Why Reverse Bits of a Number in DSA Javascript?

The Big Idea

What if you could flip a number's bits as easily as flipping a light switch?

The Scenario

Imagine you have a long row of light switches representing bits in a number. You want to flip the order of these switches so the first becomes last and the last becomes first.

Doing this by hand means checking each switch one by one and moving it to the opposite end.

The Problem

Manually flipping each bit is slow and easy to mess up, especially if the number has many bits.

It's hard to keep track of positions and ensure no bit is lost or duplicated.

The Solution

Using a simple algorithm, you can reverse all bits by shifting and combining them step-by-step.

This method is fast, reliable, and works for any number size.

Before vs After

✗ Before

let reversed = 0;
for (let i = 0; i < 32; i++) {
  let bit = (number >> i) & 1;
  reversed |= bit << (31 - i);
}

✓ After

function reverseBits(number) {
  let reversed = 0;
  for (let i = 0; i < 32; i++) {
    reversed = (reversed << 1) | (number & 1);
    number >>>= 1;
  }
  return reversed;
}

What It Enables

This lets you quickly flip bits to solve problems in encryption, graphics, and data compression.

Real Life Example

In image processing, reversing bits helps flip pixel data for effects or format conversions.

Key Takeaways

Manual bit reversal is slow and error-prone.

Algorithmic bit reversal uses shifts and masks for speed and accuracy.

This technique is useful in many computer science fields like cryptography and graphics.

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