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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of reversing bits for a small number

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

DSA Javascript

function reverseBits(num) {
  let result = 0;
  for (let i = 0; i < 8; i++) {
    result <<= 1;
    result |= (num & 1);
    num >>= 1;
  }
  return result;
}

console.log(reverseBits(13));

A 176

B 104

C 212

D 91

💡 Hint

Think about the binary form of 13 and reversing its bits in 8-bit form.

The number 13 in 8-bit binary is 00001101. Reversing the bits gives 10110000 which is 176 in decimal.

❓ Predict Output

intermediate

Output of reversing bits for a power of two

What is the output of reversing the bits of the number 16 (in 8-bit representation)?

DSA Javascript

function reverseBits(num) {
  let result = 0;
  for (let i = 0; i < 8; i++) {
    result <<= 1;
    result |= (num & 1);
    num >>= 1;
  }
  return result;
}

console.log(reverseBits(16));

A 4

B 1

C 8

D 128

💡 Hint

16 in binary is 00010000. Reverse the bits carefully.

16 in 8-bit binary is 00010000. Reversing bits gives 00001000 which is 8 in decimal.

🔧 Debug

advanced

Identify the error in bit reversal code

What error does the following code produce when reversing bits of a number?

DSA Javascript

function reverseBits(num) {
  let result = 0;
  for (let i = 0; i < 8; i++) {
    result = result << 1 | num & 1
    num = num >> 1
  }
  return result
}

console.log(reverseBits(5));

A SyntaxError due to missing semicolons

B No error, outputs 160

C TypeError because of bitwise operation on undefined

D Wrong output: 10 instead of 160

💡 Hint

JavaScript allows missing semicolons in many cases.

The code runs fine and outputs 160, which is the reversed bits of 5 (00000101 reversed to 10100000).

❓ Predict Output

advanced

Output of reversing bits for a 16-bit number

What is the output of reversing the bits of the number 4660 (in 16-bit representation)?

DSA Javascript

function reverseBits16(num) {
  let result = 0;
  for (let i = 0; i < 16; i++) {
    result <<= 1;
    result |= (num & 1);
    num >>= 1;
  }
  return result;
}

console.log(reverseBits16(4660));

A 13325

B 13320

C 13335

D 11336

💡 Hint

4660 in hex is 0x1234. Reverse its bits carefully in 16-bit form.

4660 decimal is 0001001000110100 in binary. Reversing bits gives 0010110001001000 which is 11336 decimal.

🧠 Conceptual

expert

Number of set bits after reversing bits

If a number has 5 bits set to 1 in its 8-bit binary form, how many bits will be set to 1 after reversing its bits?

A Always 5

B Depends on the number

C Always 3

D Always 8

💡 Hint

Reversing bits changes their positions but not their count.

Reversing bits only changes the order of bits, not the number of bits set to 1.

Practice

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

easy

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

B. Changing all 0 bits to 1 bits

C. Adding 1 to the number

D. Multiplying the number by 2

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.

3. Final Answer:

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

4. Quick Check:

   Reverse bits = flip order [OK]

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

Common Mistakes:

• Confusing reversing bits with flipping bits (0 to 1)
• Thinking reversing bits changes the number by adding or multiplying
• Assuming reversing bits means reversing digits in decimal

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

easy

A. let result = 0; for(let i=0; i<8; i++) { result += (n & 1) << i; n <<= 1; }

B. let result = 0; for(let i=0; i<8; i++) { result |= (n & 1) << i; n >>= 1; }

C. let result = 0; for(let i=0; i<8; i++) { result <<= 1; result |= (n & 1); n >>= 1; }

D. let result = 0; for(let i=7; i>0; i--) { result |= (n & 1) << i; n >>= 1; }

Solution

1. Step 1: Analyze the loop and bit operations

   let result = 0; for(let i=0; i<8; i++) { result <<= 1; result |= (n & 1); n >>= 1; } shifts result left, adds least significant bit of n, then shifts n right. This reverses bits correctly.

2. Step 2: Check other options for errors

   let result = 0; for(let i=0; i<8; i++) { result |= (n & 1) << i; n >>= 1; } does not reverse bits, it copies bits in same order. let result = 0; for(let i=7; i>0; i--) { result |= (n & 1) << i; n >>= 1; } shifts bits incorrectly. let result = 0; for(let i=0; i<8; i++) { result += (n & 1) << i; n <<= 1; } shifts n left, which is wrong.

3. Final Answer:

   let result = 0; for(let i=0; i<8; i++) { result <<= 1; result |= (n & 1); n >>= 1; } -> Option C

4. Quick Check:

   Shift result left + add bit from n right [OK]

Hint: Shift result left, add n's right bit, shift n right [OK]

Common Mistakes:

• Shifting n left instead of right
• Not shifting result before adding bit
• Using wrong loop direction or bit positions

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

function reverseBits(n) {
  let result = 0;
  for(let i = 0; i < 4; i++) {
    result <<= 1;
    result |= (n & 1);
    n >>= 1;
  }
  return result;
}

console.log(reverseBits(13));

medium

A. 14

B. 11

C. 7

D. 13

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

   Loop 4 times: result builds as follows:
   i=0: result=0<<1=0 + (13&1=1) =1
   n=13>>1=6 (0110)
   i=1: result=1<<1=2 + (6&1=0) =2
   n=6>>1=3 (0011)
   i=2: result=2<<1=4 + (3&1=1) =5
   n=3>>1=1 (0001)
   i=3: result=5<<1=10 + (1&1=1) =11

3. Final Answer:

   11 -> Option B

4. Quick Check:

   Reverse 1101 = 1011 (binary 11 decimal) [OK]

Hint: Trace bit shifts and OR operations carefully [OK]

Common Mistakes:

• Confusing decimal and binary values
• Not shifting result before OR
• Looping wrong number of times

4. Find the error in this bit reversal function and choose the corrected version:

function reverseBits(n) {
  let result = 0;
  for(let i = 0; i < 8; i++) {
    result |= (n & 1);
    result <<= 1;
    n >>= 1;
  }
  return result;
}

medium

A. Change loop to run 16 times

B. Shift n left instead of right

C. Initialize result with 1 instead of 0

D. Swap the order: shift result left before OR operation

Solution

1. Step 1: Identify order of operations

   Current code ORs bit then shifts result left, causing last bit to be lost.

2. Step 2: Correct by shifting result left before OR

   Shift result left first, then OR with current bit to build reversed bits correctly.

3. Final Answer:

   Swap the order: shift result left before OR operation -> Option D

4. Quick Check:

   Shift before OR to keep all bits [OK]

Hint: Always shift result left before adding new bit [OK]

Common Mistakes:

• Shifting result after OR loses last bit
• Shifting n left instead of right
• Wrong loop count for bit size

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

hard

A. Reverse bits using a loop, then check if reversed number equals its own reverse

B. Reverse bits using a loop, then reverse again and compare with original

C. Reverse bits using a loop, then compare reversed number with original

D. Reverse bits using a loop, then convert to decimal and check if even

Solution

1. Step 1: Reverse bits of the number

   Use a loop to reverse all 16 bits correctly.

2. Step 2: Check palindrome by comparing reversed number with its own reverse

   If reversed number equals its reverse, it is a binary palindrome.

3. Final Answer:

   Reverse bits using a loop, then check if reversed number equals its own reverse -> Option A

4. Quick Check:

   Palindrome check = reversed == reverse(reversed) [OK]

Hint: Check palindrome by comparing reversed number to its reverse [OK]

Common Mistakes:

• Comparing reversed number directly to original (wrong for palindrome)
• Checking decimal evenness instead of binary palindrome
• Reversing bits twice unnecessarily