   Reversing requires shifting reversed left and OR with last bit, not shifting bits by i.

3. Final Answer:

   The bits are not reversed; they are copied in the same order -> Option C

4. Quick Check:

   Shifting bits by i copies order, not reverse [OK]

Hint: Reversing needs shifting reversed left each step, not shifting bits by i [OK]

Common Mistakes:

• Using bit shift by loop index instead of shifting reversed
• Incorrect loop count for bit size
• Initializing reversed incorrectly

5. You want to reverse the bits of a 16-bit unsigned integer and then check if the reversed number is a palindrome in binary (reads the same forwards and backwards). Which approach correctly combines reversing bits and palindrome check?

hard

A. Invert bits using bitwise NOT, then check if inverted equals original

B. Reverse bits using a loop shifting reversed left and OR with last bit, then compare reversed with original

C. Shift original number left by 16 bits, then compare with original

D. Reverse bits by shifting bits by index, then check if reversed equals original

Solution

1. Step 1: Reverse bits correctly

   Use loop to shift reversed left, OR with last bit of original, shift original right.

2. Step 2: Check palindrome by comparing reversed and original

   If reversed equals original, bits form a palindrome.

3. Final Answer:

   Reverse bits using a loop shifting reversed left and OR with last bit, then compare reversed with original -> Option B

4. Quick Check:

   Reverse bits + compare = palindrome check [OK]

Hint: Reverse bits properly, then compare to original for palindrome [OK]

Common Mistakes:

• Using bitwise NOT instead of reversing bits
• Shifting bits incorrectly causing wrong reverse
• Comparing inverted bits instead of reversed bits